Vol

November

doi

ARTICLES

High-resolution

structure

prediction

and

the

crystallographic

phase

problem

Bin

Srivatsan

Rhiju

Philip

Airlie

J.

Randy

J.

David

The

energy-based

refinement

of

low-resolution

protein

structure

models

to

atomic-level

accuracy

is

a

major

challenge

for

computational

structural

biology

Here

we

describe

a

new

approach

to

refining

protein

structure

models

that

focuses

sampling

in

regions

most

likely

to

contain

errors

while

allowing

the

whole

structure

to

relax

in

a

physically

realistic

all-atom

force

field

In

applications

to

models

produced

using

nuclear

magnetic

resonance

data

and

to

comparative

models

based

on

distant

structural

homologues

the

method

can

significantly

improve

the

accuracy

of

the

structures

in

terms

of

both

the

backbone

conformations

and

the

placement

of

core

side

chains

Furthermore

the

resulting

models

satisfy

a

particularly

stringent

test

they

provide

significantly

better

solutions

to

the

X-ray

crystallographic

phase

problem

in

molecular

replacement

trials

Finally

we

show

that

all-atom

refinement

can

produce

de

novo

protein

structure

predictions

that

reach

the

high

accuracy

required

for

molecular

replacement

without

any

experimental

phase

information

and

in

the

absence

of

templates

suitable

for

molecular

replacement

from

the

Protein

Data

Bank

These

results

suggest

that

the

combination

of

high-resolution

structure

prediction

with

state-of-the-art

phasing

tools

may

be

unexpectedly

powerful

in

phasing

crystallographic

data

for

which

molecular

replacement

is

hindered

by

the

absence

of

sufficiently

accurate

previous

models

High-resolution

prediction

of

protein

structures

from

their

amino

acid

sequences

and

the

refinement

of

low-resolution

protein

structure

models

to

produce

more

accurate

structures

are

long-standing

challenges

in

computational

structural

The

refinement

problem

has

become

particularly

important

in

recent

years

as

the

continued

increase

in

the

number

of

experimentally

determined

protein

structures

together

with

the

explosion

of

genome

sequence

information

has

made

it

possible

to

produce

comparative

models

of

a

large

number

of

protein

structures

with

wide

Ideally

these

models

would

consistently

approach

the

resolution

offered

by

X-ray

crystallography

enabling

precise

drug

design

and

a

deeper

understanding

of

catalysis

and

binding

Accurate

high-resolution

models

can

in

principle

be

achieved

by

searching

for

the

lowest

energy

structure

given

the

sequence

of

the

protein

However

despite

the

large

number

of

degrees

of

freedom

in

a

protein

chain

and

the

ruggedness

of

the

energy

landscape

produced

by

strong

atomic

repulsion

at

short

distances

greatly

complicate

this

search

for

sequences

lacking

close

homologues

of

known

structure

An

important

application

for

predicted

structures

is

to

help

solve

the

X-ray

crystallographic

phase

Converting

X-ray

diffraction

data

into

electron

density

maps

of

proteins

requires

the

inference

of

phases

associated

with

each

diffraction

peak

Although

phase

estimates

can

be

obtained

through

the

preparation

of

heavy

atom

derivatives

the

problem

can

be

solved

without

additional

experimental

information

by

the

technique

of

molecular

given

a

structure

model

that

has

high

structural

similarity

-LRB-

better

than

A

root-mean-squared

-LRB-

r.m.s.

-RRB-

deviation

-RRB-

to

the

crystallized

protein

over

a

large

fraction

of

the

molecule

As

an

example

of

the

stringency

of

this

condition

models

of

protein

structures

derived

from

nuclear

magnetic

resonance

-LRB-

NMR

-RRB-

data

typically

do

not

give

good

molecular

replacement

models

for

crystallographic

data

on

the

same

Perhaps

the

most

successful

approach

to

molecular

replacement

is

the

use

of

previous

crystal

structures

of

highly

sequence-similar

-LRB-

-RRB-

templates

as

search

models

In

cases

of

lower

sequence

similarity

structure

prediction

tools

can

frequently

help

build

comparative

models

that

give

better

molecular

replacement

solutions

however

the

success

rate

drops

rapidly

as

the

template

sequence

identity

falls

below

In

cases

where

structurally

similar

experimental

models

are

not

available

ab

initio

phasing

techniques

have

had

some

success

for

targets

with

simple

folds

of

high

or

with

new

structures

that

have

been

rationally

designed

from

first

but

ab

initio

phasing

of

diffraction

data

for

natural

globular

proteins

remains

an

unsolved

problem

In

this

study

we

present

a

new

energy-based

rebuilding-andrefinement

method

that

consistently

improves

models

derived

from

NMR

from

sequence-distant

templates

and

from

de

novo

folding

methods

The

final

models

include

high-resolution

features

not

present

in

the

starting

models

including

the

packing

of

core

side

chains

Bringing

together

these

results

from

all-atom

structure

prediction

with

state-of-the-art

algorithms

for

molecular

replacement

and

automated

we

show

that

distant-template-based

and

de

novo

models

can

reach

the

accuracy

required

to

solve

the

X-ray

crystallographic

phase

problem

Targeted

rebuilding-and-refinement

protocol

We

have

developed

a

new

approach

for

refining

protein

models

that

combines

the

targeting

of

aggressive

sampling

to

regions

most

likely

to

be

in

error

with

powerful

global

optimization

techniques

The

new

protocol

is

outlined

in

Fig.

The

first

step

of

this

protocol

is

the

energy-based

optimization

of

an

input

ensemble

of

models

using

the

previously

described

Rosetta

all-atom

refinement

method

This

method

combines

Monte

Carlo

minimization

with

side-chain

remodelling

to

relieve

inter-atomic

clashes

and

to

optimize

side-chain

packing

and

hydrogen

bonding

as

encoded

by

an

all-atom

force

Briefly

in

each

Monte

Carlo

move

a

random

perturbation

to

the

protein

backbone

torsion

angles

is

followed

by

discrete

University

of

Washington

Department

of

Biochemistry

and

Howard

Hughes

Medical

Institute

Box

Seattle

USA

of

Haematology

University

of

Cambridge

Cambridge

Institute

for

Medical

Research

Wellcome

Trust/MRC

Building

Hills

Road

Cambridge

UK

These

authors

contributed

equally

to

this

work

Nature

Publishing

Group

ARTICLES

NATURE

Vol

November

optimization

of

the

side-chain

which

allows

efficient

crossing

of

side-chain

torsional

barriers

Then

quasi-Newton

optimization

of

the

side-chain

and

backbone

torsion

angles

is

carried

out

before

the

decision

on

whether

to

accept

the

move

Because

of

the

final

minimization

each

point

on

the

landscape

is

mapped

to

the

closest

local

minimum

flattening

energy

Although

making

it

possible

to

recognize

near-native

predictions

based

on

their

low

this

all-atom

refinement

alone

does

not

consistently

produce

significant

improvements

in

model

quality

-LRB-

Supplementary

Fig.

-RRB-

The

second

step

in

the

new

protocol

is

the

identification

of

regions

of

variation

in

the

ensemble

of

refined

models

We

have

found

a

marked

correlation

between

the

extent

of

variation

in

the

coordinates

of

a

residue

in

the

refined

structures

and

the

deviation

of

the

coordinates

of

the

residue

in

the

refined

models

from

the

native

structure

An

example

is

shown

in

Fig.

c

positions

exhibiting

small

variance

across

the

models

are

usually

quite

close

to

the

correct

structure

whereas

positions

for

which

the

variance

is

large

often

deviate

considerably

from

the

native

structure

This

correlation

arises

from

the

relatively

short

range

of

the

force

field

and

the

energy

gap

between

the

native

structure

and

the

models

because

the

energy

of

the

entire

system

is

roughly

equal

to

the

sum

of

its

parts

for

most

portions

of

the

protein

the

correct

conformation

will

be

lower

in

energy

than

non-native

conformations

Regions

of

the

protein

that

can

access

the

native

conformation

are

likely

to

converge

on

this

conformation

and

thus

exhibit

less

variation

whereas

locally

incorrect

conformations

are

likely

to

be

spread

throughout

the

landscape

and

exhibit

more

variation

We

observe

this

correlation

for

many

different

proteins

in

both

the

cartesian

coordinates

and

the

internal

torsion

angles

a

related

principle

has

recently

been

used

in

the

Pcons

method

for

assessing

protein

The

third

step

in

the

new

protocol

targets

aggressive

sampling

to

the

regions

most

likely

to

be

in

error

A

fragment-based

segment

rebuilding

method

-LRB-

see

Supplementary

Material

-RRB-

is

used

to

rebuild

completely

regions

of

models

with

relatively

high

variation

in

the

model

population

Because

the

precise

regions

that

are

incorrect

can

not

be

identified

unambiguously

we

carry

out

many

independent

calculations

in

which

different

segments

in

the

higher

variation

regions

are

randomly

selected

for

complete

rebuilding

The

partially

rebuilt

models

are

then

subjected

to

the

Rosetta

all-atom

refinement

protocol

described

In

the

segment

rebuilding

process

side

chains

are

initially

represented

as

soft

interaction

centres

and

the

connectivity

of

the

chain

is

temporarily

broken

thus

permitting

the

traversal

of

much

larger

barriers

than

those

crossed

by

all-atom

refinement

alone

As

indicated

in

Fig.

