Advanced biochemistry and its methods Lectures 4 and 5 Lukáš Žídek lzidek@chemi.muni.cz Finkelstein and Ptitsyn: Protein Physics, Academic Press 2002 Daune: Molecular Biophysics, Molecular Biophysics, Oxford University Press 1999 □ in? - = Lukáš Zídek C6215 1/146 Amino acids connected by peptide bonds Protein structure = conformation defined by torsion angles (0, ^ X1 , • • •) Lukáš Zídek C6215 2/146 h—ry j H"2 Gly (G) H-ry r Ala (A) h—ry aw j H" rf3 Ser (S) H-N Cľ2(Hľ2), N' 'VÍ™i HT3 \ | H" hP3' Pro (P) H-ry P'1W1), Val (V) I C52(H52)3 H-N T?1 — C51(H51)3 I H" H?2 Leu (L) H—N ^V— C51(H51) °^c^C_C\"""cT2(hT2)3 | H° HP I ď H522 I V / H-Ň C-rŕ2 j H* rf3 Asn (N) I Hľ2 ,0«1 H—N |Hí HP2 hÍ21 Gin (Q) , / \ H5-^C51 V-2—hf2 I \ / h—ry J!—cy j H" HP3 Phe (F) W1 O11 hfi \ f1 / h—ry ď—cy vri HS u: H — \^—Cŕ2H52 Asp (D) i p12 p' h—Ň p<—c° a2HE2 J H V Glu (E) HJ 2 T--NWl Lys (K) ^21 Hf V—Hl22 \. /ľ HT3HT2 T-CX H-\ /-v / j H" HP3 -Hl12 Thr (T) h—ry s^HT I H" HP3 Cys (C) lle(l) I H72 C(H«) H-N T)ľ_s* \ľ —J Met (M) Tyr (Y) NeJ__£2 rf2 \ A Í cVr/ W *3 j H" V Trp (W) Hi3 Arg (R) f2 I \\ / h—n ď—rŕ1 ■y "V v His (H) □ rS1 5 ^) (\(y Lukáš Žídek C6215 3/146 Amino acid sequence SAKIIHLTDDSFDTDVLKAILVDFW AEWCGPCKMIAPILDEIADEYQGKL TAPKYGIRGIPTLLLFKNGEVAATK VGALSKGQLKEFLDANLA Lukáš Žídek C6215 4/146 Conformation of protein backbone regular universal repetitive motifs o-helix antiparallel /3-sheet parallel /3-sheet Lukáš Žídek C6215 5/146 Protein samples in biochemistry: many molecules with multiple possible conformational states in thermal equilibrium (statistical) thermodynamics Energy U: First law: AU = J3^ + J/V^ heat work Second law: TAS > Q Entropy S = filnft (ft = number of microstates, combinations) Taken together, AU - TAS < 0 if W = 0, including work due to expansion (pA V = 0) A = U - TS (Helmholtz free energy) has minimum at equilibrium at constant temperature & volume d T = 0, d V = 0. Enthalpy H= U + pV: G = H - TS (Gibbs free energy) has minimum at equilibrium at constant temperature & pressure d T = 0, dp = 0 Lukáš Žídek C6215 9/146 Boltzmann's law: numbers of molecules in states 1 and 2 of the most probable macrostate (with the highest number of microstates): Ol = e-(Ui-U2)/RT n2 "Small" energy is < RT « 2 500 J/mol at 300 K (room temp.) Ideal gas: Vm = 0.0224 m3, patm = 105 Pa patm = 2 240 J/mol Liquid water: \/m = Mr/p = 1.8x10~5 m3 patm l/m = 1.8 J/mol 1/« H, /A « G in biochemistry Lukáš Žídek C6215 10/146 Chemistry: electromagnetic force only Coulomb's law: F = 1 QiQt 4-K60 ŕ U = / Fdŕ = Q1Q2 f 1 4ne0 OO OO 1 QlQ2 47ľe0 Force is a vector: F = t^-^J^ 47reo ľc unit vector Electric intensity: E 1 Q . r 47re0 r2 ' r • U = itto^ if expressed in kJ/mol Lukáš Zídek C6215 11/146 Quantum mechanics O Oa reference energy lower energy q^q higher energy <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 12/146 1000 o -1000 h o bond 0.2 r / nm 0.4 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 13/146 • Define primary structure • Covalent bonds defining tertiary structure: • Metal coordination • Disulfide bridges S-S bridges important (and frequent) in extracellular proteins but play marginal structural role in intracellular proteins: Exchange with glutathione (AG « 0) 7Glu Cy s-S-S-Cy s +2 Cy s-S H v-T-' Giy protein 7 7GIU 7GIU Cys-SH HS-Cys+ Cys-S-S-Cys N-r"-' Giy Giy protein 3 3 les reference energy <2> ^Cbi lower energy IMPOSSIBLE ! Lukáš Zídek C6215 15/146 les 0.1 0 -0.1 0 0.2 r / nm rmin ropt 0.4 Lukáš Zídek C6215 16/146 0.1 o E 0 -0.1 I 1 \Pauli (approximation)" Total / Dispersion 0 0.2 r / nm rmin ropt 0.4 Lukáš Zídek C6215 17/146 intermolecular energy: relative repulsive energy is identical relative attractive energy =-1/ r total relative intermolecular attractive energy =-(1/7+1/5+1/7+1/5) =-4.114 reference energy 1/9 * \n<— V total relative intermolecular attractive energy =-(1/5+1/3+1/9+1/7) =-4.724 lower energy -K1/7 -►1/9 © (3$©i© © $ total relative intermolecular attractive energy =-(1/5+1/3+1/9+1/7) =-4.724 lower energy Lukáš Zídek C6215 18/146 ulsion in proteins van der Waals interactions • Dispersion force: universal (polar and nonpolar molecules/groups) backbone and sidechains • Pauli repulsion: steric hindrance - limits possible torsion angles backbone: (a;) Ramachandran diagram sidechains: x\x2,... Lennard-Jones potential: U = U opt Lukáš Zídek C6215 20/146 Atom--atom l/0pt / kJ mol-1 ropt / nm rmin/nm He-- •He 0.05 0.28 0.25 -H-- •H- 0.50 0.24 0.20 -C-- •C- 0.50 0.34 0.30 -N-- • N- 0.85 0.31 0.27 -0-. •0- 0.95 0.30 0.27 Lukáš Žídek C6215 21/146 Repulsion of backbone C and N only Repulsion including backbone amide H and O Repulsion including Repulsion including side chains (all, Charged groups (ions): F = 1 Q^Q2 47re0 r2 U = 1 47re0 AG = 460 kJ/mol for charges 0.3 nm appart Lukáš Zídek C6215 26/146 h—ry j H"2 Gly (G) H-ry r Ala (A) h—ry aw j H" rf3 Ser (S) H-N Cľ2(Hľ2), N' 'VÍ™i HT3 \ | H" hP3' Pro (P) H-ry P'1W1), Val (V) I C52(H52)3 H-N T?1 — C51(H51)3 I H" H?2 Leu (L) H—N ^V— C51(H51) °^c^C_C\"""cT2(hT2)3 | H° HP I ď H522 I V / H-Ň C-rŕ2 j H* rf3 Asn (N) I Hľ2 ,0«1 H—N |Hí HP2 hÍ21 Gin (Q) , / \ H5-^C51 V-2—hf2 I \ / h—ry J!—cy j H" HP3 Phe (F) W1 O11 hfi \ f1 / h—ry ď—cy vri HS u: H — \^—Cŕ2H52 Asp (D) i p12 p' h—Ň p<—c° a2HE2 J H V Glu (E) HJ 2 T--NWl Lys (K) ^21 Hf V—Hl22 \. /ľ HT3HT2 T-CX H-\ /-v / j H" HP3 -Hl12 Thr (T) h—ry s^HT I H" HP3 Cys (C) lle(l) I H72 C(H«) H-N T)ľ_s* \ľ —J Met (M) Tyr (Y) NeJ__£2 rf2 \ A Í cVr/ W *3 j H" V Trp (W) Hi3 Arg (R) f2 I \\ / h—n ď—rŕ1 ■y "V v His (H) □ rS1 5 ^) (\(y Lukáš Žídek C6215 27/146 Polar molecules Permanent electric dipoles: zero net charge but