All-atom

molecular

dynamics

simulations

using

orientational

constraints

from

anisotropic

NMR

samples

Orientational

constraints

obtained

from

solid

state

NMR

experiments

on

anisotropic

samples

are

used

here

in

molecular

dynamics

-LRB-

MD

-RRB-

simulations

for

determining

the

structure

and

dynamics

of

several

different

membrane-bound

molecules

The

new

MD

technique

is

based

on

the

inclusion

of

orientation

dependent

pseudo-forces

in

the

COSMOS-NMR

force

field

These

forces

drive

molecular

rotations

and

re-orientations

in

the

simulation

such

that

the

motional

time-averages

of

the

tensorial

NMR

properties

approach

the

experimentally

measured

parameters

The

orientational-constraint-driven

MD

simulations

are

universally

applicable

to

all

NMR

interaction

tensors

such

as

chemical

shifts

dipolar

couplings

and

quadrupolar

interactions

The

strategy

does

not

depend

on

the

initial

choice

of

coordinates

and

is

in

principle

suitable

for

any

flexible

molecule

To

test

the

method

on

three

systems

of

increasing

complexity

we

used

as

constraints

some

deuterium

quadrupolar

couplings

from

the

literature

on

pyrene

cholesterol

and

an

antimicrobial

peptide

embedded

in

oriented

lipid

bilayers

The

MD

simulations

were

able

to

reproduce

the

NMR

parameters

within

experimental

error

The

alignment

of

the

three

membrane-bound

molecules

and

some

aspects

of

their

conformation

were

thus

derived

from

the

NMR

data

in

good

agreement

with

previous

analyses

Furthermore

the

new

approach

yielded

for

the

first

time

the

distribution

of

segmental

orientations

with

respect

to

the

membrane

and

the

order

parameter

tensors

of

all

three

systems

Introduction

Using

anisotropic

media

such

as

partially

oriented

bicelles

or

macroscopically

oriented

membranes

NMR

investigations

can

reveal

a

wealth

of

information

about

molecular

properties

namely

conformation

orientation

and

dynamics

In

many

solid

state

NMR

studies

of

membrane-active

peptides

and

transmembrane

proteins

the

samples

are

conveniently

prepared

with

macroscopically

oriented

bilayers

to

obtain

structural

information

The

NMR

data

analysis

relies

on

a

uniform

alignment

of

all

molecules

with

respect

to

the

static

magnetic

field

as

it

makes

use

of

the

orientation

dependence

of

the

chemical

shift

quadrupolar

coupling

or

dipolar

coupling

interactions

In

contrast

to

single

crystal

studies

where

the

molecules

are

immobilized

in

a

unique

conformation

in

the

case

of

lipid

membranes

and

liquid

crystalline

systems

one

has

to

consider

a

wide

distribution

of

molecular

orientations

and

anisotropic

motions

Here

we

apply

for

the

first

time

a

new

MD

strategy

to

deduce

such

structural

and

dynamics

information

on

three

representative

compounds

in

biomembranes

with

increasing

complexity

-LRB-

i

-RRB-

pyrene

-LRB-

ii

-RRB-

cholesterol

and

-LRB-

iii

-RRB-

the

antimicrobial

peptide

PGLa

A

convenient

nucleus

for

solid

state

NMR

investigations

of

oriented

membranes

is

deuterium

for

several

reasons

-LRB-

for

reviews

see

e.g.

Vold

Davis

Ulrich

and

Grage

-RRB-

First

the

influence

of

substitutions

on

the

molecular

structure

and

dynamics

is

negligible

More

importantly

in

most

biologically

relevant

cases

the

quadrupolar

interaction

tensor

of

a

carbon-bound

deuterium

is

to

a

good

approximation

aligned

parallel

to

the

C

bond

and

directly

reflects

the

local

molecular

orientation

and

dynamics

of

the

labelled

segment

Using

the

alignment

and

dynamic

behaviour

of

lipids

small

organic

guest

molecules

and

membrane-active

peptides

has

been

studied

in

numerous

examples

Most

previous

strategies

to

extract

the

molecular

orientation

from

NMR

data

however

have

been

restricted

to

molecules

with

a

rigid

conformation

e.g.

peptides

assuming

an

ideal

α-helix

with

fixed

backbone

torsion

angles

In

these

studies

several

individual

labels

are

usually

placed

into

strategic

positions

on

the

rigid

molecular

part

The

measured

quadrupolar

splittings

are

then

compared

in

a

least

squares

RMSD

analysis

with

the

predicted

values

upon

systematically

varying

the

molecular

alignment

The

best-fit

molecular

orientation

is

determined

from

a

error

plot

as

the

one

yielding

minimal

differences

between

the

observed

and

calculated

NMR

parameters

However

this

RMSD

-LRB-

root

mean

square

deviation

-RRB-

analysis

can

only

give

preliminary

results

for

flexible

molecules

such

as

peptides

or

proteins

with

a

high

degree

of

internal

mobility

A

proper

way

to

account

for

motional

averaging

of

the

NMR

parameters

caused

by

molecular

mobility

is

to

run

all-atom

MD

simulations

When

applied

to

biomembranes

however

such

simulations

pose

two

closely

connected

problems

-LRB-

i

-RRB-

large

size

of

the

system

and

-LRB-

ii

-RRB-

long

simulation

times

In

particular

water

surrounding

the

lipid

bilayer

has

to

be

included

into

the

MD

simulations

and

time-spans

have

to

be

covered

approaching

the

NMR

time

scale

Moreover

the

volume

of

interest

has

to

be

surrounded

by

multiple

copies

of

the

central

cell

to

avoid

boundary

effects

Nevertheless

such

simulations

have

been

demonstrated

to

be

feasible

for

moderately

sized

membrane

segments

hosting

medium

size

molecules

-LRB-

see

e.g.

Tieleman

et

al.

-RRB-

In

the

present

contribution

we

propose

an

alternative

strategy

in

which

the

oriented

medium

is

not

explicitly

considered

but

instead

the

ordering

membrane

environment

is

replaced

in

the

MD

simulations

by

pseudo-forces

derived

from

the

measured

NMR

parameters

This

way

sufficiently

long

MD

runs

become

possible

and

allow

to

calculate

the

motionally

averaged

parameters

observed

in

the

NMR

experiments

As

a

result

the

full

information

about

molecular

orientation

order

segmental

motions

and

even

aspects

of

the

molecular

conformation

could

be

revealed

There

is

one

remarkable

advantage

in

the

calculations

involving

orientational

constraints

Since

an

experimentally

observed

NMR

value

usually

represents

a

time

average

over

the

motions

of

the

molecules

knowledge

of

the

geometry

and

strength

of

these

molecular

motions

is

a

prerequisite

for

properly

interpreting

the

NMR

data

in

terms

of

structural

parameters

The

order

parameter

which

is

typically

used

to

describe

the

effect

of

molecular

motion

on

the

NMR

spectra

however

is

often

not

known

a

priori

In

the

present

approach

the

molecular

motions

are

intrinsically

included

and

the

order

parameters

are

obtained

as

part

of

the

simulation

result

Theory

NMR

interaction

tensors

and

coordinate

transformations

The

orientation

dependence

of

the

observed

frequencies

or

splittings

of

an

NMR

property

can

be

described

by

a

rank

tensor

P

whose

components

are

specified

in

the

context

of

a

coordinate

system

On

the

one

hand

a

description

in

a

molecule-fixed

frame

of

reference

is

required

to

follow

changes

in

orientation

but

on

the

other

hand

the

NMR

observables

are

extracted

from

the

interaction

tensor

in

the

laboratory

frame

related

to

the

static

magnetic

field

We

will

define

the

molecule-fixed

frames

in

the

following

way

from

the

coordinates

of

the

three

bonded

atoms

A

B

C

-LRB-

see

Fig.

-RRB-

Fig.

coordinate

system

used

to

define

a

tensorial

NMR

property

on

atom

A

The

bond

from

A

to

atom

B

is

taken

as

the

local

z-direction

the

plane

spanned

by

A

B

and

C

defines

the

x-direction

in-plane

and

the

y-direction

is

perpendicular

to

that

plane

Atom

A

is

selected

as

the

position

of

the

nucleus

of

interest

-LRB-

for

instance

-RRB-

whose

property

PA

is

to

be

calculated

In

case

there

are

several

possible

ways

of

selecting

atoms

B

and

C

they

will

be

defined

such

that

the

valence

of

bond

B

C

is

a

maximum

-LRB-

the

valence

can

be

estimated

from

the

bond

length

see

O'Keefe

and

Brese

-RRB-

This

selection

ensures

that

the

y-axis

will

be

perpendicular

to

a

π-system

if

it

exists

and

the

x-axis

will

be

positioned

within

the

π-plane

Once

we

have

selected

a

coordinate

system

that

is

fixed

to

the

molecule

we

can

calculate

the

columns

of

the

transformation

matrix

D

from

the

unit

vectors

along

of

this

frame

given

in

coordinates

of

the

laboratory

frame

Matrix

D

can

be

used

to

transform

the

tensorial

properties

from

the

molecular

to

the

laboratory

frame

The

tensor

components

of

P

in

the

molecular

frame

are

thus

transformed

to

yield

P

in

the

laboratory

frame

according

to

where

D

is

the

transformation

matrix

as

given

in

Eq

-LRB-

the

Einstein

sum

convention

is

used

for

Greek

subscripts

and

α

β

-LCB-

x

y

z

-RCB-

the

second

index

indicating

the

unit

vector

-RRB-

For

most

deuterium

quadrupolar

couplings

as

well

as

vicinal

dipolar

couplings

like

and

the

tensor

PA

will

be

to

a

good

approximation

diagonal

in

this

coordinate

system

hence

we

can

easily

assign

the

principal

values

of

PA

to

the

three

axes

In

cases

where

the

chemical

shift

tensor

is

to

be

analysed

the

same

molecular

coordinate

system

can

be

used

as

in

those

calculations

based

on

the

bond

polarization

theory

-LRB-

BPT

see

Sternberg

-RRB-

Therefore

all

these

types

of

NMR

interactions

can

be

treated

within

the

same

formalism

In

static

NMR

experiments

the

tensor

components

are

observed

in

a

coordinate

system

of

reference

whose

z-axis

is

aligned

with

In

this

frame

the

measured

frequency

or

splitting

is

given

by

the

zz-component

of

the

tensor

P.