if

the

lowest

energy

refined

structures

have

not

converged

the

rebuilding-and-refinement

protocol

is

applied

iteratively

using

a

selection

process

inspired

by

natural

evolution

to

guide

convergence

on

the

global

minimum

At

each

iteration

a

subset

of

models

that

are

low

in

energy

yet

structurally

diverse

is

chosen

to

seed

the

next

round

the

regions

to

be

rebuilt

are

determined

on

the

basis

of

the

backbone

variation

in

the

selected

population

Bringing

together

ideas

from

tabu

and

conformational

space

the

selection

process

alternates

between

the

propagation

of

a

structurally

diverse

population

into

the

next

round

-LRB-

diversification

-RRB-

and

focusing

in

on

the

lowest

energy

regions

of

the

energy

landscape

explored

thus

far

-LRB-

intensification

-RRB-

The

lowest

energy

models

after

ten

iterations

are

selected

as

the

final

predictions

As

illustrated

in

Fig.

models

with

progressively

lower

energies

and

more

nativelike

structures

can

be

obtained

with

increasing

number

of

iterations

results

on

a

number

of

refinement

problems

are

summarized

in

Supplementary

Fig.

Improving

NMR

models

As

a

first

test

of

the

new

rebuilding-and-refinement

method

we

sought

to

improve

the

accuracy

of

protein

structure

models

derived

from

moderate-resolution

NMR

experiments

NMR

is

an

important

method

for

determining

structures

of

proteins

at

atomic

resolution

that

has

the

advantage

of

not

requiring

crystals

In

some

cases

however

NMR

models

can

contain

errors

due

to

either

insufficient

data

or

ambiguities

in

interpretation

of

the

input

NMR

We

applied

the

method

outlined

in

Fig.

to

ten

ensembles

of

NMR

models

deposited

in

the

Protein

Data

Bank

-LRB-

PDB

-RRB-

for

which

independently

determined

high-resolution

X-ray

crystal

structures

a

b

Average

per-residue

C

deviation

to

the

crystal

structure

c

d

Energy

Average

per-residue

C

deviation

to

the

structure

model

cluster

centre

C

r.m.s.

deviation

-LRB-

-RRB-

Figure

Overview

of

the

rebuilding-and-refinement

method

a

Schematic

diagram

of

the

rebuilding-and-refinement

method

applied

to

structures

from

NMR

from

comparative

modelling

-LRB-

CM

-RRB-

and

from

de

novo

-LRB-

DN

-RRB-

modelling

approaches

b

Strong

correlation

between

the

per-residue

backbone

conformation

variation

in

the

model

ensemble

and

the

deviation

from

the

native

structure

for

target

from

the

sixth

critical

assessment

of

structure

prediction

-LRB-

-RRB-

c

Superposition

of

the

native

structure

of

target

with

low-energy

all-atom

refined

models

The

native

structure

backbone

is

shown

as

a

thick

line

and

the

models

are

shown

as

thinner

lines

Residues

in

the

native

structure

are

coloured

by

the

average

per-residue

Ca

r.m.s.

deviation

to

the

native

from

A

-LRB-

red

-RRB-

to

A

-LRB-

blue

-RRB-

d

Iterative

rebuilding

and

refinement

yields

low-energy

native-like

models

The

energy

and

the

Ca

r.m.s.

deviation

of

models

generated

during

three

iterations

of

the

loop-relax

protocol

are

displayed

for

iteration

-LRB-

green

-RRB-

iteration

-LRB-

red

-RRB-

and

iteration

-LRB-

black

-RRB-

The

Rosetta

all-atom

energy

includes

the

enthalpy

plus

the

solvation

contribution

to

the

entropy

but

not

the

configurational

entropy

Nature

Publishing

Group

NATURE

Vol

November

ARTICLES

provide

tests

of

model

Regions

with

high

variation

in

initial

all-atom

refined

ensembles

were

stochastically

rebuilt

as

well

as

regions

assessed

as

poorly

packed

-LRB-

see

Methods

-RRB-

to

allow

for

possible

over-convergence

of

the

initial

NMR

ensemble

in

regions

with

incorrect

constraints

In

eight

of

the

ten

cases

the

lowest

energy

refined

model

was

closer

to

the

crystal

structure

than

any

member

of

the

starting

NMR

ensemble

-LRB-

typically

members

-RRB-

in

terms

of

backbone

agreement

as

assessed

by

GDT-HA

-LRB-

geometric

distance

test

-LRB-

high

accuracy

-RRB-

-RRB-

Comparison

of

the

best

of

five

lowest

energy

refined

models

to

the

NMR

ensemble

indicates

improvement

in

backbone

accuracy

and

core

packing

in

all

cases

-LRB-

see

Table

and

Supplementary

Figs

and

-RRB-

In

addition

the

quality

of

the

lowest

energy

models

was

consistently

better

than

the

starting

NMR

models

in

terms

of

clash

score

number

of

rotamer

outliers

and

number

of

backbone

-LRB-

Ramachandran

-RRB-

outliers

as

assessed

by

the

MolProbity

server

-LRB-

Supplementary

Table

-RRB-

Four

examples

of

this

energy-based

structural

improvement

are

shown

in

Fig.

d

It

should

be

noted

that

no

NMR

data

were

included

in

these

rebuilding-and-refinement

tests

judicious

use

of

experimental

NMR

information

to

focus

allatom

refinement

-LRB-

for

example

using

inferential

structure

-RRB-

could

yield

still

better

results

As

noted

above

NMR

structures

often

do

not

give

good

molecular

replacement

models

for

crystallographic

and

we

hypothesized

that

the

all-atom

refined

models

would

yield

better

solutions

Indeed

we

found

such

improvement

in

molecular

replacement

scores

for

all

eight

cases

in

which

diffraction

data

were

publicly

available

-LRB-

Table

-RRB-

using

the

sensitive

and

widely

used

Phaser

Furthermore

using

phases

from

the

molecular

replacement

trial

with

the

highest

translation

function

Z-score

electron

density

maps

were

generated

and

in

seven

of

the

eight

cases

the

widely

used

or

automatic

map

tracing

programs

could

build

the

majority

of

the

residues

with

no

human

intervention

-LRB-

Table

-RRB-

An

example

of

the

improvement

in

density

is

shown

in

Fig.

b

These

results

suggest

that

all-atom

rebuilding

and

refinement

may

be

a

powerful

supplement

to

existing

strategies

of

trial-and-error

trimming

of

NMR

ensembles

to

improve

molecular

replacement

solutions

for

crystallographic

Improved

blind

predictions

based

on

templates

As

a

further

challenging

test

we

used

the

new

energy-based

rebuildingand-refinement

method

to

make

blind

structure

predictions

for

proteins

with

lengths

less

than

residues

that

had

distant

homologues

-LRB-

sequence

identity

lower

than

-RRB-

with

known

structure

during

the

seventh

Critical

Assessment

of

Techniques

for

Protein

Structure

Prediction

-LRB-

-RRB-

Ensembles

of

starting

models

based

on

different

alignments

to

one

or

more

of

these

distant

homologues

were

generated

as

described

in

the

Supplementary

Information

and

the

rebuilding-and-refinement

protocol

was

carried

out

with

several

rounds

of

iteration

to

explore

more

broadly

conformational

space

-LRB-

Fig.