partial charges ±q separated by distance d polar groups in molecules Lukáš Žídek C6215 28/146 h—ry j H"2 Gly (G) H-ry r Ala (A) h—ry aw j H" rf3 Ser (S) H-N Cľ2(Hľ2), N' 'VÍ™i HT3 \ | H" hP3' Pro (P) H-ry P'1W1), Val (V) I C52(H52)3 H-N T?1 — C51(H51)3 I H" H?2 Leu (L) H—N ^V— C51(H51) °^c^C_C\"""cT2(hT2)3 | H° HP I ď H522 I V / H-Ň C-rŕ2 j H* rf3 Asn (N) I Hľ2 ,0«1 H—N |Hí HP2 hÍ21 Gin (Q) , / \ H5-^C51 V-2—hf2 I \ / h—ry J!—cy j H" HP3 Phe (F) W1 O11 hfi \ f1 / h—ry ď—cy vri HS u: H — \^—Cŕ2H52 Asp (D) i p12 p' h—Ň p<—c° a2HE2 J H V Glu (E) HJ 2 T--NWl Lys (K) ^21 Hf V—Hl22 \. /ľ HT3HT2 T-CX H-\ /-v / j H" HP3 -Hl12 Thr (T) h—ry s^HT I H" HP3 Cys (C) lle(l) I H72 C(H«) H-N T)ľ_s* \ľ —J Met (M) Tyr (Y) NeJ__£2 rf2 \ A Í cVr/ W *3 j H" V Trp (W) Hi3 Arg (R) f2 I \\ / h—n ď—rŕ1 ■y "V v His (H) □ S1 5 ^) (\(y Lukáš Žídek C6215 29/146 Moment of forces (torque) rotates the dipole I Q 0 if d « r Ar Ar 2 Ar = c/cose F= F Lukáš Zídek C6215 30/146 Charge Q - permanent dipóle q d Charge and permanent dipóle in the same molecule 1 qOd Aireo r r Charge and permanent dipole in different molecules (U) = - 1 1 qQd\ 3RT \4ire0 r r J Lukáš Zídek C6215 31/146 Why d/r ? Potential energy of rotating dipole from perpendicular orientation to orientation tilted by 0 from electric force lines: r+Ar r-Ar u = J F^rf+ J F2dr r+Ar r—Ar 47re0 J r2 47re0 1 ■ôŕ = qQ 2Ar 1 dqQ 47re0 r2 47re0 r2 cos 6 Lukáš Zídek C6215 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O 32/146 Permanent e Why ( -)2/3RT? orientation (9) is averaged in solution Averaging in general: (X) = Yl P\X\ —> J P{u)X(u)du Pf probability that X = X,; P(u) probability that X = X{u) Averaging of electric dipoles: u = cos 9 orientation; ^ = = - sin 9 - sin 9d9 = du U = -^l-^o cos 9 = -^^u energy of a dipole tilted by 9 Boltzmann: P(u) = z-^e~u^/RT = Z"1e^; w = Z = sum of all possible euw ("partition function"): 7T -1 Z = J P(cos 9) sin #d# = / -euwdu = o 1 w □ S Lukáš Zídek C6215 33/146 -1 (U) P(u)U(u)du RTw -1 e^ + e e"" - e euwudu = RT I w ew - e — w — w — w -1 -1 where / ue~uwdu was solved using the chain rule. 1 If w is small (relatively small dipole relatively far from Q), e±w ^1 ±w+±w2±lw3 + --- RT ( wew+e~w _ 1 III \ VV gW_0—IV 1 (M,-1)9»-(tl,+1)9-» w(ew+e-"')-(e"'-e-"') III _ 1/1/ III _ 1/1/ qW_0— W ew - e~w « 1 + i/ih-----1+iv- ,I/V 2w but H^e"" + e~w) - (ew - e~w) more tricky: W(ew + e-wj (Qw _Q-w}^ w(2+wz + ...) - (2w+±w3 + •••) (2w + IV3 H----) - (2m/+ gW3 H----) : I"3 AT (W/_1)eM'-(^+i)e L l/V L— l/V RT^— 2w RTw2 1 1 QOÍQ 3fl7 V 4vreo r2 Lukáš Zídek C6215 34/146 4 charges in space =4> must be analyzed in 3D d i« r x □ s Lukáš Zídek C6215 35/146 Permanent dipole - d^- permanent dipole q2 d2 Permanent dipoles in the same molecule U = _L^l*^L^k (Sjn0 Sin02cos(0i - fa) - 2 cos ^ cos#2) 47re0 r r r Permanent