However

in

the

approach

presented

here

we

can

incorporate

further

tensor

components

in

the

MD

simulations

which

are

accessible

for

example

by

measuring

the

sample

at

further

tilt

angles

Constraints

and

calculation

of

molecular

properties

To

include

experimental

constraints

in

the

MD

simulations

pseudo-energy

terms

are

added

to

the

molecular

energy

provided

by

the

force

field

These

pseudo-energies

are

defined

as

functions

of

the

difference

between

the

experimental

and

a

calculated

tensor

property

Pi

where

k

is

a

force

constant

which

is

chosen

to

adjust

the

size

and

unit

of

the

energy

The

first

sum

runs

over

all

observed

tensor

components

and

does

not

need

to

include

all

possible

elements

In

a

NMR

measurement

of

a

single

label

in

an

oriented

or

monocrystalline

sample

only

the

zz-value

of

the

tensor

of

this

site

can

be

experimentally

determined

However

any

additional

tensor

component

introduced

into

the

calculations

will

improve

the

characterization

of

the

orientation

of

the

system

Because

of

the

nature

of

the

tensor

transform

-LRB-

Eq

-RRB-

each

principal

axis

of

the

tensor

can

be

inverted

without

changing

the

observed

NMR

frequency

Therefore

eight

discrete

tensor

orientations

are

equivalent

even

if

all

elements

of

the

observed

tensor

are

used

as

constraints

If

however

only

the

three

principal

values

of

the

tensor

are

known

then

in

addition

to

this

eightfold

degeneracy

a

continuous

set

of

orientations

-LRB-

instead

of

discrete

possibilities

-RRB-

will

be

compatible

with

the

experimental

data

from

a

single

label

Therefore

a

larger

number

of

orientational

constraints

from

several

labels

are

necessary

to

determine

the

orientation

of

a

rigid

molecular

segment

in

an

unambiguous

way

Obviously

if

a

molecule

is

intrinsically

flexible

an

even

higher

number

of

constraints

will

be

required

The

experimental

NMR

values

represent

an

ensemble

average

over

a

large

number

of

molecules

as

well

as

a

time

average

The

relevant

time

scale

for

averaging

is

given

by

the

inverse

of

the

frequency

range

that

results

from

the

anisotropy

of

the

relevant

interaction

When

motions

are

faster

than

this

time

scale

a

time

average

of

the

corresponding

NMR

parameters

is

observed

Motions

slower

than

this

time

scale

will

result

in

a

distribution

of

the

respective

NMR

property

In

all-atom

MD

simulations

of

larger

molecules

we

can

only

perform

calculations

for

a

single

molecular

system

and

for

time

spans

on

the

order

of

a

Larmor

period

Assuming

that

the

NMR

interactions

are

already

completely

averaged

within

this

time

averaged

properties

can

be

simulated

This

is

likely

to

be

the

case

for

motions

within

the

molecule

and

for

the

rotational

diffusion

of

small

molecules

in

oriented

media

such

as

the

lipid

bilayer

considered

here

which

are

on

the

time

scale

of

ps

to

ns

-LRB-

see

Brüschweiler

-RRB-

We

thus

can

assume

that

the

time

averages

over

the

shorter

period

accessible

for

MD

simulations

do

reflect

the

longer

time

averages

observed

by

the

NMR

measurement

For

the

average

of

Ptheo

we

obtain

using

Eq

If

the

NMR

property

does

not

change

with

time

we

have

to

perform

the

time

averaging

only

over

the

products

of

the

transformation

matrix

elements

For

most

deuterium

quadrupolar

couplings

and

vicinal

dipolar

couplings

any

conformational

influence

on

the

NMR

interaction

can

be

neglected

In

the

case

of

chemical

shift

tensors

however

the

change

of

the

tensors

in

the

course

of

the

MD

simulation

has

to

be

considered

Since

MD

simulations

are

started

with

random

velocities

we

have

to

run

many

time

steps

before

a

thermal

equilibrium

is

reached

and

before

the

kinetic

energy

is

redistributed

properly

between

the

different

degrees

of

freedom

of

our

system

During

this

equilibration

phase

of

the

MD

the

pseudo-energies

will

be

large

and

unrealistic

since

the

proper

mean

values

for

the

interaction

tensors

are

not

yet

reached

Therefore

the

time

averaging

is

performed

here

using

an

exponential

memory

function

-LRB-

Torda

and

van

Gunsteren

-RRB-

The

memory

time

constant

is

denoted

with

τ

and

N

is

the

norm

of

the

integral

This

memory

function

serves

to

scale

down

the

contributions

from

the

beginning

of

the

MD

calculation

exponentially

By

proper

selection

of

τ

it

can

be

ensured

that

we

average

mainly

over

the

late

relevant

time

span

of

interest

Since

in

conventional

MD

simulations

the

equations

of

motion

are

integrated

in

finite

time

steps

Δt

the

integral

in

Eq

is

converted

into

a

discrete

sum

S

During

the

MD

simulation

the

sum

Sn

of

the

time

step

n

is

calculated

from

the

sum

of

the

previous

time

step

Sn

in

a

recursive

manner

In

the

course

of

the

MD

simulation

S

will

contain

the

exponentially

weighted

time

average

of

the

property

P

and

in

the

case

of

a

tensor

the

time

averaging

will

be

performed

with

all

of

its

components

Calculation

of

pseudo-forces

To

include

the

NMR

constraints

into

the

equations

of

motion

pseudo-forces

have

to

be

calculated

from

the

respective

pseudo-energies

-LRB-

Eq

-RRB-

They

are

obtained

as

the

derivatives

of

the

energies

with

respect

to

the

coordinates

of

the

atoms

In

the

case

of

orientational

pseudo-forces

we

have

to

derive

the

transformation

matrices

D

with

respect

to

the

coordinates

of

the

atoms

that

were

used

in

their

definition

-LRB-

see

Eq

-RRB-

The

pseudo-forces

in

the

Cartesian

directions

x

y

and

z

-LRB-

denoted

with

the

Greek

index

γ

-RRB-

acting

on

the

atoms

A

B

and

C

-LRB-

denoted

with

j

see

Eq

-RRB-

are

then

given

by

The

calculation

of

the

orientational

pseudo-forces

is

thus

reduced

to

determining

the

derivatives

of

the

elements

of

the

transformation

matrices

D

with

respect

to

the

Cartesian

coordinates

of

atoms

A

B

and

C

In

the

following

expressions

we

will

use

a

short

notation

for

the

derivatives

omitting

all

indices

Using

the

definitions

of

Eqs

and

these

derivatives

can

be

calculated

in

the

following

way

The

derivatives

of

the

unit

vectors

can

be

used

to

construct

the

derivatives

of

the

elements

of

the

transformation

matrices

Because

of

the

time

dependence

of

the

transformation

matrices

the

derivatives

were

calculated

continuously

during

the

MD

simulation

at

each

time

step

The

time

average

is

only

calculated

for

the

NMR

property

As

evident

from

Eq

the

pseudo-forces

depend

linearly

on

the

difference

between

theory

and

experiment

To

avoid

too

high

pseudo-forces

in

the

beginning

of

the

MD

simulation

when

the

deviation

of

the

simulated

and

experimental

values

is

still

large

the

contributions

of

the

pseudo-forces

are

scaled

down

Another

possibility

to

avoid

too

large

pseudo-forces

is

achieved

by

multiplying

the

pseudo-forces

by

weighting

factors

which

lead

to

nearly

constant

forces

if

exceeds

a

threshold

ΔP

-LRB-

see

Witter

et

al.

-RRB-

For

this

factor

behaves

similar

to

the

derivative

of

the

original

energy

expression

-LRB-

-RRB-

It

is

possible

to

choose

different

force

constants

k

-LRB-

Eq

-RRB-

and

width

parameters

ΔP

for

each

type

of

NMR

property

of

interest

Order

parameter

calculation

Besides

determining

the

structure

of

a

molecule

it

is

equally

important

to

describe

its

dynamic

behaviour

in

an

oriented

medium

such

as

a

lipid

bilayer

MD

simulations

provide

a

unique

opportunity

to

obtain

information

on

the

molecular

dynamics

which

is

difficult

to

determine

experimentally

The

traditional

way

to

account

for

motional

averages

in

NMR

investigation

is

to

introduce

order

parameters

To

this

aim

the

time

average

of

the

transformation

matrices

D

-LRB-

Eq

-RRB-

can

be

used

to

characterize

the

influence

of

restricted

molecular

motions

on

the

anisotropic

properties

of

a

molecule

In

a

similar

way

Saupe

-LRB-

-RRB-

defined

the

so

called

order

tensor

to

describe

the

average

orientation

of

a

molecule

where

denotes

the

mean

value

and

cosΘi

are

the

z

components

of

the

unit

vectors

of

a

molecule-fixed

frame

within

the

laboratory

system

of

reference

To

describe

the

dynamic

properties

of

flexible

molecules

however

the

Saupe

approach

is

not

sufficient

since

molecular

groups

like

peptide

side

chains

may

exhibit

a

larger

mobility

than

the

rest

of

the

molecule

For

this

purpose

Limmer

-LRB-

-RRB-

introduced

a

segmental

or

site-specific

order

tensor

W

which

is

the

tensorial

product

of

the

Saupe

order

tensor

and

a

conformational

order

tensor

By

calculating

the

NMR

properties

in

the

course

of

the

MD

simulation

it

is

possible

to

obtain

the

segmental

order

tensor

WA

of

the

vicinity

of

atom

A

The

principal

axis

system

of

the

tensor

property

is

used

to

represent

the

instantaneous

segmental

orientation

which

is

then

related

to

the

average

tensor

P

determined

by

Eq

The

transformation

matrices

DPAS

which

link

the

average

P

with

the

principal

axis

system

of

P

at

each

time

step

of

the

simulation

can

then

be

used

to

determine

W

-LRB-

t

denotes

the

time

average

-RRB-

This

average

is

calculated

in

every

step

of

the

MD

simulation

for

all

sites

A

for

which

the

tensorial

NMR

properties

are

calculated

In

general

the

complete

order

tensor

has

elements

which

reduce

to

nine

components

if

we

are

interested

only

in

the

zz

component

of

a

property

-LRB-

Eq

-RRB-

Since

the

order

tensor

W

-LRB-

and

S

as

well

-RRB-

is

symmetric

and

traceless

we

have

to

consider

only

five

independent

elements

The

transformation

matrices

DPAS

in

Eq

can

be

calculated

from

the

eigenvectors

corresponding

to

the

principal

values

of

PA.

After

a

full-length

MD

simulation

the

order

tensors

WA

will

contain

the

information

describing

the

time

averaged

orientation

of

all

sites

A.