-RRB-

Five

representative

low-energy

structures

from

the

final

population

were

submitted

to

the

CASP

organizers

For

of

the

cases

at

least

one

of

these

models

was

closer

to

the

correct

structure

than

the

closest

homologous

structure

in

the

PDB

as

assessed

by

the

GDT-HA

Marked

improvement

was

observed

in

seven

cases

with

a

increase

in

this

measure

of

model

quality

-LRB-

see

Table

-RRB-

Table

Improvement

of

model

accuracy

and

molecular

replacement

by

a

rebuilding

and

refinement

protocol

X-ray

structure

Starting

model

Length

-LRB-

n

-RRB-

-LCB-

Sequence

identity

to

best

template

-LRB-

-RRB-

-LCB-

Best

template

Refined

model

TFZI

in

molecular

replacement

Best

template

Refined

model

Auto-traced

residues

-LRB-

backbone

side

chain

-RRB-

Best

template

Refined

model

NMR

-LRB-

-RRB-

-LRB-

-RRB-

129 56 149 158

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

75 132 112

N/Aq

N/Aq

CM

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

DN

-LRB-

-RRB-

PDB

accession

numbers

for

the

closest

previously

known

template

-LRB-

comparative

modelling

-LRB-

CM

-RRB-

and

de

novo

modelling

-LRB-

DN

-RRB-

-RRB-

or

for

the

NMR

structure

-LCB-

Length

of

sequence

in

crystal

structure

-LRB-

number

of

monomers

in

asymmetric

unit

n

-RRB-

-LCB-

Number

of

sequence-identical

residues

across

regions

structurally

aligned

within

divided

by

the

length

of

the

shorter

sequence

Fraction

of

residues

in

model

superimposable

on

crystal

structure

with

high

accuracy

-LRB-

see

Supplementary

Information

and

ref

-RRB-

This

value

is

the

average

of

four

numbers

the

numbers

of

residues

aligned

between

model

and

experimental

structure

within

A

within

A

within

A

and

within

A.

For

the

CM

cases

GDT-HA

was

determined

for

the

residues

structurally

aligned

between

the

native

structure

and

the

closest

template

For

the

NMR

cases

the

GDT-HA

comparison

presented

for

the

best

template

is

between

the

first

member

of

the

deposited

NMR

structural

ensemble

and

the

crystal

structure

IZ-score

of

Phaser

log-likelihood

translation

function

for

molecular

replacement

solution

For

CM

and

DN

cases

molecular

replacement

for

the

best

template

was

carried

out

using

a

mixed-model

based

on

the

best

possible

structural

alignment

between

the

native

structure

and

template

no

such

alignment

was

carried

out

for

the

refined

model

however

The

TFZ

scores

for

the

next

best

model

submitted

by

all

other

predictors

were

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

and

-LRB-

-RRB-

For

NMR

cases

the

presented

results

are

from

molecular

replacement

with

the

full

deposited

NMR

ensemble

and

from

each

of

the

lowest

energy

refined

models

-LRB-

see

also

Supplementary

Table

-RRB-

In

the

NMR

cases

the

best-TFZ

structure

from

the

deposited

ensemble

-LRB-

see

Supplementary

Table

-RRB-

typically

gave

slightly

worse

results

in

subsequent

automatic

tracing

than

using

the

full

ensemble

as

In

cases

with

multiple

monomers

present

in

the

asymmetric

unit

Z-scores

for

each

monomer

are

presented

except

for

for

which

decreasing

TFZ

scores

for

molecular

replacement

of

additional

monomers

after

the

first

one

indicated

the

solutions

to

be

ambiguous

Number

of

automatically

traced

residues

starting

with

molecular

replacement

phases

given

by

Phaser

that

match

the

deposited

crystal

structure

within

A

In

all

cases

tracing

and

refinement

was

carried

out

with

the

and

programs

with

the

better

results

from

the

two

programs

presented

Predicted

model

is

for

the

smaller

of

two

domains

present

in

the

crystal

structure

and

is

thus

not

sufficient

for

molecular

replacement

q

Structure

factors

not

deposited

in

the

PDB

Solved

by

NMR

spectroscopy

Nature

Publishing

Group

ARTICLES

NATURE

Vol

November

This

is

a

particularly

notable

result

because

improving

on

the

best

template

structure

has

been

a

long

standing

challenge

for

comparative

modelling

owing

to

the

high

dimensionality

of

conformational

space

there

are

many

more

ways

to

degrade

a

reasonably

accurate

model

than

to

improve

it

Superpositions

of

the

closest

homologous

structure

the

submitted

refined

models

and

the

native

structure

for

cases

with

the

greatest

improvement

are

shown

in

Fig.

h

The

improvement

in

the

refined

structures

is

evident

even

in

core

secondary

structural

elements

Out

of

the

seven

high-resolution

predictions

there

were

four

targets

for

which

diffraction

data

were

available

and

the

modelled

sequence

constituted

the

entire

crystallized

construct

enabling

tests

of

molecular

replacement

In

each

of

these

cases

we

found

that

the

best

previous

templates

in

the

PDB

failed

to

produce

clear-cut

molecular

replacement

solutions

-LRB-

Phaser

Z-scores

greater

than

-RRB-

even

after

using

knowledge

of

structurally

alignable

regions

and

a

side-chain

truncation

approach

to

trim

back

the

search

models

to

their

most

accurate

Other

template-based

models

submitted

to

based

on

methods

that

typically

did

not

use

aggressive

all-atom

refinement

gave

similarly

low

molecular

replacement

scores

-LRB-

Table

-RRB-

For

three

of

the

four

cases

however

the

refined

models

that

we

submitted

for

gave

significantly

better

molecular

replacement

solutions

than

the

best

template

-LRB-

Table

-RRB-

For

these

targets

the

maps

produced

by

combining

phases

from

the

blindly

predicted

model

with

the

experimental

diffraction

amplitudes

were

of

sufficient

quality

to

permit

the

automatic

chain-tracing

program

to

build

a

large

fraction

of

each

structure

with

high

accuracy

-LRB-

Table

-RRB-

An

example

of

the

marked

improvement

in

electron

density

on

using

the

refined

models

is

shown

in

Fig.

d.

Ab

initio

phasing

by

ab

initio

modelling

To

the

best

of

our

knowledge

a

de

novo

structure

prediction

for

a

natural

protein

with

an

asymmetric

globular

fold

has

never

been

used

successfully

for

molecular

replacement

However

the

accuracy

of

de

novo

prediction

methods

has

been

improving

rapidly

In

particular

the

use

of

all-atom

refinement

to

follow

low-resolution

modelling

by

the

Rosetta

de

novo

modelling

led

to

several

blind

predictions

in

for

proteins

of

all-a

all-b

and

secondary

structure

classes

that

placed

most

of

the

backbone

elements

and

core

side

chains

with

high

accuracy

-LRB-

see

Fig.

c

-RRB-

This

progress

in

de

novo

modelling

along

with

the

successes

above

with

refined

NMR

and

template-based

models

encouraged

us

to

attempt

molecular

replacement

with

an

exceptional

prediction

for

the

a-helical

target

The

best

of

five

models

for

blindly

predicted

without

the

use

of

templates

matched

the

subsequently

released

crystal

structure

-LRB-

-RRB-

with

a

Ca

r.m.s.

deviation

of

A

over

residues

-LRB-

Fig.

-RRB-

The

closest

previously

known

fold

in

the

PDB

identified

from

structure

superpositions

by

assessors

-LRB-

-RRB-

was

significantly

different

from

the

crystal

structure

aligning

residues

with

a

Ca

r.m.s.

deviation

of

A

-LRB-

note

also

the

poor

GDT-HA

score

in

Table

-RRB-

After

truncating

the

Rosetta

prediction

to

a

consensus

core

-LRB-

residues

to

for

which

four

of

the

five

submitted

models

coincided

to

within

A

Ca

r.m.s.

deviation

-RRB-

molecular

replacement

by

Phaser

showed

clear

features

for

the

omitted

amino

and

carboxyterminal

helices

-LRB-

see

Supplementary

Fig.

and

caption

-RRB-

Starting

from

this

molecular

replacement

solution

the

ARP/wARP

software

was

able

to

complete

the

structure

automatically

tracing

all

residues

correctly

The

final

result

-LRB-

Fig.

-RRB-

is

in

excellent

agreement

with

the

structure

deposited

in

the

PDB

which

used

phases

experimentally

derived

by

selenium

single-wavelength

anomalous

disper

sion

with

an

r.m.s.

deviation

of

A

for

all

Ca

atoms

In

contrast

attempts

to

solve

the

structure

by

molecular

replacement

with

the

closest

existing

template

failed

to

produce

a

clear-cut

phasing

solution

-LRB-

Table

-RRB-

even

when

knowledge

of

the

optimal

superposition

was

used

to

trim

this

search

model

back

to

the

residues

that

aligned

best

to

the

actual

structure

It

will

be

of

great

interest

to

investigate

whether

this

result

can

be

generalized

to

rapidly

phase

diffraction

data

for

proteins

of

new

folds

a

b

c

d

e

f

g

h

Figure

Improvement

in

model

accuracy

produced

by

rebuilding

and

refinement

a

d

NMR

refinement

tests

displaying

superpositions

of

the

crystal

structure

-LRB-

blue

-RRB-

model

of

the

NMR

ensemble

-LRB-

red

-RRB-

and

the

lowest

energy

all-atom

refined

model

-LRB-

green

-RRB-

for

four

NMR

refinement

test

cases

-LRB-

a

acyl

CoA

binding

protein

b

domain

of

ABL

tyrosine

kinase

c

guanine

nucleotide

binding

protein

d

barstar

-RRB-

e

h

Blind

predictions

produced

by

comparative

modelling

displaying

superpositions

of

the

native

structure

-LRB-

blue

-RRB-

the

best

template

in

the

PDB

-LRB-

red

-RRB-

and

the

best

of

our

five

submitted

models

-LRB-

green

-RRB-

for

four

targets

-LRB-

e

f

g

domain

h

-RRB-

A

subset

of

the

core

side

chains

is

shown

in

stick

representation

to

illustrate

the

accuracy

of

core

packing

Figures

were

prepared

in

PyMOL

-LRB-

Delano

Scientific

Palo

Alto

California

-RRB-

Nature

Publishing

Group

NATURE

Vol

November

ARTICLES

Improving

model

accuracy

and

molecular

replacement

The

results

described

here

show

that

an

all-atom

rebuilding-andrefinement

protocol

can

produce

protein

structure

models

of

high

accuracy

The

iterative

protocol

outlined

in

Fig.

