Images of molecules in vitreous ice - …embo2017.cryst.bbk.ac.uk/embo2017/course/Lectures/Lecture...
13
Determination of the image orientation E. Orlova Lecture 11 Images: shadow, projection, Euler angles Methods of orientation determination: Projection matching: Real space & Polar Fourier coordinates Common lines in Fourier space Common lines in real space FREALIGN (Fourier REconstruction and ALIGNment) Practical Course Birkbeck College London Image processing for cryo microscopy Sep 5 - Sept 15, 2017 Images of molecules in vitreous ice Images ---??--- Object surface view, shadow, projection Object Photograph = surface view Projection Projection X-ray picture Shadow Shadow (positive) Shadow (negative)
Transcript of Images of molecules in vitreous ice - …embo2017.cryst.bbk.ac.uk/embo2017/course/Lectures/Lecture...
Det
erm
inat
ion
of
the
imag
e or
ient
atio
n
E. O
rlova
Le
ctur
e 11
Imag
es: s
hado
w, p
roje
ctio
n, E
uler
ang
les
Met
hods
of o
rient
atio
n de
term
inat
ion:
P
roje
ctio
n m
atch
ing:
R
eal s
pace
& P
olar
Fou
rier c
oord
inat
es
Com
mon
line
s in
Fou
rier s
pace
C
omm
on li
nes
in re
al s
pace
F
REA
LIG
N (F
ourie
r REc
onst
ruct
ion
an
d AL
IGN
men
t)
Pra
ctic
al C
ours
e
Birk
beck
Col
lege
Lo
ndon
Imag
e pr
oces
sing
fo
r cry
o m
icro
scop
y
Sep
5 - S
ept 1
5, 2
017
Imag
es o
f mol
ecul
es i
n vi
treo
us ic
e
Im
ages
---?
?---
Obj
ect
sur
face
vie
w,
sha
dow
, pr
ojec
tion
Obj
ect
Phot
ogra
ph =
su
rfac
e vi
ew
Proj
ectio
n Pr
ojec
tion
ojec
toX
-ray
pic
ture
Shad
ow
Shad
ow(p
ositi
ve)
Shad
ow
(neg
ativ
e)
3D
obj
ect
->
(x,y,
z)
Proj
ectio
n: 2
D, 1
D, S
inog
ram
= ?
=
(x,y
,z)
dxz
yx
zy
p)
,,
()
,(
dxy
xp
yl
),
()
(p(y,z
) – 2
D p
roje
ctio
n
l(y) –
1D
pro
ject
ion
Rib
osom
es in
vitr
eous
ice
– tra
nsla
tiona
l fre
edom
X
y X
and
Y
2
J.Fr
ank,
Ann
u. R
ev. B
ioph
ys. B
iom
ol. S
truct
. 200
2. 3
1:30
3–19
Rib
osom
es in
vitr
eous
ice
– ro
tatio
nal f
reed
om
and
→ 3
(IMAG
IC)
- ro
tatio
n in
th
e im
age
plan
e
(or a
roun
d ne
w
Z ax
is)
- ro
tatio
n ar
ound
X a
xis
– ro
tatio
n
arou
nd o
ld
Z a
xis)
Leon
hard
Eul
er
http
://en
.wik
iped
ia.o
rg/w
iki/L
eonh
ard_
Eule
r
Eule
r sp
ent
mos
t of
his
adu
lt lif
e in
St.
Pete
rsbu
rg,
Rus
sia,
an
d in
Be
rlin,
Pr
ussi
a.
He
is
the
pre-
emin
ent
mat
hem
atic
ian
of t
he 1
8th
cent
ury,
and
on
e of
the
grea
test
mat
hem
atic
ians
eve
r. hi
s co
llect
ed
wor
ks
fill
60–8
0 qu
arto
vo
lum
es
(15
April
170
7 –
18 S
epte
mbe
r 178
3)
was
a
pion
eerin
g Sw
iss
mat
hem
atic
ian
and
phys
icis
t. H
e m
ade
impo
rtant
dis
cove
ries
in f
ield
s as
div
erse
as
infin
itesi
mal
cal
culu
s an
d gr
aph
theo
ry. H
e al
so in
trodu
ced
muc
h of
the
mod
ern
mat
hem
atic
al
term
inol
ogy
and
nota
tion,
He
is a
lso
reno
wne
d fo
r hi
s w
ork
in m
echa
nics
, flu
id
dyna
mic
s,
optic
s,
and
astro
nom
y.
Met
hods
of o
rient
atio
n de
term
inat
ion:
1.
Con
ical
Tilt
– M
.Rad
erm
ache
r, J.
Fra
nk
2.P
roje
ctio
n M
atch
ing
– P.