To

calculate

the

molecular

Saupe

order

tensor

a

coordinate

system

has

to

be

fixed

to

the

molecule

In

a

perfectly

rigid

molecule

any

set

of

three

atoms

could

be

selected

at

will

However

as

most

molecules

are

intrinsically

flexible

it

does

not

make

sense

to

define

the

coordinate

system

that

way

as

the

Saupe

order

tensor

would

then

depend

on

this

selection

We

therefore

decided

to

use

the

principal

axis

system

of

the

tensor

of

inertia

to

represent

the

orientation

of

the

entire

molecule

-LRB-

see

Burnell

and

De

Lange

-RRB-

This

way

we

can

calculate

a

molecular

order

tensor

that

is

independent

of

any

particular

choice

of

coordinates

The

axes

of

inertia

are

denoted

with

a

b

and

c

corresponding

to

the

moments

of

inertia

in

increasing

order

For

rod-like

molecules

the

long

axis

will

thus

be

the

a-axis

of

least

inertia

In

many

cases

it

is

convenient

to

diagonalize

the

order

tensor

to

introduce

a

principal

frame

of

order

-LRB-

Low

-RRB-

Within

this

frame

there

are

only

two

independent

parameters

the

order

parameter

S

and

a

biaxality

parameter

ξ

By

ordering

the

principal

components

as

one

gets

If

the

biaxiality

ξ

is

zero

the

orientational

distribution

of

the

molecule

is

defined

by

a

single

axis

which

is

called

director

In

the

biaxial

case

with

a

non-zero

ξ

there

exists

a

second

distinct

direction

orthogonal

to

the

director

and

the

molecular

motions

are

characterized

by

two

axes

A

perfectly

axially

symmetric

molecule

that

is

oriented

parallel

to

the

membrane

normal

will

lead

to

the

following

order

tensor

When

the

molecular

Saupe

tensor

is

used

to

interpret

the

NMR

observables

the

conformational

tensors

CA

have

to

be

known

as

well

These

tensors

mediate

between

the

orientation

and

order

of

a

site

A

and

the

molecular

coordinate

system

If

the

transformation

matrices

leading

from

the

molecular

coordinate

system

to

the

individual

tensor

systems

of

the

sites

A

are

known

CA

can

be

calculated

the

same

way

as

the

order

tensor

-LRB-

see

Limmer

-RRB-

Only

in

the

case

of

rigid

molecules

simple

expressions

for

CA

can

be

derived

from

the

molecular

geometry

Since

in

our

MD

simulations

the

segmental

order

tensors

WA

and

the

molecular

Saupe

order

tensor

are

calculated

directly

the

conformational

order

tensors

become

obsolete

Molecular

dynamics

simulation

The

integration

of

the

equations

of

motions

is

based

on

Verlet

's

algorithm

-LRB-

Verlet

-RRB-

and

time

steps

of

fs

were

employed

to

sample

all

high

frequency

hydrogen

atom

vibrations

In

constrained

MD

simulations

it

is

generally

necessary

to

control

the

temperature

during

the

simulation

time

This

is

accomplished

by

coupling

the

molecular

system

to

a

heat

bath

which

dissipates

the

heat

generated

by

the

pseudo-forces

All

prevailing

differences

between

the

constraints

and

their

calculated

values

are

sources

of

heat

To

obtain

an

NTV

assemble

-LRB-

with

conserved

particle

number

N

temperature

T

and

volume

V

-RRB-

we

introduced

a

proper

thermostating

procedure

-LRB-

see

Evans

and

Morriss

-RRB-

The

coupling

to

the

thermostat

is

controlled

by

a

coupling

time

constant

η

which

should

be

much

larger

than

the

time

step

This

time

span

η

allows

an

adjustment

of

the

range

of

thermal

fluctuations

in

the

simulated

molecular

system

To

prevent

too

large

pseudo-forces

at

the

start

of

the

MD

simulation

the

pseudo-forces

were

gradually

increased

towards

their

final

values

during

the

MD

simulation

To

this

aim

we

introduced

time

dependent

scaling

factors

which

approach

the

value

in

an

exponential

fashion

The

time

constant

was

set

in

most

cases

to

ps

leading

to

a

relatively

smooth

course

of

the

temperature

When

applying

the

NMR

orientational

constraints

during

an

MD

run

the

resulting

pseudo-forces

will

heat

up

the

system

and

enhance

its

rotational

degrees

of

freedoms

Because

the

averaging

procedure

depends

on

the

molecular

re-orientations

caused

by

the

NMR

constraints

some

net

rotational

motion

will

prevail

up

to

the

end

of

the

simulation

In

standard

MD

simulations

any

overall

molecular

rotations

and

translations

are

subtracted

from

the

velocities

since

these

external

degrees

of

freedom

are

not

of

interest

In

the

present

orientationally

constrained

calculations

however

only

the

net

translations

of

the

systems

are

removed

Parametrization

For

NMR

spectroscopic

considerations

it

is

convenient

to

introduce

the

quadrupolar

coupling

tensor

CQ

in

frequency

units

where

Q

is

the

quadrupolar

moment

of

the

deuterium

nucleus

and

V

the

electric

field

gradient

tensor

at

the

nuclear

position

The

trace

of

CQ

is

zero

because

of

and

in

the

case

of

carbon-bonded

deuterons

the

quadrupolar

coupling

tensor

can

be

considered

to

a

good

approximation

as

diagonal

in

the

coordinate

system

aligned

with

the

C

bond

If

the

electron

distribution

is

axially

symmetric

there

is

only

one

linearly

independent

tensor

component

otherwise

there

are

two

In

the

general

high

temperature

case

we

observe

two

quadrupolar

resonances

with

frequencies

symmetric

to

zero

If

the

z-axis

of

the

local

electric

field

gradient

points

into

the

direction

of

the

magnetic

field

the

corresponding

quadrupolar

splitting

Δ

ν

is

In

the

case

of

a

C

bond

the

deuterium

quadrupolar

coupling

depends

only

weakly

on

the

molecular

surrounding

hence

representative

values

from

static

solid

state

NMR

measurements

of

characteristic

substances

can

be

used

as

quadrupolar

constants

-LRB-

Table

-RRB-

In

this

selection

we

have

to

keep

in

mind

that

the

quadrupolar

coupling

constants

depend

strongly

on

the

hybridization

of

the

carbon

and

to

some

extent

also

on

the

polarization

of

the

C

bonds

by

partial

charges

caused

by

electronegative

groups

The

coordinate

system

for

the

local

tensors

is

defined

in

Fig.

The

zz-component

is

aligned

with

the

C

bond

direction

and

the

yy-component

is

perpendicular

to

any

π

system

For

an

aromatic

C

-LRB-

-RRB-

bond

an

asymmetry

parameter

of

with

-RRB-

was

assumed

and

the

tensor

axes

were

assigned

according

to

calculations

of

Bailey

-LRB-

-RRB-

The

value

for

the

group

is

obtained

from

the

C

-LRB-

-RRB-

value

scaled

by

assuming

rapid

rotation

around

the

C

axis

Program

implementation

The

routines

to

apply

the

proposed

orientational

constraints

are

included

into

the

COSMOS-NMR

force

field

which

has

been

used

in

a

number

of

previous

applications

but

which

had

so

far

been

restricted

to

distance

and

chemical

shift

constraints

-LRB-

see

e.g.

Sternberg

et

al.

Witter

et

al.

-RRB-

and

for

the

force

field

-LRB-

Möllhoff

and

Sternberg

Sternberg

et

al.

-RRB-

These

two

types

of

NMR

constraints

can

be

combined

with

the

new

orientational

constraints

as

will

be

demonstrated

in

the

example

of

PGLa

below

The

authors

provide

the

backend

version

of

the

full

COSMOS

program

containing

all

computational

procedures

without

the

graphics

and

modelling

interface

-LRB-

GUI

-RRB-

-LRB-

see

-RRB-

The

COSMOS-backend

-LRB-

C++

-RRB-

was

compiled

for

several

operation

systems

including

Windows

Unix

and

Linux

Applications

The

use

of

NMR

orientational

constraints

is

particularly

well

suited

to

gain

insight

into

the

alignment

and

dynamics

of

molecules

embedded

in

biomembranes

In

the

three

examples

presented

here

we

will

first

demonstrate

our

new

MD

approach

on

pyrene

as

a

simple

model

compound

dissolved

in

lipid

bilayers

then

we

will

apply

it

to

cholesterol

as

an

intrinsic

membrane

lipid

and

finally

to

the

antimicrobial

peptide

PGLa

which

forms

an

amphiphilic

α-helix

in

membranes

Pyrene

Pyrene

was

used

as

a

first

example

not

only

because

of

its

relatively

simple

and

rigid

structure

but

also

because

a

full

set

of

data

is

available

from

a

recent

analysis

in

oriented

lipid

bilayers

-LRB-

Hoff

et

al.

-RRB-

The

same

publication

included

an

all-atom

MD

simulation

of

four

pyrene

molecules

in

a

POPC

-LRB-

1-palmitoyl-2-oleoyl-phosphatedylcholine

-RRB-

membrane

Those

previous

results

will

thus

allow

a

direct

comparison

of

our

new

strategy

with

established

simulation

techniques

The

present

orientational

constraint-driven

simulation

utilizes

the

experimental

data

of

deuterium-labelled

pyrene

-LRB-

see

Fig.

-RRB-

embedded

at

mol

in

POPC

bilayers

Spectra

had

been

acquired

at

two

discrete

sample

orientations

namely

with

the

membrane

normal

aligned

parallel

and

perpendicular

to

the

field

In

both

orientations

two

pairs

of

narrow

lines

were

observed

-LRB-

corresponding

to

the

sites

and

respectively

-RRB-

whose

splittings

changed

by

a

factor

of

This

situation

can

only

originate

from

axially

symmetric

averaged

quadrupolar

tensors

that

are

aligned

with

the

membrane

normal

This

means

that

the

pyrene

molecules

reorient

quickly

-LRB-

on

the

time

scale

of

the

NMR

interaction

-RRB-

about

the

membrane

normal

Since

the

principal

axis

system

of

each

averaged

quadrupolar

deuterium

coupling

tensor

coincides

with

the

membrane-fixed

coordinate

system

the

absolute

values

of

all

or

linearly

independent

components

of

the

averaged

coupling

tensor

are

known

and

can

be

included

in

the

present

MD

simulation

In

this

case

we

could

even

make

use

of

the

signs

of

the

principal

quadrupolar

components

as

they

had

been

deduced

from

the

previous

MD

simulations

mentioned

above

-LRB-

Hoff

et

al.

-RRB-

Fig.

deuterated

pyrene

molecule

with

three

kinds

of

labelled

sites

-LRB-

and

-RRB-

illustrating

the

principal

axes

of

the

local

deuterium

quadrupolar

tensors

and

of

the

principal

axes

of

inertia

a

b

and

c

Using

the

data

from

the

literature

we

performed

two

MD

simulations

on

pyrene

constrained

by

the

complete

tensors

In

the

first

run

only

the

contributions

to

the

pseudo-energy

arising

from

the

three

diagonal

elements

-LRB-

first

sum

in

Eq

-RRB-

were

considered

and

in

a

second

run

also

the

three

off

diagonal

values

-LRB-

in

this

case

-RRB-

were

included

In

the

first

run

ns

were

simulated

with

the

MD

parameters

set

as

given

in

Table

To

study

the

time

behaviour

of

the

pseudo-forces

they

were

not

scaled

up

exponentially

as

in

the

other

two

case

studies

below

The

width

parameter

was

set

equal

to

the

experimental

error

as

ΔP

kHz

and

the

memory

time

was

τ

ps

The

time

development

of

the

simulated

tensor

components

for

the

first

nanosecond

can

be

seen

in

Fig.

The

trajectories

are

shown

for

the

site

which

possesses

an

experimental

splitting

of

kHz

After

an

initial

time

period

of

about

ps

the

final

average

coupling

tensor

components

are

reached

and

their

values

fluctuate

only

weakly

The

residual

fluctuations

depend

on

four

parameters

-LRB-

i

-RRB-

the

thermal

fluctuations

controlled

by

the

coupling

to

the

heat

bath

-LRB-

ii

-RRB-

the

pseudo-energy

-LRB-

iii

-RRB-

the

width

parameter

ΔP

given

in

Eq

and

-LRB-

iv

-RRB-

the

memory

time

τ

of

Eq

In

the

simulated

spectra

-LRB-

Fig.

-RRB-

these

prevailing

small

fluctuations

translate

into

line

broadening

and

the

resulting

line

shapes

are

indeed

very

similar

to

the

experimentally

observed

spectrum

-LRB-

Hoff

et

al.