brings

together

the

individually

quite

powerful

global

optimization

ideas

underlying

Monte

Carlo

tabu

and

conformational

space

while

targeting

aggressive

sampling

to

regions

most

likely

to

be

incorrect

The

substantial

improvements

achieved

in

prediction

quality

in

several

cases

enabling

molecular

replacement

phasing

of

X-ray

diffraction

data

suggest

that

structure

prediction

has

matured

considerably

Nevertheless

we

emphasize

that

there

is

still

considerable

room

for

improvement

our

high-resolution

rebuilding-and-refinement

protocol

does

not

always

improve

starting

models

and

is

the

only

target

predicted

de

novo

for

which

the

models

were

accurate

enough

for

molecular

replacement

We

look

forward

to

advances

in

both

the

energy

function

notably

the

addition

of

configurational

entropy

and

in

conformational

sampling

The

significant

energy

gap

between

the

refined

models

and

the

refined

crystal

for

most

of

the

cases

studied

here

suggests

that

sampling

is

still

the

primary

bottleneck

for

high-accuracy

all-atom

structure

prediction

At

present

the

Protein

Structure

Initiative

lists

hundreds

of

proteins

with

lengths

less

than

residues

that

have

been

crystallized

but

not

yet

solved

Publication

of

diffraction

data

sets

that

have

not

yielded

to

experimental

phasing

could

catalyse

the

development

of

new

hybrid

prediction/phasing

algorithms

much

like

the

blind

CASP

trials

have

accelerated

progress

in

the

field

of

structure

prediction

With

continuing

advances

in

high-resolution

structure

prediction

in

molecular

replacement

tools

and

in

the

interface

between

these

two

fields

we

expect

that

in

silico

phasing

will

become

an

increasingly

important

component

of

the

crystallographer

's

toolkit

In

the

present

study

aggressive

all-atom

refinement

was

carried

out

in

the

absence

of

any

experimental

information

The

incorporation

of

experimental

data

into

the

rebuilding-and-refinement

protocol

could

help

overcome

the

current

shortcomings

in

both

the

energy

function

and

conformational

sampling

and

allow

more

consistent

high-resolution

structural

inference

In

practical

applications

to

molecular

replacement

trials

the

diffraction

data

do

not

need

to

be

set

aside

as

a

stringent

post

facto

test

of

model

accuracy

as

was

carried

out

in

this

study

Diffraction

data

without

phases

would

be

useful

in

screening

larger

numbers

of

trial

structures

for

molecular

replacement

or

in

complementing

the

physical

energy

terms

with

diffraction-data-derived

likelihood

during

rebuilding

and

refinement

Weak

phase

information

for

example

based

on

anomalous

scattering

from

intrinsic

sulphur

could

also

be

exploited

for

instance

by

using

an

initial

molecular

replacement

model

to

locate

the

anomalous

scatterer

Although

not

used

in

the

present

study

NMR

chemical

shift

nuclear

Overhauser

effect

and

residual

dipolar

coupling

data

can

help

to

pinpoint

regions

of

the

models

to

rebuild

and

regions

to

constrain

during

all-atom

refinement

On

a

larger

scale

mass

spectrometry

techniques

coupled

with

hydrogen/deuterium

chemical

and

radical

show

great

promise

for

providing

highthroughput

residue-level

information

that

may

rapidly

constrain

structure

prediction

and

in

the

absence

of

crystallographic

data

help

validate

models

We

anticipate

that

the

combination

of

highresolution

modelling

with

limited

experimental

structural

data

will

a

b

d

c

Figure

Improvement

in

electron

density

using

models

from

rebuilding

and

refinement

in

molecular

replacement

searches

Examples

are

presented

for

the

NMR

structure

of

acyl

CoA

binding

protein

-LRB-

a

b

-RRB-

and

comparative

modelling

target

-LRB-

c

and

d

-RRB-

Black

mesh

represents

electron

density

-LRB-

s

contour

-RRB-

using

experimental

structure

factors

and

phases

from

molecular

replacement

with

the

starting

model

-LRB-

a

and

c

-RRB-

or

the

refined

model

-LRB-

b

and

d

-RRB-

The

coordinates

deposited

in

the

PDB

determined

using

experimental

phase

information

are

shown

in

stick

representation

Note

that

the

refinement

applied

to

the

models

refers

to

the

all-atom

energy-based

protocol

-LRB-

see

Fig.

and

text

-RRB-

and

not

to

refinement

against

the

diffraction

data

The

accurate

modelling

of

side

chains

by

Rosetta

was

critical

for

the

illustrated

map

improvement

molecular

replacement

trials

gave

significantly

better

solutions

if

the

Rosetta-predicted

side

chains

were

retained

rather

than

truncated

Figure

Ab

initio

phasing

by

ab

initio

modelling

a

c

Superpositions

of

blind

Rosetta

de

novo

structure

predictions

-LRB-

green

-RRB-

and

the

subsequently

released

crystal

structures

-LRB-

blue

-RRB-

for

targets

-LRB-

a

-RRB-

domain

of

-LRB-

b

-RRB-

and

-LRB-

c

-RRB-

Buried

side

chains

and

backbone-aligned

residues

are

displayed

d

Electron

density

map

-LRB-

contour

-RRB-

produced

by

automatic

refinement

of

the

molecular

replacement

solution

obtained

from

the

structure

prediction

-LRB-

black

mesh

contour

-RRB-

agrees

with

the

coordinates

deposited

in

the

PDB

-LRB-

red

-RRB-

solved

with

experimental

phase

information

The

electron

density

map

immediately

after

molecular

replacement

is

shown

in

Supplementary

Fig.

Nature

Publishing

Group

ARTICLES

NATURE

Vol

November

become

an

increasingly

powerful

approach

for

characterizing

the

structures

of

biological

macromolecules

and

complexes

in

the

years

to

come

METHODS

SUMMARY

Models

produced

using

NMR

data

comparative

modelling

and

de

novo

structure

prediction

were

refined

using

the

targeted

rebuilding-and-refinement

protocol

introduced

in

this

paper

To

assess

accuracy

the

resulting

models

were

compared

to

high-resolution

crystal

structures

by

the

GDT-HA

-LRB-

geometric

distance

test

-LRB-

high

accuracy

-RRB-

-RRB-

the

average

percentage

of

Ca

atoms

agreeing

within

and

A

As

a

final

test

of

accuracy

and

of

practical

utility

models

were

screened

for

suitability

in

phase

estimation

for

crystallographic

diffraction

data

using

the

Phaser

molecular

replacement

The

widely

used

and

programs

were

then

used

to

refine

automatically

the

electron

density

maps

and

build

density-constrained

protein

coordinates

Full

Methods

and

any

associated

references

are

available

in

the

online

version

of

the

paper

at

Received

May

accepted

September

Published

online

October

Misura

K.

M.

Baker

D.

Progress

and

challenges

in

high-resolution

refinement

of

protein

structure

models

Proteins

-LRB-

-RRB-

Pieper

U.

et

al.

MODBASE

a

database

of

annotated

comparative

protein

structure

models

and

associated

resources

Nucleic

Acids

Res

-LRB-

-RRB-

Moult

J

A

decade

of

CASP

progress

bottlenecks

and

prognosis

in

protein

structure

prediction

Curr

Opin

Struct

Biol

-LRB-

-RRB-

Schwarzenbacher

R.

Godzik

A.

Grzechnik

S.

K.

Jaroszewski

L

The

importance

of

alignment

accuracy

for

molecular

replacement

Acta

Crystallogr

D

-LRB-

-RRB-

Giorgetti

A.

Raimondo

D.

Miele

A.

E.

Tramontano

A.

Evaluating

the

usefulness

of

protein

structure

models

for

molecular

replacement

Bioinformatics

-LRB-

suppl

-RRB-

-LRB-

-RRB-

Chen

Y.

W.

Dodson

E.

J.

Kleywegt

G.

J.

