Crystallography 03-03-06

7/21/2019 Crystallography 03-03-06

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X-ray Crystallography

Kalyan Das


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Electromagnetic Spectrum

10-1to 10 nm

400 to 700 nm

10-4to 10 -1nm

10 to 400 nm

700 to 104nm

X-ray radiation was discovered byRoentgen in 1!"#X-rays are generated by bombardingelectrons on an metallic anode

Emitted X-ray has a characteristicwavelength depending upon whichmetal is present#e#g# $avelength o% X-rays %rom Cu-anode & 1#"417 '

E& h& h(c)*

('*& 1+#,!)E(e.*

/R10 um - 10 mm


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X-ray Sources %orCrystallographic Studies

ome Source 2 Rotating 3node

-orbital

5-orbital

-orbital

-absorption1 +

Cu(1*& 1#"401" '6 Cu(+*& 1#"44,, '

Cu(K

)= 1.54015

Cu(*& 1#,!,17 '

Wave-lengths


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Synchrotron X-rays

Electron)positron inection

Storage RingX-ray

X-rays

agnetic 8ieldsElectron)positronbeam


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Crystalli9ation

Slow aggregation process

Protein Sample for Crystallization:

:ure and homogenous (identi%ied by S;S-:3


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Conditions E%%ect Crystalli9ation

- p (bu%%er*- :rotein Concentration- Salt (Sodium Chloride= 3mmonium Chloride

etc#*- :recipitant- ;etergent (e#g# n->ctyl--;-glucoside*- etal ions and)or small molecules

- Rate o% di%%usion- ?emperature- Si9e and shape o% the drops- :ressure (e#g# micro-gravity*


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:recipitant

;rop containing protein sample%or crystalli9ation

anging-drop .apor ;i%%usion

Cover Slip

$ell


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Screening %or Crystalli9ation

p gradient

:recipitan

tConcentration

4 " @ 7 !

10 A

1" A

+0 A

,0 A

:recipitate Crystalline precipitate8iber lieicro-crystals

Small crystals

Bdeal crystal


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3 crystal has long range ordering o% building blocsthat are arranged in an conceptual ,-; lattice#

3 building bloc o% minimum volume de%ines unit cell

?he repeating units (protein molecule* are insymmetry in an unit cell

?he repeating unit is called asymmetric unit2 3crystal is a repeat o% an asymmetric unit

:eriodicity and Symmetryin a Crystal


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3rrangement o% asymmetric unit

in a lattice de%ines the crystalsymmetry#

?he allowed symmetries are +-=

,= 4= @-%old rotational= mirror(m*=and inversion (i* symmetry (D)-*translation#

Rotation D translation & screw

Rotation D mirror & glide

+,0 space groups= ,+ point groups= 14 ravais lattice= and 7 crystal systems


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Crystal

Cryo-loop

;etector


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Diffractin


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ragg ;i%%raction

d

d sin

8or constructive inter%erence +d sin= d- Spacing between two atoms

-3ngle o% incidence o% X-ray- $avelength o% X-ray


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Diffraction from a frozenarginine deiminasecrystal

at CHESS F2-beam line

zoom

1.6 resolution


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!lectrn Density "a#s

4 reslutin electrn $ensity ma# %.5 reslutin electrn $ensity ma#

&rtein 'lvent


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Structure %actor at a point (h==l*

8(h==l*& fneFp G+i(hFDyDl9*H

f2 atomic scattering %actor

/ 2 number o% all atoms

8 is a compleF number

8(h==l*& I8(h==l*IeFp(-i*

/

n&1

:hase :roblem in Crystallography

amplitude

phase

easured intensity

B(h==l*& I8(h==l*I+

ReciprocalSpace

h==l

bacground

(

(h

=-

=l*


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!lectrn Density

Structure 8actor

Electron ;ensity

8(h==l*& fneFp G+i(hF*H

8riedelJs law 8(h* & 8K(-h*


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1. electrn $ensity ma#


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Solving :hase :roblem


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"lecular *e#lacement ("*)

Lsing an available homologous structure astemplate

+$vantages,Relatively easy and %ast to getsolution#3pplied in determining a series o% structures

%rom a nown homologue 2 systematic%unctional= mutation= drug-binding studies

imitatins, /o template structure no solution=Solution phases are biased with thein%ormation %rom its template structure


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smrhus *e#lacement ("*)

eavy atom derivatives are prepared by soaingor co-crystalli9ing

;i%%raction data %or heavy atom derivatives are

collected along with the native data

8:& 8:D 8

:atterson %unction :(u*& 1). I8(h*I+ cos(+u.h*& (r* F (r* dv

strong peas %or in :atterson map when r andrM are two heavy atom positions

h

r


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"ulti#le +nmalus Dis#ersin ("+D)

3t the absorption edge o% an atom= its scattering%actor fano= f + f + if

+tm f f f g 0 -"#0 7#7 Se ,4 -0#! 1#1

8(h==l* & 8(-h=-=-l*anomalous di%%erencespositions o% anomalous scatterers :rotein :hasing

fanoif

f freal

imaginary


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'e-"et "+D

ost common method o% ab initiomacromoleculestructure determination

3 protein sample is grown in Se-et instead o% et#

inimum 1 well-ordered Se-position)7" amino acids

3nomolous data are collected %rom 1 crystal at Se -edge (1+#"7 e.*#

3; data are collected at Edge= Bn%lection= andremote wavelengths


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"$el /uil$ing an$ *efinement


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east-'uares *efinement

5ist-sNuares re%inement o% atoms (F=y=9= and *against observed I8(h==l*I

?arget %unction that is minimi9ed

O& w(h==l*(I8obs(h==l*I - I8cal(h==l*I*+

dO)du&06 u- all atomic parameters


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emetric *estraints in *efinement

Each atom has 4 (F=y=9=* parameters and each parametersreNuires minimum , observations %or a %ree-atom least-sNuares re%inement# 3 protein o% / atoms reNuires 1+/observations#

8or proteins di%%racting P +#0 ' resolution observation toparameter ratio is considerable less#

:rotein Restraints (bond lengths= bond angles= planarity o% anaromatic ring etc#* are used as restraints to reduce thenumber o% parameters


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*-factr

Rcryst& hlI8obs(hl* - 8cal(hl*I ) hlI8obs(hl*I

2ree-*

R-%actor calculated %or a test-set o% re%lectionsthat is never included in re%inement#

R-%ree is always higher than R#

;i%%erence between R and R-%ree is smaller %orhigher resolution and well-re%ined structures


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Radius o% convergence in a least-sNuaresre%inement is= in general= low# >%ten manualcorrections (model building* are needed#

odel uilding and Re%inement are carried outin iterative cycles till R-%actor converges toan appropriate low value with appreciablegeometry o% the atomic model#


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1#0' +#"'

,#"' 4'


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Crystallography 03-03-06

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