-RRB-

Table

quadrupolar

coupling

tensorsGroupCzzQ/kHzCyyQ/kHzCxxQ

kHzSourceC

-LRB-

-RRB-

Benzene

naphthalene

-LRB-

Rinné

and

Depireux

-RRB-

C

-LRB-

-RRB-

Acenaphthene

bridge

-LRB-

Rinné

and

Depireux

-RRB-

C

-LRB-

-RRB-

The

values

of

the

quadrupolar

coupling

constant

are

scaled

by

to

take

into

account

the

free

methyl

rotationTable

parameters

for

the

MD

simulations

with

orientational

constraintsParameterValueTarget

KMD

time

fsCoupling

time

η

to

the

heat

psPseudo-force

width

ΔP

-LRB-

Eq

-RRB-

kHzMemory

decay

time

τ

for

the

average

-LRB-

Eqs

-RRB-

psTime

constant

ρ

for

the

exponential

rise

of

psTotal

MD

nsFig

of

the

time

development

of

the

averaging

for

the

deuterium

tensor

components

for

of

pyrene

Under

the

influence

of

orientational

pseudo-forces

all

components

approach

their

final

values

after

a

period

of

about

ps

The

component

at

about

kHz

is

experimentally

observable

in

an

oriented

sample

with

the

membrane

normal

parallel

to

The

component

at

kHz

would

correspond

to

an

experiment

with

a

perpendicular

sample

alignmentFig

spectrum

from

the

MD

simulation

of

deuterated

pyrene

using

orientational

constraints

from

an

NMR

measurement

in

oriented

POPC

membranes

-LRB-

Hoff

et

al.

-RRB-

In

this

first

simulation

we

had

constrained

only

the

three

principal

components

of

the

quadrupolar

tensor

It

turned

out

that

in

this

case

small

off-diagonal

values

did

not

approach

zero

but

remain

in

the

range

of

to

kHz

up

to

the

end

of

the

simulation

-LRB-

see

Fig.

-RRB-

At

the

beginning

of

the

simulation

a

high

pseudo-energy

of

kJ/mol

was

encountered

which

dropped

to

kJ/mol

by

the

end

of

the

simulation

Because

of

the

large

pseudo-energies

at

the

start

we

realized

that

it

is

preferable

to

first

run

a

preliminary

MD

simulation

-LRB-

ns

-RRB-

with

much

smaller

pseudo-forces

and

then

to

step

up

the

pseudo

forces

after

some

initial

averaging

has

been

performed

In

the

next

two

cases

studies

the

pseudo-forces

were

switched

on

exponentially

to

avoid

long

preliminary

equilibration

periods

In

a

second

MD

simulation

of

pyrene

over

ns

we

also

constrained

the

three

off-diagonal

tensor

components

Cxy

Cxz

and

Cyz

to

zero

which

are

averaged

by

rotations

of

the

molecule

about

the

membrane

normal

The

corresponding

values

calculated

from

the

MD

run

yielded

off-diagonal

elements

with

absolute

values

smaller

than

kHz

The

pseudo-energy

increased

by

a

factor

of

two

as

it

now

contains

contributions

from

both

the

diagonal

and

off-diagonal

tensor

components

In

an

attempt

to

compensate

for

the

higher

pseudo-energy

we

set

the

memory

time

to

a

higher

value

of

τ

ps

-LRB-

see

Eq

-RRB-

Altogether

we

obtained

smaller

fluctuations

of

the

coupling

tensor

components

and

much

narrower

lines

in

simulated

spectra

which

can

be

most

likely

attributed

to

the

damping

effect

of

the

memory

function

outweighing

the

higher

pseudo-energies

Table

summarizes

the

calculated

quadrupolar

splittings

corresponding

to

the

results

of

the

second

simulation

in

which

all

tensor

components

were

constrained

The

values

were

averaged

for

any

sites

on

pyrene

with

mutually

parallel

C

bond

directions

so

that

the

splitting

is

a

mean

value

of

two

and

the

others

are

mean

values

of

four

sites

each

The

MD

simulation

is

seen

to

reflect

the

experimental

data

very

well

in

several

aspects

First

of

all

the

calculated

quadrupolar

splittings

reproduce

the

experimental

values

very

well

The

marginally

lower

values

found

for

the

simulated

splittings

might

be

explained

by

a

slightly

elevated

temperature

encountered

during

the

simulation

Namely

the

mean

temperature

of

this

simulation

was

K

and

the

final

temperature

K

Since

the

target

temperature

of

the

simulation

was

K

the

NMR

constraints

produced

a

constant

temperature

increase

of

about

K

This

difference

would

explain

the

slightly

smaller

simulated

splittings

compared

to

the

experiment

In

full

agreement

with

the

experimental

data

no

significant

difference

was

found

for

the

sites

and

In

the

simulations

the

difference

between

their

splittings

was

within

the

scatter

of

the

individual

sites

and

this

difference

could

neither

be

resolved

experimentally

Furthermore

also

the

averaging

of

the

pyrene

molecule

in

the

membrane

is

reflected

correctly

in

the

simulation

The

values

for

the

tensor

components

perpendicular

to

the

field

direction

are

negative

and

half

of

the

values

of

Table

indicating

that

the

simulation

does

indeed

lead

to

an

averaged

axially

symmetric

tensor

aligned

parallel

to

the

membrane

normal.Table

quadrupolar

splittings

in

a

ns

constrained

MD

simulation

of

pyrene

compared

with

the

experimental

values

obtained

from

a

measurement

of

the

deuterated

pyrene

in

oriented

POPC

membranesSiteSign

of

tensor

componentaConstrained

MD

splitting

Δν

-LRB-

kHz

-RRB-

NMR

experimentalb

splitting

Δ

ν

-LRB-

kHz

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

a

The

sign

is

given

for

the

orientation

of

the

membrane

normal

in

field

directionb

Hoff

et

al.

-LRB-

-RRB-

c

Range

of

simulated

values

for

two

or

four

sites

respectively

The

experimental

data

only

reflect

dynamic

averages

of

e.g.

the

C

bond

orientation

but

can

access

only

little

information

on

the

dynamic

processes

leading

to

the

observed

splittings

Here

the

constraint-driven

MD

simulation

provides

a

way

to

obtain

details

on

molecular

motions

that

are

compatible

with

the

experimental

data

In

the

example

of

pyrene

the

symmetry

of

the

molecule

and

its

motions

in

the

membrane

allowed

us

to

derive

information

on

the

dynamic

behaviour

of

the

molecule

from

its

observed

splittings

Since

in

our

case

the

coupling

tensors

are

diagonal

within

the

bond

coordinate

system

and

the

segmental

order

tensor

is

also

diagonal

simple

expressions

for

the

quadrupolar

splittings

are

obtained

and

for

the

case

of

an

axially

symmetric

coupling

tensor

CQ

we

get

The

latter

expression

is

especially

useful

since

the

quadrupolar

splitting

of

a

site

A

is

directly

related

to

a

single

segmental

order

parameter

Assuming

that

the

order

tensor

is

diagonal

in

the

laboratory

frame

Eq

applies

to

dipolar

splittings

as

well

since

the

static

dipolar

coupling

tensor

is

always

axially

symmetric

and

traceless

and

the

same

holds

for

a

rapidly

rotating

However

since

the

coupling

tensor

CQ

for

the

C

-LRB-

-RRB-

bonds

is

not

axially

symmetric

-LRB-

see

Table

-RRB-

the

three

principal

elements

of

the

order

tensors

WA

contribute

to

the

splitting

as

in

Eq

It

is

therefore

not

possible

to

extract

the

order

parameter

tensor

components

from

a

single

experimental

splitting

From

the

course

of

our

MD

simulation

on

the

other

hand

all

components

of

the

orders

tensors

WA

-LRB-

Table

-RRB-

are

available

and

the

terms

of

Eq

can

be

readily

analysed.Table

order

parameters

for

pyrene

in

POPCSiteWxxWyyWzz

Wxy

Wxz

Wyz

SbbSccSaa

Sab

Sac

Sbc

Moleculea

a

The

values

for

the

molecular

Saupe

order

tensor

are

ordered

in

the

columns

such

that

the

axes

of

inertia

fit

to

the

corresponding

coordinate

axes

of

the

site

-LRB-

see

Fig.

-RRB-

For

a

perfectly

rigid

pyrene

molecule

the

molecular

Saupe

order

tensor

S

and

the

segmental

order

tensors

WA

are

linked

by

fixed

conformation

tensors

With

our

choice

of

the

molecular

coordinate

system

S

and

WA

are

identical

for

the

site

and

for

the

other

two

sites

the

tensors

are

related

by

simple

geometric

expressions

Comparing

the

molecular

order

tensor

S

-LRB-

last

row

in

Table

-RRB-

and

the

segmental

order

tensor

W

-LRB-

e.g.

of

the

site

which

is

expressed

in

the

same

coordinate

system

first

row

in

Table

-RRB-

it

is

noticed

that

most

of

the

molecular

S

tensor

components

are

slightly

smaller

than

the

corresponding

values

of

the

segmental

order

tensor

W

This

effect

is

caused

by

bond

vibrations

and

molecular

twists

occurring

during

the

MD

simulation

However

as

these

contributions

to

the

dynamics

-LRB-

manifested

in

the

difference

between

segmental

and

molecular

order

-RRB-

are

small

the

mobility

of

the

pyrene

in

the

membrane

is

well

described

by

the

molecular

order

tensor

S.

Further

qualitative

conclusions

on

the

behaviour

of

the

pyrene

molecule

in

the

membrane

can

thus

be

drawn

from

the

order

tensor

Because

Saa

constitutes

the

largest

-LRB-

signed

value

-RRB-

component

it

is

obvious

that

the

corresponding

axis

a

-LRB-

in

the

system

of

inertia

-RRB-

and

with

it

the

long

molecular

axis

of

pyrene

shows

some

preference

for

an

orientation

in

the

direction

of

the

membrane

normal

Since

Scc

and

Sbb

are

different

the

molecular

motions

are

not

axially

symmetric

but

display

a

preference

for

a

second

axis

expressed

in

a

biaxiality

parameter

ξ

-LRB-

see

Eq

-RRB-

This

pronounced

biaxiality

is

a

consequence

of

the

restricted

motions

of

the

flat

pyrene

molecule

within

the

lipid

matrix

A

further

indication

for

such

a

restricted

motion

is

the

fact

that

the

smallest

component

of

the

order

tensor

S

is

found

along

the

c-axis

direction

perpendicular

to

the

aromatic

ring

system

This

direction

has

thus

the

smallest

average

component

along

the

membrane

normal

and

is

most

conserved

as

expected

for

the

planar

shape

of

the

molecule

In

their

all-atom

MD

simulation

including

lipid

molecules

and

water

Hoff

et

al.

-LRB-

-RRB-

obtained

essentially

the

same

results

as

in

this

work

with

the

exception

that

they

found

a

much

higher

Saupe

order

component

Szz

-LRB-

in

this

work

denoted

with

Scc

-RRB-

Cholesterol

Cholesterol

is

a

constituent

of

many

biomembranes

and

its

orientation

and

motion

within

the

lipid

bilayer

is

of

great

interest

to

explain

its

influence

on

membrane

properties

The

behaviour

of

cholesterol

in

membranes

has

been

studied

extensively

especially

by

in

view

of

its

sensitivity

towards

molecular

alignment

and

dynamics

-LRB-

Smith

and

Oldfield

-RRB-

We

have

based

our

MD

analysis

on

a

recent

study

by

Marsan

et

al.