Does

NMR

mean

not

for

molecular

replacement

Using

NMR-based

search

models

to

solve

protein

crystal

structures

Structure

-LRB-

-RRB-

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Proteins

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Nakamura

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Markley

J.

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Proc

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R.

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M.

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K.

Chance

M.

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A.

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Protein

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Supplementary

Information

is

linked

to

the

online

version

of

the

paper

at

Acknowledgements

We

thank

Rosetta@home

participants

for

contributing

computing

power

that

made

testing

of

many

new

ideas

possible

the

DOE

INCITE

program

for

access

to

Blue

Gene/L

at

Argonne

National

Laboratory

and

the

IBM

Blue

Gene

Watson

supercomputers

and

the

NCSA

SDSC

and

Argonne

National

Laboratory

supercomputer

centres

for

computer

time

and

help

with

porting

Rosetta

to

Blue

Gene

We

thank

D.

Kim

and

K.

Laidig

for

developing

the

computational

infrastructure

underlying

Rosetta@home

J.

Abendroth

for

help

with

RESOLVE

and

ARP/wARP

software

M.

Kennedy

of

NESG

for

the

NMR

structure

coordinates

of

protein

and

for

help

with

the

molecular

replacement

calculations

and

J.

Abendroth

J.

Bosch

J.

Havranek

and

C.

Wang

for

comments

on

the

manuscript

We

also

thank

the

CASP

organizers

and

contributing

structural

biologists

for

providing

an

invaluable

test

set

for

new

structure

refinement

methods

This

work

was

funded

by

the

National

Institute

of

General

Medical

Sciences

National

Institutes

of

Health

-LRB-

to

D.B.

-RRB-

the

Wellcome

Trust

UK

-LRB-

to

R.J.R.

-RRB-

the

Howard

Hughes

Medical

Institute

-LRB-

D.B.

-RRB-

a

Leukemia

and

Lymphoma

Society

Career

Development

fellowship

-LRB-

to

B.Q.

-RRB-

and

a

Jane

Coffin

Childs

fellowship

-LRB-

to

R.D.

-RRB-

Author

Contributions

B.Q.

S.R.

and

R.D.

contributed

equally

to

this

work

Structure

predictions

for

NMR-based

comparative-model-based

and

de

novo

predictions

were

carried

out

by

S.R.

B.Q.

and

R.D.

respectively

with

advice

and

software

from

D.B.

and

P.B.

Phasing

trials

were

performed

by

R.J.R.

B.Q.

S.R.

and

R.D.

with

advice

from

R.J.R.

and

A.J.M.

All

authors

discussed

results

and

commented

on

the

manuscript

Author

Information

Rosetta

software

and

source

code

are

available

to

academic

users

free

of

charge

at

Reprints

and

permissions

information

is

available

at

Correspondence

and

requests

for

materials

should

be

addressed

to

D.B.

-LRB-

dabaker@u.washington.edu

-RRB-

Nature

Publishing

Group

doi

METHODS

We

present

detailed

descriptions

of

six

methods

discussed

in

the

main

text

-LRB-

-RRB-

rebuilding-and-refinement

protocol

-LRB-

-RRB-

identification

of

regions

to

rebuild

from

the

NMR

structure

ensemble

-LRB-

-RRB-

preparation

of

blind

predictions

-LRB-

-RRB-

metrics

for

comparing

models

with

crystal

structures

-LRB-

-RRB-

screening

of

models

for

suitability

for

molecular

replacement

-LRB-

-RRB-

assessing

model

quality

with

MolProbity

Rebuilding-and-refinement

protocol

We

describe

below

the

three

key

steps

of

the

rebuilding-and-refinement

protocol

segment

rebuilding

all-atom

refinement

and

iterative

evolution

For

the

first

of

these

three

steps

we

used

a

new

segment

rebuilding

protocol

to

rebuild

regions

with

high

structural

variation

in

the

model

population

as

these

regions

are

often

incorrect

-LRB-

see

for

example

Fig.