Penc
zek,
J.F
rank
3.
Pol
ar F
ourie
r Tra
nsfo
rm –
T. B
acke
r 4.
Com
mon
Lin
es in
Fou
rier S
pace
(viru
ses,
ph
age
tails
) T.C
row
ther
- MR
C p
acka
ge +
nu
mer
ous
mod
ifica
tion
(S. F
ulle
r) 5.
Com
mon
Lin
es in
real
spa
ce
Ang
ular
Rec
onst
itutio
n, M
. Van
Hee
l 6.
Frea
lign
-> p
roje
ctio
n m
atch
ing
in F
ourie
r sp
ace
, N. G
rigor
ieff
Con
ical
tilt
, mor
e ef
fect
ive
for n
egat
ivel
y st
aine
d sa
mpl
es
RA
DER
MA
CHER
M. T
hree
-Dim
ensi
onal
Rec
onst
ruct
ion
of S
ingl
e Pa
rticl
es
From
Ran
dom
and
Non
rand
om T
ilt S
erie
s. J
OU
RN
AL
OF
ELE
CTR
ON
M
ICR
OS
CO
PY
TEC
HN
IQU
E 9
:359
-394
(198
8)
Con
ical
tilt
Proj
ectio
n M
atch
ing
P. P
encz
ek &
J. F
rank
Proj
ectio
n M
atch
ing
P. P
encz
ek &
J. F
rank
PFT
Met
hod:
Th
ere
is a
noth
er w
ay to
hel
p de
term
ine
and
refin
e or
igin
and
vie
w o
rient
atio
n pa
ram
eter
s fo
r 3D
R s
tudi
es
PFT
= Po
lar F
ourie
r Tra
nsfo
rm EM
PFT
Hel
ps d
eter
min
e (
,x,y
) for
cry
oEM
imag
es
of p
artic
les
with
icos
ahed
ral s
ymm
etry
From
Tim
Bak
er
Asym
met
rical
tria
ngle
for s
ymm
etry
532
BPV
Proj
ectio
ns: 1
/2 Ic
osah
edra
l ASU
0 3
6 9
12
15
18
21
24
27
30
90
87
84
81
78
75
72
69
From
Tim
Bak
er
EMPF
T
r (ra
dius
)
r
(azi
mut
hal a
ngle
)
Com
pute
Pol
ar P
roje
ctio
ns
Car
tesi
an
Pola
r
From
Tim
Bak
er
EMPF
T
Com
pute
Pol
ar F
ourie
r Tra
nsfo
rm
r (ra
dius
)
(azi
mut
hal a
ngle
) (s
patia
l fre
quen
cy)
Pola
r Pro
ject
ion
Pola
r FT
(Rea
l + R
ecip
roca
l)
From
Tim
Bak
er
Com
pute
Pol
ar F
ourie
r Tra
nsfo
rm
EMPF
T
5F
5F
Rea
l Dat
a Fr
om
Tim
Bak
er
The
sect
ion/
proj
ectio
n th
eore
m:
F [
g(x,
y,z)d
x ] =
G(0
,Y,Z
)
USE
: Th
e Fo
urie
r tra
nsfo
rm o
f a p
roje
ctio
n of
a 3
D o
bjec
t is
equa
l to
a ce
ntra
l sec
tion
of th
e 3D
Fou
rier t
rans
form
of t
he o
bjec
t. An
ele
ctro
n m
icro
grap
h is
a p
roje
ctio
n of
a 3
D o
bjec
t. Its
tran
sfor
m p
rovi
des
one
slic
e of
the
3D tr
ansf
orm
of t
he 3
D
obje
ct.
By c
ombi
ning
the
trans
form
s of
diff
eren
t vie
ws,
one
bui
lds
up
the
3D tr
ansf
orm
sec
tion
by s
ectio
n. O
ne th
en u
ses
the
Inve
rsed
Fou
rier T
trans
form
to
conv
ert t
he 3
D tr
ansf
orm
into
a
3D im
age.