-LRB-

-RRB-

who

had

measured

and

interpreted

spectra

of

partially

deuterated

cholesterol

in

oriented

DMPC

-LRB-

dimyristoylphosphatidylcholine

-RRB-

bilayers

The

labelled

sites

in

the

sterol

ring

system

are

indicated

in

Fig.

Fig.

molecule

with

sites

indicated

for

which

experimental

orientational

constraints

were

available

From

the

MD

simulation

quadrupolar

splittings

were

calculated

for

all

deuterons

in

the

ring

system

The

authors

examined

six

different

models

of

cholesterol

structures

proposed

in

the

literature

using

an

RMSD

analysis

to

assign

all

observed

lines

in

the

spectrum

In

this

analysis

the

quadrupolar

splittings

were

calculated

from

the

respective

rigid

molecular

models

treating

the

molecular

orientation

and

the

Saupe

tensor

as

free

variables

It

turned

out

that

the

results

depended

crucially

on

the

selection

of

the

molecular

coordinates

and

only

the

data

from

a

neutron

diffraction

analysis

-LRB-

McMullan

et

al.

-RRB-

of

a

cholesterol

derivative

-LRB-

-RRB-

produced

convincing

results

This

strong

dependence

on

the

exact

coordinates

is

regarded

as

one

of

the

main

drawbacks

of

RMSD

analyses

of

rigid

molecular

models

In

the

analysis

presented

here

we

performed

MD

simulations

for

both

methylpregnenediol

and

cholesterol

having

modelled

the

latter

with

COSMOS

-LRB-

see

Fig.

-RRB-

As

constraints

for

the

MD

simulations

we

used

the

splittings

of

the

eight

experimentally

observed

deuterium

labels

of

Marsan

et

al.

-LRB-

-RRB-

together

with

their

best

assignment

-LRB-

see

Table

-RRB-

In

addition

from

the

MD

simulations

we

predicted

the

putative

quadrupolar

splittings

of

all

other

protonated

sites

of

the

sterol

ring

system

This

new

data

from

our

MD

simulations

can

thus

be

used

in

the

future

to

assign

further

spectra

without

the

need

for

any

special

labelling

schemes

or

particular

molecular

coordinates

As

outlined

above

we

again

used

the

full

quadrupolar

tensors

as

constraints

Two

short

preliminary

MD

runs

were

performed

to

determine

the

signs

of

the

coupling

constants

since

this

information

is

required

for

the

full

tensorial

constraints

All

quadrupolar

splittings

of

cholesterol

which

had

been

measured

in

oriented

samples

with

the

membrane

normal

parallel

to

yielded

negative

coupling

constants

-LRB-

giving

correspondingly

positive

values

for

the

perpendicular

orientation

see

Table

-RRB-

As

in

the

example

of

pyrene

MD

simulations

over

ps

were

sufficient

to

reproduce

all

features

of

molecular

motion

To

avoid

too

large

pseudo-forces

at

the

start

of

the

simulation

the

pseudo-forces

were

exponentially

increased

to

their

final

values

during

the

MD

run

The

parameters

used

in

the

simulations

are

summarized

in

Table

Table

deuterium

quadrupolar

splittings

from

a

constrained

MD

simulation

compared

with

the

experimental

data

-LRB-

Marsan

et

al.

-RRB-

SiteConstrained

MD

splitting

of

methyl-pregnenediol

-LRB-

kHz

-RRB-

Constrained

MD

splitting

of

cholesterol

-LRB-

kHz

-RRB-

Experimental

NMR

splitting

-LRB-

kHz

-RRB-

The

final

results

for

the

quadrupolar

splittings

obtained

from

the

constrained

MD

simulations

of

both

sterols

are

summarized

in

Table

The

corresponding

simulated

spectrum

of

cholesterol

is

shown

in

Fig.

indicating

the

peak

positions

of

all

ring

deuterons

This

presentation

can

be

helpful

in

the

future

for

assigning

the

signals

of

fully

deuterated

cholesterol

derivatives

Overall

the

theoretical

and

experimental

values

agree

very

well

within

kHz

-LRB-

except

for

-RRB-

The

only

noteworthy

deviation

is

seen

for

where

the

calculated

splitting

of

methylpregnenediol

differs

by

kHz

from

the

experiment

Overall

the

simulated

cholesterol

quadrupolar

couplings

agree

slightly

better

with

the

experimental

values

than

the

respective

methylpregnenediol

values

This

finding

is

also

reflected

in

the

lower

mean

temperature

reached

in

the

simulation

of

cholesterol

-LRB-

K

-RRB-

than

for

methylpregnenediol

-LRB-

K

-RRB-

The

higher

mean

temperature

of

the

latter

is

probably

also

responsible

for

the

slight

differences

between

the

calculated

splittings

of

the

two

molecules

in

some

of

the

other

sites

too

-LRB-

see

Table

-RRB-

Fig.

spectrum

from

the

MD

simulation

of

deuterated

cholesterol

in

an

oriented

membrane

with

the

membrane

normal

parallel

to

Pseudo-forces

were

applied

in

the

MD

simulation

to

a

sub-set

of

deuterons

for

which

experimental

data

was

available

-LRB-

see

Fig.

-RRB-

The

peak

positions

of

all

other

deuterons

connected

to

the

ring

skeleton

are

also

predicted

and

indicated

-LRB-

see

Table

-RRB-

The

intensity

of

the

has

to

be

multiplied

by

a

factor

of

three

The

constrained

MD

simulation

showed

that

both

cholesterol

derivatives

essentially

assume

an

upright

orientation

in

the

membrane

and

perform

rotations

mainly

around

their

long

molecular

a-axis

of

inertia

This

behaviour

is

reflected

in

the

molecular

Saupe

order

tensor

-LRB-

see

Table

-RRB-

whose

values

are

not

far

from

the

ideal

axially

symmetric

case

of

Eq

with

a

low

biaxiality

of

ξ

Previous

calculations

of

the

order

tensor

from

the

NMR

data

-LRB-

Marsan

et

al.

-RRB-

had

given

similar

results

as

the

present

MD

simulation

We

find

that

the

preferred

orientation

of

the

long

a-axis

of

the

molecule

displays

a

small

mean

tilt

angle

Θ

a

of

with

respect

to

the

membrane

normal

A

similar

result

was

obtained

by

Marsan

et

al.

-LRB-

-RRB-

who

reported

a

tilt

of

the

long

molecular

axis

-LRB-

as

defined

in

the

paper

of

Dufourc

et

al.

-RRB-

with

respect

to

the

membrane

normal

of

-LRB-

provided

that

in

their

RMSD

data

analysis

the

restriction

to

a

rotationally

symmetric

order

tensor

was

dropped

-RRB-

Table

Saupe

order

tensor

derived

from

the

constrained

MD

simulation

compared

with

the

values

derived

from

the

previous

RMSD

analysis

-LRB-

Marsan

et

al.

-RRB-

Tensor

componentMD

simulation

of

methylpregnenediolMD

simulation

of

cholesterolStatic

RMSD

Sbb

Scc

We

note

that

the

axially

symmetric

averaging

of

cholesterol

does

not

imply

that

its

motion

resembles

a

smooth

rotation

about

a

fixed

axis

In

the

MD

simulation

we

observed

frequent

jumps

of

the

long

axis

by

to

accompanied

by

a

change

of

the

conformation

of

the

aliphatic

tail

of

the

molecule

This

behaviour

can

be

examined

more

closely

by

inspecting

the

trajectory

of

the

angle

Θ

a

between

the

a-axis

of

inertia

and

the

membrane

normal

-LRB-

z-axis

see

Fig.

-RRB-

Under

the

influence

of

the

full

pseudo-forces

after

ps

the

long

axis

of

cholesterol

frequently

jumps

off

the

most

preferred

orientation

of

Θ

a

As

a

consequence

the

mean

orientation

and

the

most

frequent

orientation

do

not

coincide

Methylpregnenediol

behaves

clearly

different

in

the

MD

simulation

since

it

has

only

a

short

aliphatic

tail

that

does

not

give

rise

to

conformational

changes.Fig

of

the

time

development

of

the

angle

Θa

between

the

a-axis

of

inertia

and

the

z-direction

-LRB-

membrane

normal

-RRB-

The

axis

frequently

jumps

off

its

most

preferred

orientation

due

to

conformational

changes

in

the

aliphatic

tail

of

the

molecule

hence

the

mean

tilt

-LRB-

-RRB-

and

the

most

preferred

tilt

-LRB-

-RRB-

do

not

coincide

PGLa

In

our

third

case

study

the

new

MD

approach

was

applied

to

a

membrane

bound

peptide

PGLa

is

a

cationic

peptide

-LRB-

-RRB-

from

the

magainin

family

of

antibiotics

present

in

frog

skin

which

folds

into

an

amphiphilic

α-helix

when

bound

to

lipid

bilayers

The

mechanism

of

antimicrobial

activity

has

been

addressed

in

numerous

studies

and

is

attributed

to

the

perturbation

of

bacterial

membranes

Solid

state

NMR

has

yielded

much

insight

into

its

structure

and

dynamic

behaviour

in

model

membranes

-LRB-

Bechinger

-RRB-

For

our

MD

simulations

we

used

the

constraints

from

the

investigations

of

Strandberg

et

al.

-LRB-

-RRB-

who

had

labelled

four

native

alanine

residues

-LRB-

positions

and

-RRB-

and

two

isoleucines

-LRB-

positions

and

-RRB-

one

by

one

with

At

a

peptide-to-lipid

ratio

of

in

DMPC

it

was

found

from

the

quadrupolar

splittings

of

these

six

that

the

α-helical

PGLa

is

aligned

flat

in

the

plane

of

the

membrane

and

the

peptide

undergoes

fast

rotational

diffusion

about

the

membrane

normal

at

°C

From

the

same

data

we

now

derived

the

full

quadrupolar

coupling

tensors

for

the

six

sites

including

the

sign

of

the

tensor

elements

and

used

these

as

constraints

for

the

MD

simulations

For

the

quadrupolar

coupling

tensors

we

used

the

parameters

of

the

-LRB-

Table

-RRB-

both

for

the

native

Ala

substitutions

as

well

as

for

the

nominal

constraint

along

the

Cα

Cβ

segment

of

isoleucine

It

is

known

from

previous

NMR

studies

-LRB-

Strandberg

et

al.