-RRB-

Because

of

uncertainties

in

the

precise

locations

of

incorrect

regions

the

portions

of

the

model

to

be

rebuilt

were

chosen

stochastically

from

the

regions

with

high

variance

at

the

beginning

of

each

simulation

Up

to

of

all

the

separate

regions

were

rebuilt

in

a

given

run

this

allows

for

compensatory

changes

in

interacting

segments

to

occur

The

coordinates

in

the

region

to

be

rebuilt

were

generated

using

the

Rosetta

fragment-insertion-based

de

novo

folding

After

each

fragment

insertion

the

decision

to

accept

or

reject

was

made

according

to

the

standard

Metropolis

criterion

based

on

the

total

energy

of

the

system

To

maintain

the

connectivity

of

the

protein

chain

cyclic

coordinate

descent

-LRB-

-RRB-

was

used

to

close

the

chain

break

at

a

stochastically

selected

position

of

the

region

rebuilt

The

rebuilding

process

was

divided

into

ten

stages

At

each

successive

stage

an

increasing

chain-break

score

-LRB-

a

penalty

to

the

deviation

of

the

peptide

bond

length

at

the

chain

break

from

the

ideal

peptide

bond

length

-RRB-

was

applied

In

each

of

the

first

five

stages

the

number

of

fragment

insertion

trials

was

ten

times

the

number

of

residues

in

the

region

being

rebuilt

In

a

fragment

insertion

trial

randomly

chosen

nine-residue

three-residue

or

one-residue

fragments

were

inserted

into

randomly

chosen

positions

in

the

region

being

rebuilt

and

the

Metropolis

Monte

Carlo

criterion

was

used

to

accept

or

reject

the

newly

inserted

fragment

based

on

the

Rosetta

low-resolution

energy

In

each

of

the

five

last

stages

in

addition

to

the

fragment

insertion

trials

we

also

performed

cyclic-coordinate-descent-based

backbone

torsion

angle

moves

-LRB-

CCD

moves

-RRB-

in

which

the

cyclic

coordinate

descent

solution

was

calculated

and

the

backbone

torsion

angles

for

five

randomly

picked

positions

in

the

region

being

rebuilt

were

modified

according

to

the

CCD

solution

If

after

the

ten

rebuilding

stages

described

above

any

chain

break

remained

larger

than

A

the

region

to

be

rebuilt

was

expanded

by

one

residue

on

both

sides

The

above

fragment

insertion

and

chain-break

closing

process

was

repeated

using

a

harmonic

tether

to

the

starting

values

of

the

torsion

angles

in

the

newly

included

regions

-LRB-

which

may

fall

into

regions

with

low

variance

in

the

starting

population

-RRB-

and

another

stochastically

selected

chain-break

position

The

regions

to

be

rebuilt

were

allowed

to

expand

by

up

to

five

residues

upstream

and

downstream

of

the

original

starting

and

ending

positions

until

chain

closure

was

achieved

This

procedure

was

usually

sufficient

to

ensure

the

recovery

of

a

continuous

peptide

chain

In

very

rare

cases

where

the

chain

could

not

be

closed

in

a

rebuilt

region

it

was

merged

with

an

adjacent

region

to

be

rebuilt

along

with

the

fixed

portion

of

the

model

between

these

two

regions

and

the

rebuilding

process

was

repeated

With

the

added

flexibility

of

a

larger

region

being

rebuilt

the

peptide

chain

could

essentially

always

be

closed

Variable

regions

at

the

chain

termini

were

rebuilt

using

the

fragment

insertion-based

de

novo

protocol

without

steps

for

chain-break

closure

The

segment

rebuilding

protocol

is

implemented

in

the

subroutine

in

the

freely

available

Rosetta

source

code

The

segment

rebuilding

protocol

described

above

aggressively

employs

fragment

insertion

moves

to

sample

a

broad

range

of

conformations

The

all-atom

refinement

protocol

the

second

key

step

of

the

rebuilding-and-refinement

protocol

then

searches

for

local

minima

in

the

vicinity

of

the

structures

produced

by

segment

rebuilding

using

a

detailed

all-atom

force-field

The

Rosetta

all-atom

energy

function

is

largely

dominated

by

short-range

primarily

Lennard

Jones

interactions

orientation-dependent

hydrogen

bonding

and

the

Laziridis

Karplus

implicit

solvation

The

torsional

states

of

backbone

and

side

chains

are

evaluated

using

knowledgebased

potentials

derived

from

amino-acid-specific

Ramachandran

maps

and

the

rotamer

probabilities

and

x

angle

standard

deviations

in

the

backbonedependent

rotamer

library

developed

by

ref

During

all-atom

refinement

all

the

backbone

and

side-chain

atoms

in

the

protein

are

explicitly

represented

The

bond

lengths

and

angles

are

kept

fixed

at

ideal

and

the

polypeptide

chain

is

described

in

internal

coordinates

-LRB-

the

backbone

and

side-chain

torsion

angles

-RRB-

A

single

move

in

the

all-atom

refinement

protocol

consists

of

the

following

steps

-LRB-

-RRB-

one

of

the

several

types

of

perturbations

to

the

backbone

torsion

angles

described

below

-LRB-

-RRB-

greedy

optimization

of

the

side-chain

rotamer

conformations

-LRB-

rotamer

trials

-RRB-

for

the

new

backbone

conformation

-LRB-

-RRB-

minimization

of

the

energy

with

respect

to

either

the

backbone

degrees

of

freedom

only

-LRB-

first

half

of

refinement

procedure

-RRB-

or

backbone

and

side-chain

degrees

of

freedom

-LRB-

second

half

of

refinement

procedure

-RRB-

using

the

Davidson

Fletcher

Powell

-LRB-

DFP

-RRB-

algorithm

The

convergence

criterion

for

exiting

this

quasi-Newton

minimization

was

decreased

from

to

during

the

course

of

refinement

to

enable

more

complete

minimization

in

the

final

stages

of

refinement

-LRB-

-RRB-

The

compound

move

-LRB-

steps

-RRB-

is

accepted

or

rejected

according

to

the

Metropolis

Monte

Carlo

criterion

These

compound

moves

extend

the

Monte

Carlo

minimization

procedure

found

to

be

quite

powerful

in

previous

by

incorporating

discrete

optimization

of

side-chain

conformations

this

allows

energy-directed

barrier

hopping

at

the

level

of

the

side

chains

The

following

backbone

perturbations

are

used

at

step

-LRB-

-RRB-

in

the

Monte

Carlo

minimization

move

described

above

and

in

a

previous

The

small

and

shear

moves

are

small

perturbations

of

the

backbone

at

five

to

ten

randomly

chosen

positions

In

small

moves

w

and

y

are

perturbed

randomly

by

up

to

in

helix

or

strand

regions

or

u

in

loop

regions

In

shear

moves

w

is

perturbed

randomly

by

up

to

in

helix

or

strand

regions

or

in

loop

regions

and

the

preceding

y

is

perturbed

by

the

same

amount

of

degrees

in

the

opposite

direction

to

produce

a

compensatory

shear

motion

in

the

peptide

plane

The

wobble

and

crank

moves

involve

insertion

of

fragments

and

are

more

aggressively

perturbing

than

the

small

and

shear

For

both

of

these

move

types

the

fragment

is

filtered

to

exclude

those

which

cause

a

mean

square

deviation

in

the

coordinates

of

the

downstream

atoms

of

more

than

A

and

one

of

the

remaining

fragments

is

chosen

randomly

for

insertion

In

wobble

moves

the

torsion

angles

belonging

to

the

three

residues

immediately

following

the

site

of

the

oneor

three-residue

fragment

insertion

are

varied

to

minimize

the

downstream

perturbation

still

further

In

crank

moves

one

residue

is

varied

immediately

after

the

insertion

site

and

three

more

residues

at

a

site

spaced

by

residues

from

the

fragment

insertion

site

this

produces

a

crankshaft

like

movement

of

the

intervening

portion

of

the

chain

Small-wobble

moves

involve

an

initial

random

change

in

the

torsion

angles

of

a

single

residue

followed

by

minimization

of

the

perturbation

over

the

three

adjacent

residues

The

minimization

of

the

perturbation

in

the

wobble

and

crank

moves

is

carried

out

using

the

fast

gradient-based

algorithm

described

After

all

five

move

types

the

side

chains

are

optimized

and

the

energy

is

minimized

as

described

in

the

preceding

paragraph

The

all-atom

refinement

protocol

is

divided

into

three

stages

The

first

is

ramp-up

The

ramp-up

stage

consists

of

sets

of

ten

small

and

shear

moves

preceded

by

combinatorial

optimization

of

the

side-chain

rotamer

conformations

The

weight

on

the

repulsive

part

of

the

Lennard

Jones

potential

is

progressively

increased

from

to

over

eight

such

move

sets

The

gradual

ramping

up

of

the

repulsive

weight

facilitates

a

smooth

rearrangement

of

the

side

chains

with

small

perturbations

of

the

backbone

and

ensures

a

reasonably

well-packed

low-energy

model

before

the

more

aggressive

second

stage

This

second

stage

is

the

aggressive

sampling

stage

alternating

wobble

small-wobble

and

crank

compound

Monte

Carlo

minimization

moves

are

carried

out

the

total

number

of

attempts

for

each

move

type

is

equal

to

the

number

of

residues

in

the

protein

A

full

combinatorial

search

over

side-chain

rotamer

conformations

is

carried

out

after

every

attempts

of

each

type

of

move

The

more

aggressive

nature

of

the

moves

used

at

this

stage

allows

the

traversal

of

modest

energy

barriers

The

convergence

tolerance

for

the

DFP

minimization

is

set

to

The

third

stage

is

the

fine

optimization

stage

alternating

small

and

shear

moves

are

carried

out

again

for

a

total

number

of

attempts

equal

to

the

number

of

residues

in

the

protein

The

more

subtle

backbone

conformation

changes

brought

about

by

these

moves

assist

convergence

on

a

relatively

low-energy

local

minimum

The

convergence

tolerance

for

minimization

is

set

to

After

these

three

stages

a

final

minimization

with

respect

to

all

degrees

of

freedom

is

carried

out

with

a

convergence

tolerance

of

The

refinement

protocol

described

above

is

implemented

in

the

fullatom

relax

subroutine

in

Rosetta

the

CPU

cost

is

about

min

for

a

protein

on

an

Intel

Pentium

IV

GHz

processor

The

challenge

in

refinement

is

to

focus

sampling

on

the

lowest

energy

regions

of

the

energy

landscape

identified

up

to

that

point

while

maintaining

a

broad

enough

search

to

avoid

converging

on

a

local

energy

minimum

Towards

this

end

we

developed

a

protocol

that

balances

intensification

of

the

search

in

lowenergy

regions

with

diversification

to

maintain

subpopulations

exploring

alternative

energy

minima

The

approach

the

third

key

step

of

the

rebuilding-and-refinement

protocol

that

is

ensemble

evolution

by

alternate

cycles

of

diversification

and

intensification

adopts

the

idea

of

explicit

control

of

the

search

intensity

from

tabu

and

is

a

generalization

of

the

conformational

space

annealing

-LRB-

CSA

-RRB-

technique

which

has

achieved

success

in

a

broad

range

of

optimization

Nature

Publishing

Group

doi

In

both

the

intensification

and

diversification

steps

an

input

population

of

models

was

clustered

using

the

method

described

in

ref

to

identify

distinct

populations

of

structures

The

clustering

threshold

was

chosen

such

that

the

largest

cluster

contained

of

the

models

For

each

cluster

ten

models

were

selected

-LRB-

if

there

were

fewer

than

models

in

a

cluster

all

were

selected

-RRB-

and

each

model

was

subjected

to

nine

independent

segment

rebuilding

plus

allatom

refinement

runs

initialized

with

different

random

number

seeds

In

the

diversification

stages

-LRB-

iterations

and

-RRB-

the

models

in

the

parent

population

were

kept

in

their

original

cluster

assignment

A

newly

generated

model

was

assigned

to

the

closest

cluster

if

the

root-mean-squared

deviation

over

alpha

carbons

-LRB-

Ca

r.m.s.

deviation

-RRB-

between

this

model

and

the

closest

cluster

member

was

less

than

the

current

diversity

threshold

-LRB-

see

below

-RRB-

and

the

highest

energy

member

of

the

cluster

was

thrown

away

If

the

r.m.s.

deviation

between

a

newly

generated

model

and

its

closest

cluster

member

was

higher

than

the

current

diversity

threshold

then

the

model

with

the

highest

energy

in

the

current

parent

population

was

thrown

away

and

the

newly

generated

model

formed

a

cluster

of

its

own

This

is

analogous

to

speciation

in

natural

evolution

As

a

model

is

discarded

for

each

new

model

added

the

population

size

stayed

unchanged

The

diversification

step

favours

a

broad

exploration

of

the

conformational

space

by

maintaining

the

distinct

populations

of

clusters

there

is

competition

for

low

energy

within

but

not

between

clusters

Combined

with

the

initial

clustering

step

it

ensures

that

the

new

population

will

not

be

dominated

by

overly

closely

related

structures

which

could

result

in

premature

convergence

away

from

the

global

minimum

In

the

intensification

stages

-LRB-

iterations

and

-RRB-

all

but

the

lowest

energy

of

the

entire

population

-LRB-

parents

plus

offspring

-RRB-

is

discarded

to

bring

the

population

back

to

a

size

of

The

remaining

models

from

the

parent

population

keep

their

original

cluster

assignment

A

newly

generated

model

was

assigned

to

the

closest

remaining

cluster

if

the

r.m.s.