Com
mon
line
s in
Fou
rier s
pace
Com
mon
line
s in
Fou
rier s
pace
From
S F
ulle
r
Icos
ahed
ral s
ymm
etry
, se
arch
for t
he c
omm
on li
nes
Com
paris
on o
f am
plitu
des
and
ph
ases
of r
adia
l lin
es,
asse
ssm
ent o
f ang
les
betw
een
them
An o
rient
atio
n aw
ay fr
om s
ymm
etry
axe
s
2 5
5
3
From
S F
ulle
r
Com
mon
line
s in
real
spa
ce
The
angu
lar r
econ
stitu
tion
met
hod
is
base
d on
the
“com
mon
-line
pro
ject
ion”
th
eore
m:
Any
two
2D p
roje
ctio
ns o
f a 3
D o
bjec
t ha
ve a
t lea
st O
NE
com
mon
1D
line
pr
ojec
tion
3D
2D
1
D p
roje
ctio
n
3D o
bjec
t y
x
z
dxz
yx
zy
p)
,,
()
,( p(
y,z)
2D p
roje
ctio
n
z
2Dy
Com
mon
line
s in
real
spa
ce
Com
mon
line
s in
real
spa
ce
Com
mon
line
s in
real
spa
ce
Com
mon
line
s in
real
spa
ce
Com
mon
line
s in
R/F
(our
ier)
spac
e Co
mm
on li
nes
in R
/F(o
urie
r) sp
ace
Com
mon
line
s in
R/F
(our
ier)
spac
e
2D
1D
2D p
roje
ctio
n
Sino
gram
is a
set
of
one
dim
ensi
onal
(li
ne) p
roje
ctio
ns
y
00
a
360
0
Com
mon
line
s in
real
spa
ce
900
880
920
2700
2720
2680
450
750
900
1400
1830
2700
3200
Proj
ectio
ns >
Sin
ogra
ms
0 o
360 o
180 o
0 o
360 o
180 o
25 o
50 o
50 000000000000o
90 000000000000o
25 55555o
25 555o
90 o
90 o
0 o
90 o
90 o
90 o
0 o 0 o
0 o
360 o
180 o
90 o
130 o
65 o
270 o
310 o
335 o
Cro
ssin
ocor
rela
tion
func
tion
Imag
e 2
Imag
e 1
-6-4-202468
111
2131
4151
6171
8191
101
111
121
-6-4-202468
111
2131
4151
6171
8191
101
111
121
Cro
ssin
ocor
rela
tion
func
tion
Imag
e 3
Imag
e 1
-6-4-20246
111
2131
4151
6171
8191
101
111
121
-6-4-20246
111
2131
4151
6171
8191
101
111
121
-6-4-20246
111
2131
4151
6171
8191
101
111
121
900
2700
3100
1300
Cro
ssin
ocor
rela
tion
func
tion
Imag
e 3
Imag
e 2
-6-4-202468
111
2131
4151
6171
8191
101
111
121
-6-4-202468
111
2131
4151
6171
8191
101
111
121
a b
c
d e
f
g
Proj
ectio
ns 1
and
3
Rib
osom
e A
ngul
ar R
econ
stitu
tion
a b'
c
d'
e'
f'
g'
Proj
ectio
ns 2
and
3
Rib
osom
e A
ngul
ar R
econ
stitu
tion
Com
mon
line
s
AN
GU
LA
R R
EC
ON
STIT
UT
ION
Cal
cium
rele
ase
chan
nel
RyR
1
Cro
ssin
ocor
rela
tion
func
tion
Icos
ahed
ral s
ymm
etry
Imag
e 1
Imag
e 2
Dis
tribu
tion
of c
hara
cter
istic
vie
ws
- C
6 H
SV-1
FREA
LIG
N
(Fou
rier R
econ
stru
ctio
n an
d A
LIG
Nm
ent)
The
algo
rithm
s in
FR
EALI
GN
hav
e ef
ficie
nt p
roce
dure
s fo
r re
finin
g 3D
stru
ctur
es b
y w
orki
ng e
ntire
ly in
Fou
rier s
pace
.
N. G
rigor
ieff
/ Jou
rnal
of S
truct
ural
Bio
logy
157
(200
7) 1
17–1
25
3d m
odel
2d
pro
j Im
ages
st
ack
FT o
f pro
j FT
of I
m
Mat
chin
g pr
oced
ure
CTF
re
finem
ent
New
3D
3D F
T FT
-1
EM m
grs
Rec
omm
enda
tions
1.D
on’t
star
t fro
m a
sym
met
rical
vie
w.
2.Tr
y to
sta
rt fro
m th
e ge
nera
l (co
mm
on) v
iew,
then
the
seco
nd c
an b
e sy
mm
etric
al.
3.Tr
y to
use
as
man
y D
IFFE
REN
T vi
ews
as p
ossi
ble,
idea
lly
perp
endi
cula
r to
each
oth
er.
4.D
o no
t use
a s
eque
nce
of s
imila
r vie
ws,
the
prog
ram
will
be c
onfu
sed!
5.
If th
e st
anda
rd d
evia
tion
of p
eak
heig
hts
star
ts to
incr
ease
, it
mea
ns th
at th
e pr
oces
s is
sta
rting
to d
iver
ge.
You
will
not g
et a
reas
onab
le s
olut
ion.
6.