-RRB-

that

membrane-bound

PGLa

forms

an

α-helix

in

the

range

of

the

labelled

stretch

and

further

evidence

for

an

α-helical

conformation

between

residues

and

is

provided

by

-LRB-

Bechinger

-RRB-

We

therefore

started

the

MD

simulations

with

an

idealized

α-helix

and

for

all

backbone

hydrogen

bonds

we

introduced

additional

distance

constraints

of

Å

to

keep

the

molecular

model

helical

At

the

end

of

the

simulation

the

RMSD

of

the

backbone

hydrogen

bond

lengths

from

their

ideal

values

was

only

Å

thus

confirming

that

that

the

molecule

stayed

indeed

mostly

helical

during

the

MD

simulation

It

also

had

to

be

taken

into

account

that

the

four

lysine

side

chains

and

N-terminus

are

positively

charged

Since

charged

groups

have

a

strong

tendency

to

form

hydrogen

bonds

we

added

a

water

molecule

near

each

hydrogen

atom

of

a

charged

group

This

way

any

undesired

hydrogen

bonds

of

lysines

to

the

backbone

could

be

prevented

and

indeed

at

the

end

of

the

simulation

all

water

molecules

were

still

in

contact

with

the

peptide

Compared

to

the

two

small-molecule

case

studies

above

the

NMR

data

on

PGLa

provide

only

few

constraints

on

the

large

and

rather

flexible

molecule

as

the

pseudo-forces

act

only

on

six

amino

acids

out

of

Therefore

unrealistically

large-pseudo

forces

at

the

start

of

the

MD

simulation

have

to

be

avoided

As

a

first

measure

the

pseudo-forces

were

increased

exponentially

to

their

final

values

during

the

MD

simulation

with

a

time

constant

of

ρ

ps

like

in

the

cholesterol

simulation

From

the

NMR

studies

it

was

known

that

PGLa

rotates

rapidly

-LRB-

on

the

NMR

time

scale

-RRB-

about

the

membrane

normal

This

motion

opens

up

a

second

possibility

to

scale

the

pseudo-forces

properly

We

calculated

rotational

averages

of

the

quadrupolar

tensors

in

every

step

of

the

MD.

Only

three

tensor

values

rotated

by

around

the

director

axis

-LRB-

in

this

case

the

membrane

normal

oriented

parallel

to

the

field

directions

-RRB-

are

necessary

to

obtain

a

mean

tensor

within

the

limits

of

a

fast

rotation

All

off-diagonal

values

of

the

simulated

tensors

thus

become

zero

and

only

the

principal

values

of

the

tensors

are

left

as

constraints

The

mean

temperature

at

the

end

of

the

simulation

was

only

K

above

the

target

temperature

of

K

indicating

that

exceedingly

high

pseudo-forces

have

been

successfully

avoided

indeed

which

would

otherwise

have

lead

to

additional

heat

production

As

in

the

other

two

case

studies

above

the

constraint-driven

MD

simulations

were

able

to

reproduce

the

experimental

data

correctly

as

evident

from

the

comparison

in

Table

All

calculated

frequencies

are

well

within

the

experimental

error

margins

-LRB-

as

estimated

from

the

experimental

line

widths

-RRB-

For

some

additional

sites

the

quadrupolar

frequencies

were

predicted

from

the

MD

simulation

and

it

would

be

of

interest

whether

future

measurements

can

confirm

these

values.Table

deuterium

quadrupolar

splittings

from

a

constrained

MD

simulation

of

PGLa

compared

with

the

experimental

data

-LRB-

Strandberg

et

al.

-RRB-

in

DMPCSiteMD

-LRB-

kHz

-RRB-

NMR

-LRB-

kHz

-RRB-

The

major

aim

of

the

present

NMR

data

analysis

was

the

determination

of

the

time

and

ensemble

averaged

alignment

of

the

helical

PGLa

backbone

in

the

membrane

environment

As

illustrated

in

Fig.

the

principal

axes

of

inertia

offer

a

suitable

molecule-fixed

frame

of

reference

to

describe

the

peptide

orientation

In

the

PGLa

the

a-axis

of

least

inertia

points

along

the

helix

and

the

c-axis

of

highest

inertia

is

located

between

the

hydrophilic

lysine-rich

face

and

the

hydrophobic

face

of

the

molecule

formed

by

alanines

valines

leucines

and

isoleucines

Intuitively

we

would

expect

the

helix

to

be

in

contact

with

biomembranes

just

like

it

is

displayed

in

this

view

namely

with

the

intermediate

b-axis

collinear

with

the

membrane

normal.Fig

along

the

long

axis

of

PGLa

modelled

as

an

idealized

α-helix

with

only

the

lysine

alanine

and

isoleucine

side

chains

displayed

The

latter

two

types

were

labelled

by

and

their

splittings

were

included

into

the

MD

simulation

The

principal

a-axis

of

inertia

points

along

the

helix

and

the

b-axis

of

inertia

points

radially

through

Cα

of

lysine

The

outcome

of

the

MD

simulation

is

illustrated

most

appropriately

in

Fig.

which

visualizes

the

alignment

and

dynamic

behaviour

of

PGLa

in

DMPC

Here

the

peptide

orientations

during

the

MD

simulation

are

presented

as

a

scatter

plot

of

the

inertia

axes

a

b

and

c

on

the

surface

of

a

unit

sphere

A

narrow

range

of

orientations

is

seen

for

the

a-axis

representing

the

peptide

helix

In

contrast

the

broad

scatter

for

b

and

c

indicates

that

a

high

degree

of

motional

freedom

exists

for

motions

around

the

helix

axis

The

time-averaged

tilt

angle

of

the

a-axis

with

respect

to

the

membrane

normal

in

found

to

be

with

a

mean

deviation

of

about

This

value

is

in

very

good

agreement

with

the

tilt

angle

τ

of

PGLa

that

had

been

deduced

from

an

RMSD

plot

of

the

by

Strandberg

et

al.

-LRB-

-RRB-

assuming

a

rigid

idealized

α-helix

We

note

however

that

such

helix

axis

definition

is

not

exactly

comparable

to

the

a-axis

of

inertia

used

in

our

MD

calculations

The

authors

further

described

the

azimuthal

alignment

of

the

amphiphilic

peptide

by

defining

an

angle

ρ

between

an

axis

pointing

from

the

centre

of

the

helix

radially

through

the

Cα-atom

of

lysine

and

the

membrane

plane

In

our

case

the

b-axis

of

inertia

also

happens

to

be

directed

to

Cα

of

lysine

-LRB-

see

Fig.

-RRB-

but

the

centre

of

inertia

does

not

exactly

coincide

with

the

helix

axis

As

can

be

seen

from

Fig.

the

angle

Θ

b

between

the

b-axis

and

the

membrane

normal

oscillates

between

and

with

a

mean

value

of

This

average

value

corresponds

to

an

angle

ρ

of

approximately

which

compares

well

with

ρ

extracted

from

the

previous

analysis

-LRB-

Strandberg

et

al.

-RRB-

In

this

comparison

we

have

to

keep

in

mind

that

in

our

simulations

the

PGLa

molecule

was

found

to

be

far

from

rigid

and

possesses

a

high

degree

of

mobility

around

the

helix

long

axis

The

lysine

side

chains

are

found

to

spread

out

much

more

than

in

the

initial

model

and

the

PGLa

helix

itself

exhibits

a

small

bend.Fig

of

the

alignment

and

motional

behaviour

of

the

α-helical

peptide

PGLa

-LRB-

only

lysine

side

chains

shown

-RRB-

in

a

DMPC

membrane

as

determined

by

a

ns

MD

simulation

using

experimental

constraints

-LRB-

Strandberg

et

al.

-RRB-

The

instantaneous

orientation

of

the

three

axes

of

inertia

a

b

and

c

is

displayed

as

a

scatter

plot

on

a

sphere

representing

snapshots

of

these

axes

orientations

every

picosecond

The

poles

of

the

sphere

are

oriented

parallel

to

the

membrane

normal

The

helix

long

axis

displays

only

a

small

scatter

with

a

mean

tilt

angle

of

while

the

two

other

axes

oscillate

about

this

direction

producing

a

large

scatterFig

dynamics

trajectory

of

the

angle

Θb

between

the

intermediate

b-axis

of

inertia

and

the

membrane

normal

Similarly

important

as

the

alignment

of

the

peptide

are

its

dynamic

properties

which

also

enter

into

the

observed

data

Table

lists

the

components

of

the

molecular

Saupe

tensor

which

is

again

used

to

describe

the

average

alignment

a

molecule

fixed

frame

-LRB-

i.e.

the

principal

axes

of

inertia

-RRB-

with

respect

to

the

laboratory

frame

However

in

contrast

to

the

two

previous

case

studies

this

Saupe

tensor

does

not

represents

the

fast

reorientation

of

the

molecule

around

the

membrane

normal

No

pseudo-forces

were

driving

this

motion

in

the

simulation

since

a

rotational

mean

value

was

introduced

Here

the

order

tensor

represents

only

the

wobble

of

the

long

a-axis

and

the

pronounced

oscillations

about

this

molecular

axis

-LRB-

see

Fig.

-RRB-

As

expected

from

the

distribution

of

polar

and

hydrophobic

residues

on

the

different

faces

of

the

helix

it

is

seen

that

the

Saupe

tensor

is

not

diagonal

Table

-RRB-

The

biaxiality

of

ξ

-LRB-

S

see

Eq

-RRB-

is

clear

evidence

that

the

molecule

does

not

behave

like

a

rod-shaped

object

and

rotation

about

its

long

axis

is

restricted

In

fact

oscillations

of

about

around

the

long

axis

but

no

complete

rotation

events

were

observed

in

the

MD

simulation

-LRB-

see

Fig.

-RRB-

These

oscillations

start

after

about

ps

when

the

pseudo-forces

approach

their

full

strength.Table

Saupe

order

tensor

from

a

constrained

MD

simulation

of

PGLaTensor

componentMDSaa

Sbb

Scc

Sab

Sac

Sbc

At

a

first

glance

the

rather

regular

oscillations

of

PGLa

in

Fig.

or

the

rotations

of

cholesterol

-LRB-

Fig.

-RRB-

may

not

seem

to

reflect

reality

However

we

have

to

keep

in

mind

that

our

MD

simulations

are

performed

with

single

molecules

in

vacuum

and

the

temperature

is

controlled

by

a

continuously

acting

NTV

thermostat

adjustment

In

nature

heat

is

transferred

by

stochastic

interactions

with

other

molecules

thereby

introducing

a

stochastic

behaviour

of

molecular

rotations

and

re-orientations

This

stochastic

aspect

is

not

present

in

our

MD

simulations

but

nonetheless

the

amplitudes

velocities

and

directions

of

the

motions

adopt

realistic

values

as

the

NMR

constraints

have

to

be

satisfied

The

molecule

in

the

simulation

can

not

stop

in

one

preferred

orientation

because

then

no

averaging

would

be

performed

anymore

Conclusions

Solid

state

NMR

is

a

valuable

technique

to

gain

insight

into

the

behaviour

of

peptides

and

proteins

in

oriented

media

provided

the

data

can

be

interpreted

in

terms

of

molecular

structure

and

dynamics

In

this

contribution

we

developed

a

new

strategy

in

which

all-atom

MD

simulations

and

NMR

data

obtained

from

oriented

samples

are

combined

to

obtain

such

structural

and

motional

information

To

this

aim

a

molecular

mechanics

force

field

-LRB-

in

this

case

COSMOS-NMR

-RRB-

was

extended

to

include

pseudo-forces

which

drive

the

molecular

dynamics

to

meet

the

NMR

constraints

They

heat

up

molecular

rotations

or

re-orientations

leading

to

proper

averaging

of

the

calculated

tensor

values

such

that

the

calculated

tensor

values

agree

with

the

corresponding

experimental

observations

The

orientational

constraints

can

be

further

combined

with

intramolecular

constraints

such

as

distances

or

chemical

shifts

This

way

similar

results

can

be

obtained

as

in

full

membrane

MD

simulations

but

without

the

computational

burden

of

having

to

perform

a

detailed

simulation

of

the

lipids

and

surrounding

water

molecules

Because

they

are

performed

in

vacuum

the

constrained

MD

simulations

can

be

completed

in

relatively

short

simulation

times

-LRB-

ns

-RRB-

still

reaching

a

complete

averaging

of

the

NMR

observables

In

three

case

studies

ranging

from

a

small

rigid

compound

to

a

membrane-active

peptide

the

MD

simulations

with

orientational

NMR

constraints

succeeded

to

produce

a

detailed

picture

of

the

molecular

motions

and

orientations

in

oriented

membranes

It

could

be

demonstrated

that

this

new

method

is

not

limited

to

rigid

molecules

and

does

not

depend

on

the

choice

of

the

initial

coordinates

Deuterium

quadrupolar

splittings

from

pyrene

cholesterol

and

PGLa

in

oriented

lipid

bilayers

have

been

used

as

constraints

in

the

present

examples

but

the

general

formalism

presented

will

be

applicable

to

all

kinds

of

tensorial

NMR

properties

molecular dynamics simulations
orientational nmr constraints
oriented samples
cholesterol
pyrene
order parameters