deviation

between

this

model

and

the

closest

cluster

member

was

lower

than

the

current

diversity

threshold

otherwise

it

formed

a

new

cluster

of

its

own

This

stage

differs

from

the

diversification

stage

in

that

the

energy-based

selection

is

carried

out

across

all

clusters

and

hence

higher

energy

clusters

can

be

eliminated

completely

This

stage

allows

more

thorough

exploration

of

the

most

promising

-LRB-

lowest

energy

-RRB-

regions

of

the

energy

landscape

explored

thus

far

The

diversity

threshold

used

to

maintain

distinct

populations

and

to

guide

the

spawning

of

new

populations

was

reduced

at

each

iteration

to

allow

gradual

convergence

on

the

global

energy

minimum

The

starting

value

was

the

cluster

ing

threshold

in

the

original

population

and

this

was

reduced

by

A

at

each

iteration

This

annealing

of

the

diversity

threshold

was

introduced

in

the

CSA

The

new

parent

population

generated

by

the

diversification

or

intensification

procedures

was

used

to

seed

the

next

generation

and

nine

independent

segment

rebuilding

plus

all-atom

refinement

calculations

were

again

carried

out

for

each

parent

After

ten

iterations

the

low

energy

models

were

clustered

and

the

lowest

energy

models

in

the

largest

five

clusters

were

selected

as

the

final

predictions

The

overall

iterative

procedure

took

approximately

CPU

hours

per

target

For

molecular

replacement

efforts

this

computational

effort

would

probably

be

significantly

reduced

if

phasing

trials

with

diffraction

data

are

used

to

screen

models

Identification

of

regions

to

rebuild

from

the

NMR

structure

ensemble

The

test

cases

for

NMR

refinement

were

chosen

to

be

proteins

representing

different

fold

topologies

for

which

an

NMR

structure

and

a

high-resolution

crystal

structure

-LRB-

with

structure

factors

deposited

in

PDB

-RRB-

existed

These

were

chosen

from

the

data

sets

used

by

refs

and

For

investigations

of

refinement

of

NMR

structures

we

rebuilt

two

sets

of

regions

The

first

are

regions

that

vary

within

the

NMR

ensemble

As

in

the

comparative

modelling

case

we

have

observed

that

regions

that

vary

within

the

NMR

ensemble

are

likely

to

be

the

regions

that

are

most

different

from

a

high-resolution

crystal

structure

These

are

most

likely

loops

that

are

either

inherently

dynamic

in

the

NMR

structure

or

loops

that

are

held

in

place

with

insufficient

restraints

-LRB-

Applying

all-atom

refinement

to

the

NMR

ensembles

gave

essentially

the

same

list

of

variable

regions

-LRB-

data

not

shown

-RRB-

-RRB-

The

second

set

of

regions

are

segments

that

are

internally

consistent

within

the

NMR

ensemble

but

systematically

under-packed

To

estimate

packing

we

used

a

recently

developed

packing

metric

-LRB-

W.

Sheffler

personal

communication

-RRB-

based

on

the

relative

accessible

surface

areas

of

groups

of

atoms

For

each

buried

atom

we

compute

the

largest

sphere

tangent

to

that

atom

which

can

fit

into

empty

space

within

the

protein

A

group

composed

of

all

atoms

within

A

of

the

centre

is

defined

for

each

sphere

For

each

group

of

atoms

accessible

surface

-LRB-

SASA

-RRB-

to

small

and

large

spherical

probes

-LRB-

radii

A

and

A

respectively

-RRB-

is

computed

given

that

a

ball

of

atoms

has

a

certain

area

accessible

to

a

large

sphere

less-accessible

area

to

a

small

sphere

indicates

better

packing

A

summary

percentile

score

is

computed

on

the

basis

of

a

reference

set

of

crystal

structures

approximating

the

fraction

of

native

proteins

which

are

better

packed

than

the

scored

structure

Preparation

of

blind

predictions

The

initial

set

of

template-based

models

was

obtained

from

the

and

subjected

to

all-atom

refinement

using

the

Rosetta

all-atom

energy

function

Up

to

ten

templates

from

which

the

very

lowest

energy

models

were

derived

were

used

as

the

candidate

templates

Alignment

ensembles

between

the

candidate

templates

and

the

target

sequence

were

parametrically

generated

using

the

K

Sync

alignment

The

alignment

ensemble

was

turned

into

a

model

ensemble

by

placing

the

sequence

of

the

query

onto

the

backbone

of

the

parent

based

on

each

alignment

Missing

densities

from

the

insertion

and

deletion

regions

of

the

alignment

were

modelled

using

the

segment

modelling

protocol

described

in

the

rebuildingand-refinement

protocol

section

The

full-chain

models

were

then

subjected

to

the

all-atom

refinement

procedure

as

described

in

the

same

section

constrained

by

a

set

of

Ca

Ca

distance

constraints

described

next

The

Ca

Ca

distance

constraints

were

generated

from

the

templatebased

models

with

the

lowest

Rosetta

all-atom

energies

after

all-atom

refinement

A

Ca

Ca

pair

was

used

to

derive

constraints

only

when

the

associated

distance

was

less

than

A

in

more

than

of

the

selected

constraint-generating

models

Upper

and

lower

bounds

for

each

of

these

pairs

were

determined

by

padding

the

highest

and

lowest

of

these

distances

by

one

standard

deviation

of

the

Ca

Ca

distance

distribution

function

as

described

in

ref

For

computational

efficiency

we

further

trimmed

down

the

number

of

constraint

pairs

by

eliminating

neighbouring

pairs

separated

by

one

or

two

residues

During

allatom

refinement

a

penalty

is

applied

when

the

Ca

Ca

distances

in

the

model

exceed

the

upper

or

lower

limit

of

the

corresponding

constraints

If

a

distance

exceeds

the

upper

or

lower

constraint

limit

by

d

-LRB-

in

A

-RRB-

then

the

penalty

Ec

is

when

d

A

and

-LRB-

d

A

-RRB-

when

d

A

The

resulting

ensemble

of

lowenergy

comparative

models

became

the

inputs

to

further

rounds

of

rebuildingand-refinement

-LRB-

Fig.

-RRB-

For

targets

without

clear

templates

identified

by

the

the

full

chain

was

fully

modelled

by

fragment

assembly

starting

from

an

extended

chain

followed

by

the

all-atom

refinement

procedure

described

above

The

convergence

of

the

Rosetta

de

novo

prediction

protocol

can

differ

significantly

for

different

sequence

representatives

of

a

given

For

one

of

seven

tested

sequence

homologues

gave

exceptionally

well

converged

low-energy

models

that

after

sequence

mapping

allowed

structure

prediction

for

the

target

sequence

with

the

rebuilding-and-refinement

About

all-atom

refined

models

were

generated

for

each

modelling

target

requiring

approximately

CPU

hours

As

noted

above

for

molecular

replacement

efforts

this

computational

effort

would

probably

be

significantly

reduced

if

phasing

trials

with

diffraction

data

are

used

to

screen

models

as

the

predicted

models

used

in

this

manuscript

were

prepared

as

blind

predictions

for

such

diffraction

data

were

not

available

at

the

time

of

modelling

Metrics

for

comparing

models

with

crystal

structures

As

has

been

discussed

previously

no

metric

for

comparing

structure

models

with

the

crystal

structures

is

In

this

work

we

used

three

different

structural

metrics

for

model

quality

assessment

The

Ca

r.m.s.

deviation

is

a

widely

used

metric

for

structure

comparison

but

it

can

be

distorted

by

large

deviations

in

a

small

number

of

residues

especially

at

the

termini

or

in

long

surface

loops

The

GDT-HA

-LRB-

geometric

distance

test

-LRB-

high

accuracy

-RRB-

-RRB-

score

is

the

average

percentage

of

Cas

in

the

model

within

and

A

of

the

corresponding

Ca

coordinates

in

the

crystal

structure

we

used

to

align

the

structures

This

metric

is

less

sensitive

than

the

full-chain

r.m.s.

deviation

to

deviations

in

poorly

ordered

termini

and

long

loops

and

was

used

in

the

template-based

modelling

assessment

The

core

residue

all-atom

r.m.s.