Che
ck th
e an
gula
r dis
tribu
tion
of p
roje
ctio
ns
Met
hods
of o
rient
atio
n de
term
inat
ion:
1.
Con
ical
tilt.
It is
mor
e ef
ficie
nt fo
r neg
ativ
ely
stai
ned
sam
ples
with
a p
refe
rabl
e or
ient
atio
n.
M
isse
d co
ne
Le
schz
iner
AE,
Nog
ales
E. T
he o
rtho
gona
l tilt
reco
nstr
uctio
n m
etho
d:
an a
ppro
ach
to g
ener
atin
g si
ngle
-cla
ss v
olum
es w
ith n
o m
issi
ng c
one
for a
b in
itio
reco
nstr
uctio
n of
asy
mm
etric
par
ticle
s. J
Str
uct B
iol.
2006
M
ar;1
53(3
):284
-99
2. A
ngul
ar re
cons
titut
ion.
It re
quire
s go
od s
igna
l/noi
se
ratio
, nee
ds c
lass
ifica
tion
3. C
omm
on li
nes
in F
ourie
r spa
ce a
nd P
FT a
re m
ostly
us
ed a
t ana
lysi
s of
par
ticle
s w
ith ic
osah
edra
l sy
mm
etry
4.
Pro
ject
ion
mat
chin
g, th
e m
ost p
opul
ar te
chni
que,
requ
ires
an in
itial
mod
el.
5. F
REA
LIG
N -
impl
emen
ted
in R
elio
n, F
ourie
r spe
ctra
m
atch
ing,
nee
ds a
n in
itial
mod
el
Ref
eren
ces:
1.R
adon
, J. (
1917
) Ube
r di
e B
estim
mun
g vo
n Fu
nktio
nen
durc
h ih
re In
tegr
alw
erte
lä
ngs g
ewis
ser
Man
nigf
altig
keite
n. B
er. S
achs
. Aka
d. W
iss.
Leip
zig.
Kl.,
69,
110
7-11
14
2.C
row
ther
, .A
., D
eRos
ier,
D.J.
, and
Klu
g,A
. (19
70) T
he r
econ
stru
ctio
n of
a th
ree-
dim
ensi
onal
stru
ctur
e fr
om p
roje
ctio
ns a
nd it
s app
licat
ion
to e
lect
ron
mic
rosc
opy.
Pr
oc. R
.Soc
. Lon
d, 3
17, 3
19-3
40
3.Va
n H
eel,
M. (
1987
) Ang
ular
rec
onst
itutio
n: a
pos
teri
ori a
ssig
nmen
t of p
roje
ctio
n di
rect
ions
for
3D r
econ
stru
ctio
ns. U
ltram
icro
scop
y, 21
, 114
-126
4.
Sery
shev
a, I.
, Orlo
va, E
.V.,
Sher
man
, M.,
Chi
u, W
., H
amilt
on, S
., a
nd v
an H
eel,
M.,
(199
5) T
he sk
elet
al m
uscl
e ca
lciu
m-r
elea
se c
hann
el in
its c
lose
d st
ate
visu
aliz
ed b
y el
ectr
on m
icro
scop
y an
d an
gula
r re
cons
titut
ion.
Nat
ure
Stru
ct. B
iol.
, 2, 1
8-14
5.
Rad
erm
ache
r, M
. (19
88) T
he th
ree-
dim
ensi
onal
rec
onst
ruct
ion
of si
ngle
par
ticle
s fo
rm r
ando
m a
nd n
on-r
ando
m ti
lt se
ries
. J. E
lect
ron
Mic
rosc
. Tec
h. 9
, 359
-394
6.
Penc
zek,
P.,
Gra
ssuc
i, R
.A.,
and
Fran
k, J.
(199
4) T
he r
ibos
ome
at im
prov
ed
reso
lutio
n: N
ew te
chni
ques
for
mer
ging
and
ori
enta
tion
refin
emen
t in
3D
cryo
elec
tron
mic
rosc
opy
of b
iolo
gica
l par
ticle
s. U
ltram
icro
scop
y, 53
, 251
-270
7.
Fulle
r SD
, But
cher
SJ,
Che
ng R
H, B
aker
TS
(199
6) T
hree
-dim
ensi
onal
re
cons
truc
tion
of ic
osah
edra
l par
ticle
s--t
he u
ncom
mon
line
. J S
truc
t Bio
l. 11
6, 4
8-55
.
Ref
eren
ces
Grig
orie
ff, N
. 20
07.
FREA
LIG
N: h
igh-
reso
lutio
n re
finem
ent o
f sin
gle
parti
cle
stru
ctur
es. J
Stru
ct B
iol.
157:
117–
125.
Si
ndel
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