2h-nmr
pgla peptide
force field calculations


An

Innovative

Option

for

Venous

Reconstruction

After

Pancreaticoduodenectomy

the

Left

Renal

Vein

Introduction

Pancreatic

ductal

adenocarcinoma

has

a

high

mortality

rate

with

limited

treatment

options

One

option

is

pancreaticoduodenectomy

although

complete

resection

may

require

venous

resection

Pancreaticoduodenectomy

with

venous

resection

and

reconstruction

is

becoming

a

more

common

practice

with

many

choices

for

venous

reconstruction

We

describe

the

technique

of

using

the

left

renal

vein

as

a

conduit

for

venous

reconstruction

during

pancreaticoduodenectomy

Introduction

Pancreatic

ductal

adenocarcinoma

has

a

high

mortality

which

approaches

the

incidence

and

treatment

options

remain

limited

For

those

patients

diagnosed

with

pancreatic

ductal

adenocarcinoma

resection

continues

to

offer

the

only

chance

for

cure

Historically

involvement

of

local

vasculature

was

considered

a

contraindication

to

pancreaticoduodenectomy

-LRB-

PD

-RRB-

with

early

experience

associated

with

prohibitively

high

morbidity

and

mortality

rates

As

surgeon

experience

has

grown

morbidity

and

mortality

rates

have

decreased

and

at

high-volume

pancreatic

surgery

centers

invasion

of

local

mesenteric

venous

structures

is

no

longer

a

contraindication

to

resection

Venous

resection

occurs

in

up

to

of

patients

undergoing

PD

at

several

centers

Several

techniques

are

described

for

reconstruction

of

the

venous

system

after

PD

when

necessary

primary

lateral

venorrhaphy

primary

end-to-end

anastomosis

and

interposition

grafting

Both

synthetic

grafts

and

autologous

vein

grafts

have

been

used

with

several

donor

sites

available

The

goal

of

this

report

is

to

describe

the

use

of

the

left

renal

vein

as

a

conduit

for

venous

reconstruction

after

PD

with

venous

resection

Historically

the

left

renal

vein

has

been

used

to

repair

the

portal

vein

hepatic

vein

or

inferior

vena

cava

during

resection

of

hepatic

hilar

carcinomas

and

its

use

offers

distinct

advantages

for

venous

reconstruction

during

PD

Importantly

previous

studies

have

demonstrated

the

safety

of

left

renal

vein

ligation

specifically

in

relation

to

renal

function

We

describe

the

technique

of

mesenteric

venous

reconstruction

after

PD

with

venous

resection

using

a

left

renal

vein

graft

and

report

on

a

group

of

patients

that

have

undergone

this

repair

Patient

Selection

and

Technique

Contrast-enhanced

computed

tomography

-LRB-

CT

-RRB-

is

used

to

evaluate

a

pancreatic

head

mass

and

its

relation

to

vascular

structures

CT

accurately

diagnoses

mesenteric

vein

involvement

aiding

in

operative

planning

The

CT

is

also

used

to

assess

the

length

and

caliber

of

the

left

renal

vein

the

status

of

the

kidneys

bilaterally

and

the

presence

of

the

left

gonadal

and

adrenal

veins

which

serve

as

collateral

venous

drainage

Additional

imaging

of

the

pancreas

with

endoscopic

ultrasound

-LRB-

EUS

-RRB-

is

frequently

used

to

further

evaluate

the

location

and

extent

of

any

venous

involvement

After

initiation

of

the

operation

a

Kocher

maneuver

allows

assessment

of

tumor

location

and

its

relationship

to

the

superior

mesenteric

artery

-LRB-

SMA

-RRB-

further

assessing

resectability

The

lesser

sac

is

entered

by

mobilizing

the

greater

omentum

off

of

the

transverse

colon

through

an

avascular

plane

The

middle

colic

vein

is

followed

centrally

to

identify

the

superior

mesenteric

vein

-LRB-

SMV

-RRB-

and

the

gastrocolic

venous

trunk

The

gastrocolic

venous

trunk

is

routinely

divided

-LRB-

Fig.

-RRB-

If

venous

resection

is

anticipated

to

increase

mobility

the

middle

colic

vein

and

several

other

tributaries

are

ligated

and

divided

-LRB-

Fig.

-RRB-

Figure

Division

of

gastrocolic

venous

trunk

and

middle

colic

vein

b

Mobilization

of

superior

mesenteric

vein

in

preparation

of

venous

reconstruction

The

superior

border

of

the

pancreas

is

approached

by

incising

the

gastrohepatic

ligament

The

right

gastric

and

gastroduodenal

arteries

are

routinely

ligated

and

divided

Retraction

of

the

common

hepatic

artery

cephalad

allows

dissection

of

the

portal

vein

-LRB-

PV

-RRB-

thereby

allowing

completion

of

the

plane

between

the

pancreas

and

the

PV-SMV

The

gallbladder

is

dissected

from

the

liver

and

the

hepatic

duct

is

encircled

near

the

cystic

duct

junction

If

a

pylorus-preserving

PD

is

planned

the

superior

and

inferior

aspects

of

the

duodenum

are

skeletonized

individually

ligating

the

right

gastroepiploic

vessels

The

ligament

of

Treitz

is

mobilized

and

the

proximal

jejunum

is

divided

Sequential

ligation

and

division

of

the

bowel

mesentery

exposes

the

uncinate

process

The

mobilized

duodenum

and

jejunum

are

passed

beneath

the

superior

mesenteric

vessels

into

the

right

upper

quadrant

Mobilization

is

now

complete

and

transection

begins

at

the

duodenum

approximately

cm

distal

to

the

pylorus

The

bile

duct

is

transected

and

the

margin

is

evaluated

for

malignancy

Stay

sutures

are

placed

on

the

superior

and

inferior

borders

of

the

pancreas

to

aid

in

retraction

and

hemostasis

The

neck

of

the

pancreas

is

transected

over

a

clamp

to

protect

the

portal

vein

-LRB-

Fig.

-RRB-

Reflection

laterally

allows

visualization

and

ligation

of

venous

tributaries

-LRB-

Fig.

-RRB-

Figure

The

neck

of

the

pancreas

is

transected

over

a

clamp

thereby

protecting

the

portal

vein

from

injury

b

Venous

tributaries

to

the

portal

vein

are

individually

ligated

while

mobilizing

the

head

and

uncinate

process

of

the

pancreas

Often

venous

invasion

is

not

discovered

until

this

juncture

and

although

some

resections

can

be

limited

to

tangential

excision

and

primary

lateral

venorrhaphy

there

are

oncologic

and

vascular

considerations

that

make

other

options

including

segmental

resection

with

primary

end-to-end

anastomosis

or

interposition

grafting

with

autologous

or

synthetic

material

advantageous

Early

in

our

experience

we

completed

venous

resection

before

division

of

the

arterial

branches

and

soft

tissue

along

the

right

lateral

aspect

of

the

superior

mesenteric

artery

-LRB-

SMA

-RRB-

-LRB-

Fig.

-RRB-

More

recently

we

have

altered

our

technique

by

performing

the

dissection

of

the

retroperitoneal

margin

before

venous

resection

The

advantages

of

this

are

to

avoid

the

need

for

venous

anastomosis

before

removal

of

the

specimen

minimize

venous

occlusion

time

and

allow

preservation

of

the

splenic

vein

This

is

accomplished

by

performance

of

a

generous

Kocher

maneuver

and

isolation

of

the

superior

mesenteric

artery

both

at

its

origin

and

caudad

to

the

uncinate

process

The

Kocher

maneuver

orients

the

superior

mesenteric

artery

posterior

to

the

PV-SMV

and

allows

access

for

completion

of

the

retroperitoneal

dissection

-LRB-

Fig.

-RRB-

Arterial

branches

coursing

into

the

uncinate

are

sequentially

clamped

divided

and

ligated

thereby

completely

freeing

the

pancreas

from

the

SMA

The

pancreatic

head

is

then

rotated

back

to

its

normal

anatomic

orientation

and

it

is

at

this

juncture

that

a

decision

is

made

for

primary

end-to-end

venous

reconstruction

or

renal

vein

interposition

grafting

Figure

of

the

superior

mesenteric

artery

proximal

and

distal

to

the

area

of

venous

invasion

will

limit

total

venous

occlusion

time

after

resection

is

performed

This

can

be

approached

anteriorly

-LRB-

a

-RRB-

or

posteriorly

-LRB-

b

-RRB-

as

necessary

Inflow

occlusion

of

the

SMA

during

posterior

dissection

is

used

selectively

if

maintenance

of

hemostasis

is

problematic

Mobilization

of

the

portal

vein

superior

to

the

pancreas

and

the

peritoneum

along

the

root

of

the

small

bowel

mesentery

may

provide

length

for

the

SMV

or

PV

segment

This

is

accomplished

by

ligating

and

dividing

small

branches

to

the

SMV

PV

and

splenic

vein

-LRB-

SV

-RRB-

Although

primary

end-to-end

anastomosis

is

preferred

if

interposition

grafting

is

necessary

autologous

vein

and

specifically

the

left

renal

vein

is

utilized

for

two

reasons

First

the

vein

may

be

exposed

within

the

same

operative

field

thereby

eliminating

a

second

operative

field

and

dissection

Second

the

caliber

and

wall

thickness

of

the

vein

is

similar

to

the

portal

vein

in

most

instances

providing

good

handling

and

suturing

properties

Harvest

of

the

left

renal

vein

is

undertaken

after

the

retroperitoneal

dissection

when

the

specimen

remains

attached

to

the

portal

vein

segment

only

-LRB-

before

venous

resection

-RRB-

This

allows

the

best

assessment

of

the

need

for

interposition

grafting

and

minimizes

the

amount

of

clamp

time

by

harvesting

the

graft

before

SMA

and

venous

occlusion

The

left

renal

vein

is

optimally

exposed

by

extending

the

Kocher

maneuver

to

the

left

and

elevating

the

head

of

the

pancreas

-LRB-

Fig.