deviation

describes

the

accuracy

of

both

the

backbone

and

side-chain

conformation

prediction

We

used

this

metric

in

the

evaluation

of

NMR

refinement

because

it

can

be

applied

to

both

the

starting

-LRB-

NMR

ensemble

-RRB-

and

ending

-LRB-

Rosetta

refined

-RRB-

models

In

template-based

modelling

this

metric

is

not

practical

as

the

template

usually

does

not

have

the

same

amino

acid

sequence

as

the

target

to

be

modelled

In

addition

successful

molecular

replacement

using

the

predicted

structure

can

be

regarded

as

a

stringent

test

for

model

quality

assessment

as

suggested

in

ref

Screening

of

models

for

suitability

for

molecular

replacement

Searching

for

molecular

replacement

solutions

involves

applying

rigid-body

transformations

along

the

six

rotational

and

translational

degrees

of

freedom

We

carried

out

this

search

with

the

Phaser

software

which

is

described

in

ref

and

references

therein

For

completeness

the

algorithms

are

briefly

summarized

here

Phaser

uses

likelihood

functions

to

judge

how

well

molecular

replacement

models

agree

with

the

measured

diffraction

data

after

they

have

been

first

rotated

and

then

also

translated

Brute-force

likelihood

calculations

over

grids

of

orientations

and

Nature

Publishing

Group

doi

positions

are

computationally

expensive

so

fast-fourier-transform-based

approximations

are

used

to

compute

sets

of

possible

solutions

which

are

rescored

with

the

full

likelihood

targets

By

using

a

tree-search-with-pruning

strategy

almost

all

solutions

that

would

be

found

with

a

full

six-dimensional

search

are

found

but

with

a

much

lower

computational

cost

As

well

this

strategy

allows

effective

searches

for

multiple

copies

in

crystals

with

more

than

one

molecule

in

the

asymmetric

unit

For

each

molecule

to

be

placed

a

rotation

search

is

first

carried

out

A

translation

search

is

then

carried

out

for

each

plausible

orientation

All

plausible

rotation/translation

solutions

are

checked

for

packing

in

the

lattice

and

solutions

that

pack

successfully

are

subjected

to

rigid

body

refinement

If

more

than

one

copy

is

present

all

plausible

partial

solutions

are

fixed

in

turn

while

carrying

out

rotation

and

translation

searches

for

subsequent

copies

In

molecular

replacement

trials

with

Phaser

the

clearest

indication

of

success

comes

from

high

values

of

the

Z-score

-LRB-

number

of

standard

deviations

above

the

mean

-RRB-

computed

by

comparing

the

log-likelihood-gain

-LRB-

LLG

-RRB-

for

the

peak

with

LLG

scores

for

a

random

sample

of

search

points

For

molecular

replacement

in

each

of

the

NMR

modelling

cases

we

evaluated

the

combined

NMR

ensemble

as

a

potential

search

model

and

compared

these

results

to

trials

with

the

lowest

energy

Rosetta

models

from

rebuilding

and

refinement

-LRB-

Table

-RRB-

Furthermore

we

have

carried

out

molecular

replacement

trials

with

each

of

the

members

of

the

deposited

NMR

ensemble

individually

with

results

given

in

Supplementary

Table

Finally

for

an

actual

search

for

a

good

molecular

replacement

solution

a

larger

set

of

models

from

rebuilding

and

refinement

can

be

screened

rapidly

We

thus

extended

the

search

to

the

lowest

energy

models

from

Rosetta

rebuilding

and

refinement

and

the

results

notably

improved

are

presented

in

Supplementary

Table

For

molecular

replacement

in

comparative

modelling

cases

we

prepared

search

models

from

the

best

existing

templates

and

from

our

comparative

modelling

predictions

For

the

best

templates

we

followed

the

mixed

model

protocol

described

in

ref

for

optimizing

molecular

replacement

Furthermore

on

the

basis

of

the

structure

alignment

between

the

native

structure

and

the

best

template

structure

the

template

structure

was

trimmed

to

contain

only

the

structurally

alignable

regions

Then

the

native

sequence

was

threaded

onto

the

backbone

of

the

corresponding

template

structure

while

retaining

the

side-chain

coordinates

of

the

identical

residues

between

the

template

and

native

sequences

Non-identical

side

chains

longer

than

serine

were

mutated

to

serine

followed

by

Rosetta

side-chain

packing

to

model

the

mutated

serine

and

the

shorter

non-identical

side

chains

while

keeping

the

identical

side-chain

conformation

fixed

To

prepare

search

models

for

these

predictions

we

superimposed

low-energy

models

from

the

final

round

of

refinement

and

defined

the

model

that

has

the

lowest

average

r.m.s.

deviation

to

the

rest

of

the

models

as

the

reference

model

Then

we

calculated

the

average

per-atom

distance

Da

between

each

of

the

superimposed

models

and

the

reference

model

The

Rosetta

temperature

factor

is

calculated

as

Te

for

each

atom

and

inserted

to

the

B-factor

column

of

the

refined

model

files

The

Rosetta

temperature

factor

is

intended

to

represent

the

uncertainty

in

the

final

refined

models

after

extensive

refinement

in

the

Rosetta

all-atom

force

field

As

suggested

by

using

the

B-factor

effectively

to

smear

each

atom

over

its

possible

positions

the

correlation

of

the

modelled

electron

density

with

the

true

electron

density

can

be

maximized

For

the

de

novo

modelling

case

target

search

models

for

molecular

replacement

were

trimmed

according

to

residues

for

which

there

was

consensus

among

submitted

models

Supplementary

Fig.

gives

a

more

detailed

description

and

illustration

of

the

molecular

replacement

solution

Assessing

model

quality

with

MolProbity

For

the

investigations

of

refinement

of

NMR

models

we

used

the

MolProbity

to

investigate

the

quality

of

the

refined

models

versus

that

of

the

starting

NMR

ensemble

For

purposes

of

comparison

we

chose

the

lowest

energy

refined

model

and

the

first

member

of

the

deposited

NMR

structure

Supplementary

Table

shows

the

clash

score

number

of

rotamer

outliers

and

number

of

Ramachandran

outliers

of

the

NMR

and

refined

models

The

refined

models

consistently

have

better

model

quality

than

the

starting

NMR

structure

based

on

these

metrics

Simons

K.

T.

Kooperberg

C.

Huang

E.

Baker

D.

Assembly

of

protein

tertiary

structures

from

fragments

with

similar

local

sequences

using

simulated

annealing

and

Bayesian

scoring

functions

J.

Mol

Biol

-LRB-

-RRB-

Canutescu

A.

A.

Dunbrack

R.

L.

Jr.

Cyclic

coordinate

descent

A

robotics

algorithm

for

protein

loop

closure

Protein

Sci

-LRB-

-RRB-

Lazaridis

T.

Karplus

M.

Effective

energy

function

for

proteins

in

solution

Proteins

-LRB-

-RRB-

Dunbrack

R.

L.

Jr

Cohen

F.

E.

Bayesian

statistical

analysis

of

protein

side-chain

rotamer

preferences

Protein

Sci

-LRB-

-RRB-

Engh

R.

A.

Huber

R.

Accurate

bond

and

angle

parameters

for

X-ray

protein

structure

refinement

Acta

Crystallogr

A

-LRB-

-RRB-

Wang

C.

Schueler-Furman

O.

Baker

D.

Improved

side-chain

modeling

for

protein-protein

docking

Protein

Sci

-LRB-

-RRB-

Li

Z.

Scheraga

H.

A.

Monte

Carlo-minimization

approach

to

the

multipleminima

problem

in

protein

folding

Proc

Natl

Acad

Sci

USA

-LRB-

-RRB-

Garbuzynskiy

S.

O.

Melnik

B.

S.

Lobanov

M.

Y.

Finkelstein

A.

V.

Galzitskaya

O.

V.

Comparison

of

X-ray

and

NMR

structures

is

there

a

systematic

difference

in

residue

contacts

between

X-ray

and

NMR-resolved

protein

structures

Proteins

-LRB-

-RRB-

Ginalski

K.

Elofsson

A.

Fischer

D.

Rychlewski

L.

a

simple

approach

to

improve

protein

structure

predictions

Bioinformatics

-LRB-

-RRB-

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D.

Baker

D.

Homology

modeling

using

parametric

alignment

ensemble

generation

with

consensus

and

energy-based

model

selection

Nucleic

Acids

Res

-LRB-

-RRB-

Sali

A.

Blundell

T.

L.

Comparative

protein

modelling

by

satisfaction

of

spatial

restraints

J.

Mol

Biol

-LRB-

-RRB-

Bonneau

R.

Strauss

C.

E.

Baker

D.

Improving

the

performance

of

Rosetta

using

multiple

sequence

alignment

information

and

global

measures

of

hydrophobic

core

formation

Proteins

-LRB-

-RRB-

Moult

J.

Fidelis

K.

Rost

B.

Hubbard

T.

Tramontano

A.

Critical

assessment

of

methods

of

protein

structure

prediction

-LRB-

CASP

-RRB-

round

Proteins

-LRB-

suppl

-RRB-

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Petsko

G.

A

The

grail

problem

Genome

Biol

-LRB-

-RRB-

Plewczynski

D.

Pas

J.

Von

Grotthuss

M.

Rychlewski

L.

Comparison

of

proteins

based

on

segments

structural

similarity

Acta

Biochim

Pol

-LRB-

-RRB-

Kuhlman

B.

Baker

D.

Native

protein

sequences

are

close

to

optimal

for

their

structures

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Sci

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