-RRB-

The

vein

is

divided

at

the

junction

of

the

left

gonadal

and

left

adrenal

veins

always

preserving

these

vessels

as

collateral

venous

outflow

for

the

left

kidney

The

vein

is

divided

again

flush

with

the

inferior

vena

cava

-LRB-

Fig.

-RRB-

This

typically

provides

a

to

venous

segment

For

venous

division

we

prefer

a

linear

stapling

device

The

vein

segment

is

placed

in

heparinized

saline

and

then

can

be

used

as

an

interposition

graft

-LRB-

Fig.

-RRB-

Figure

The

Kocher

maneuver

is

extended

to

the

left

and

elevation

of

the

pancreatic

head

allows

exposure

of

the

entire

left

renal

vein

and

the

left

adrenal

and

gonadal

veins

b

The

vein

is

transected

with

a

linear

stapling

device

distal

to

the

insertion

of

the

left

adrenal

and

gonadal

veins

and

again

flush

with

the

inferior

vena

cava

c

The

left

renal

vein

is

used

as

an

interposition

graft

to

restore

continuity

to

the

mesenteric

venous

system

Vascular

control

includes

the

SMA

with

placement

of

a

Rummel

tourniquet

-LRB-

in

addition

to

venous

occlusion

proximal

and

distal

-RRB-

and

is

obtained

immediately

before

resection

This

allows

inflow

occlusion

during

the

resection

and

reconstruction

decreasing

the

amount

of

intestinal

engorgement

thereby

facilitating

an

easier

pancreaticojejunostomy

The

patient

is

not

systemically

heparinized

Venous

resection

is

done

sharply

to

obtain

a

margin

-LRB-

Fig.

-RRB-

If

the

specimen

has

not

been

entirely

freed

from

the

SMA

the

remaining

branches

are

now

ligated

Communication

between

the

surgical

and

pathological

teams

is

crucial

to

fully

evaluate

the

specimen

Of

specific

importance

is

the

venous

segment

for

margin

status

and

invasion

and

the

retroperitoneal

-LRB-

uncinate

-RRB-

margin

-LRB-

Fig.

-RRB-

Frozen

section

analysis

allows

additional

margin

to

be

obtained

if

necessary

before

reconstruction

After

completion

of

both

anastomoses

intraoperative

ultrasound

is

routinely

utilized

to

evaluate

the

reconstruction

for

patency

After

satisfactory

venous

reconstruction

the

remainder

of

the

gastrointestinal

reconstruction

is

completed

-LRB-

Fig.

-RRB-

Figure

clamps

are

used

to

control

the

superior

mesenteric

vein

splenic

vein

and

portal

vein

before

sharp

dissection

and

resection

of

the

involved

venous

segment

Inflow

occlusion

of

the

superior

mesenteric

artery

during

reconstruction

reduces

bowel

engorgement.Figure

specimen

is

carefully

marked

for

all

margins

including

the

venous

segment

margin

The

portal

vein

groove

and

the

retroperitoneal

margin

should

be

inked

and

the

venous

segment

should

be

evaluated

histologically

for

malignant

invasion

-LRB-

posterior

view

-RRB-

Figure

the

example

shown

reconstruction

of

the

PV-SMV

confluence

with

an

interposition

graft

utilizing

left

renal

vein

was

performed

initially

followed

by

reimplantation

of

the

splenic

vein

into

the

graft

-LRB-

end-to-side

-RRB-

Gastrointestinal

reconstruction

is

performed

in

a

standard

fashion

after

completion

of

venous

reconstruction

Results

Nine

patients

have

undergone

reconstruction

of

the

SMV-PV

during

PD

with

an

autologous

left

renal

vein

graft

There

were

seven

men

and

two

women

with

a

mean

age

of

years

-LRB-

range

-RRB-

Preoperative

abdominal

CT

had

suggested

mesenteric

vein

involvement

in

seven

of

the

nine

patients

EUS

was

completed

in

three

patients

In

one

patient

EUS

suggested

there

was

no

vein

involvement

while

in

the

remaining

two

patients

EUS

did

suggest

involvement

Preoperative

serum

creatinine

levels

ranged

from

to

mg/dl

in

these

patients

-LRB-

normal

values

mg/dl

-RRB-

Mean

follow-up

was

months

The

procedure

consisted

of

three

standard

PD

and

six

pylorus-preserving

PD

Venous

reconstruction

consisted

of

eight

interposition

grafts

and

one

patch

graft

The

patch

graft

was

located

on

the

lateral

edge

of

the

SMV

and

PV

Five

of

the

interposition

grafts

were

placed

in

the

SMV

inferior

to

the

confluence

One

interposition

graft

was

placed

between

the

SMV

and

PV

with

reimplantation

of

the

splenic

vein

an

additional

was

placed

between

the

SMV

and

PV

without

reimplantation

of

the

splenic

vein

and

the

final

graft

was

in

the

portal

vein

The

mean

operating

time

was

hours

-LRB-

range

-RRB-

The

mean

tumor

size

was

cm

-LRB-

range

-RRB-

The

mean

estimated

blood

loss

was

ml

-LRB-

range

-RRB-

Eight

patients

were

found

to

have

node-positive

disease

with

six

of

these

patients

noted

to

have

histological

involvement

of

the

venous

segment

while

one

additional

patient

had

pathologically

negative

lymph

nodes

and

no

evidence

of

malignant

invasion

of

the

vein

In

two

patients

the

uncinate

margin

was

microscopically

positive

One

patient

was

monitored

overnight

in

the

intensive

care

unit

There

were

no

operative

mortalities

and

reoperation

was

not

required

in

any

of

the

patients

The

mean

length

of

hospitalization

was

days

-LRB-

range

-RRB-

Immediate

perioperative

morbidity

included

a

superficial

wound

infection

in

one

patient

delayed

gastric

emptying

in

one

patient

and

postoperative

gastrointestinal

bleeding

in

one

patient

of

the

patients

experienced

a

pancreatic

leak

No

hematuria

was

noted

One

patient

was

diagnosed

with

ascites

and

stenosis

of

the

left

renal

vein

interposition

graft

anastomosis

month

after

the

operation

This

patient

had

a

congenitally

cystic

-LRB-

nonfunctioning

-RRB-

left

kidney

The

left

renal

vein

was

reduced

in

caliber

but

felt

to

be

adequate

for

grafting

at

the

time

of

the

original

operation

The

patient

underwent

stenting

of

the

graft

by

interventional

radiology

with

resolution

of

her

symptoms

Eight

patients

underwent

adjuvant

treatment

which

included

radiation

therapy

in

six

patients

of

the

six

patients

receiving

radiation

therapy

experienced

a

decrement

in

renal

function

after

radiation

therapy

Two

patients

had

died

and

months

after

the

operation

of

recurrent

disease

Median

survival

has

not

been

reached

After

discharge

all

patients

were

evaluated

with

contrast-enhanced

CT.

All

grafts

were

patent

and

both

kidneys

were

perfused

well

Renal

function

was

monitored

by

following

serum

creatinine

levels

After

the

operation

creatinine

levels

transiently

increased

but

normalized

by

discharge

-LRB-

Table

-RRB-

Creatinine

values

were

available

for

a

mean

of

months

postoperatively

with

all

levels

within

the

normal

range

One

patient

was

anticoagulated

with

clopidogrel

while

subsequent

patients

were

treated

with

aspirin

Our

current

protocol

is

to

treat

all

patients

with

daily

aspirin

if

no

clot

is

noted

on

the

postoperative

imaging

and

heparin

transitioned

to

coumadin

if

clot

is

noted

Table

Comparison

of

Creatinine

LevelsSerum

Creatinine

Concentrations

-LRB-

mg/dL

-RRB-

PatientPreoperativePeakTime

of

.11.11.121.11.41.1311.5140.91.31.1511.3160.91.31.370.80.90.980.81.10.990.80.80.7

Discussion

Venous

resection

and

reconstruction

is

not

uncommon

during

PD

at

high

volume

centers

Involvement

of

the

vein

by

malignancy

is

not

always

suggested

preoperatively

by

imaging

and

is

often

discovered

at

a

time

during

the

operation

after

commitment

has

already

been

made

to

resection

This

fact

necessitates

that

the

surgeon

has

a

plan

for

completing

the

resection

and

reconstruction

of

the

venous

system

Whereas

many

such

cases

can

be

completed

with

segmental

resection

and

primary

end-to-end

anastomosis

a

number

will

require

either

patch

repair

or

interposition

grafting

Other

groups

routinely

use

the

internal

jugular

or

superficial

femoral

as

a

conduit

While

these

groups

have

demonstrated

good

results

with

these

conduits

the

use

of

the

left

renal

vein

for

autologous

grafting

offers

some

significant

advantages

and

avoids

the

handling

difficulties

that

can

be

encountered

with

the

internal

jugular

vein

and

the

risk

of

lymphedema

or

venous

thrombosis

that

can

be

encountered

with

use

of

the

superficial

femoral

vein

The

left

renal

vein

provides

a

graft

with

good

length

good

caliber

and

is

easily

accessible

The

left

renal

vein

typically

provides

a

graft

of

cm

in

length

when

harvested

from

the

junction

of

the

left

gonadal

and

left

adrenal

vein

proximally

and

the

inferior

vena

cava

distally

although

some

reports

have

indicated

lengths

up

to

cm

The

caliber

of

the

graft

allows

for

excellent

flow

as

demonstrated

by

CT

and

Doppler

ultrasound

The

ease

of

harvesting

the

graft

also

is

an

important

consideration

Exposure

of

the

left

renal

vein

can

be

accomplished

through

a

standard

PD

incision

without

requiring

any

further

prepping

an

additional

incision

or

the

need

for

an

additional

operating

team

Furthermore

use

of

the

left

renal

vein

leaves

the

patient

with

all

possible

routes

of

central

venous

access

Importantly

the

operation

is

tolerated

well

from

a

renal

standpoint

Previous

work

demonstrated

that

good

collateral

flow

and

functional

capacity

of

the

left

kidney

is

preserved

despite

ligation

of

the

left

renal

vein

McCullough

and

colleagues

reported

that

after

a

right

nephrectomy

and

ligation

of

the

left

renal

vein

for

malignancy

only

one

of

three

patients

experienced

transient

renal

insufficiency

In

our

series

serum

creatinine

levels

transiently

increased

after

operation

but

all

normalized

before

discharge

Creatinine

levels

remained

normal

throughout

follow-up

Conclusions

Resection

offers

the

only

chance

at

cure

for

patients

with

pancreatic

cancer

and

potentially

curative

resection

may

require

venous

resection

When

reconstruction

of

the

venous

system

necessitates

the

use

of

interposition

grafting

autologous

vein

interposition

grafts

are

preferred

The

left

renal

vein

provides

an

additional

choice

for

an

autologous

graft

and

its

use

is

distinguished

by

ease

of

harvest

and

maintenance

of

renal

function

The

use

of

the

left

renal

vein

for

interposition

grafting

and

patch

repair

should

be

considered

by

surgeons

experienced

in

SMV-PV

reconstruction

during

PD

O O O O O O O B O O B I I O O O O O O O O O O O O O O O O O B O O O O O O B I O B O B I O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O B I O O O O B I I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O

pancreatic cancer
pancreaticoduodenectomy
venous resection
portal vein
superior mesenteric vein
left renal vein