dipoles in different molecules (U) = - 1 giCfecr|Cfe\ 3RT \4ne0 r r r J Lukáš Zídek C6215 36/146 Calculation is even more tedious, analysis of all forces gives 47T60 r vr r \ r r which can be expressed in terms of angles 6\, 6>2, i, fall = -X- — — — (sin eA sin 92 cos(0i - 2) - 2 cos QA cos 02) 47T60 r r Probability that the dipoles have a particular orientation is again given by the Bolzmann's law P(f91,02, i, 2) = Z-1e-^1'^1^/Hr, but (7 depends on 4 angles 0!, 6>2, fa, 2. Therefore, averaging (integration) must be performed over all 4 angles. Lukáš Zídek C6215 37/146 Induced electric dipoles: polar and nonpolar groups in molecules the induced dipole is proportional to the inducing force: qd = ae$E Ě is electric intensity (F/q, force per unit charge) a is polarizability (how easy is to move electrons) Charge Q - induced dipole q d Lukáš Žídek C6215 38/146 We already derived that U = -——^^-cosO = -qdE cos 9 47ie0 r2 If we assume that the dipole is induced in the direction of Ě, at each point of the molecule, dUř = -qd • dĚ' = -ae0Ěř • dĚ' = -^ae0d(Eř)2 U=~ /-0d(E')2 = -\ae0E* = -\ae0 (^^) o Lukáš Zídek C6215 39/146 In principle, the same relation like permanent dipoles □ i5P Lukáš Žídek C6215 40/146 In reality vibrations: (U) = -3hau/4r6 (identical molecules) □ in? - = Lukáš Žídek C6215 41/146 ctions Interaction Energy ion - ion ion - permanent dipóle - in different molecules permanent dipóle - permanent dipóle - in different molecules charge - induced dipóle permanent dipóle - induced dipóle - in different molecules induced dipole - induced dipole c Q1Q2 c9^- cos 9 C2 q2 d2 Q2 3RT cQ1diQ2Qf2/ir 2C2 Q2d2q2d2 3RT -6 C2e0 cxQ2 2 ŕ C2e0^ŕ(3cos2^+1) — C2 a q2d2 e0 2 v\ +h>2 r6 C = 1 /47re0, K = sin 9^ sin 92 cos(01 - 02) - 2cos 9^ cos92 5 >0 Q.O Lukáš Zídek C6215 42/146 teins backbone (C=0, N-H =4> dipole of a-helices) sidechains (nonpolar/polar/charged) WATER □ rS1 Lukáš Zídek C6215 43/146 Interaction of charges with water dipoles greatly reduces interaction between charges Lukáš Zídek C6215 44/146 atic interactions • polarization/orientation of atoms/groups in the molecule • orientation of solvent molecules o to maximize energy (enthalpy) of their electrostatic interactions at the cost of lowering entropy • water does not work as an electrostatic "barrier" • formally decreases constant in Coulomb's law =4> increases e0 -> ere0 F_ _J_Q1Q2 47rererj f2 AG = 6 kJ/mol for charges 0.3 nm appart Lukáš Zídek C6215 45/146 Effect of orientation of water molecules, water does not need to be between charges □ s Lukáš Žídek C6215 46/146 water *9 A A □ rS1 ~ = Lukáš Zídek C6215 47/146 water Lukáš Žídek C6215 48/146 ein sufrace □ - = Lukáš Zídek C6215 49/146 Lukáš Žídek C6215 50/146 protein Lukáš Žídek C6215 52/146 0.30 nm v 0.18 nm 4 >\ 0.28 nm Lukáš Žídek C6215 53/146 Hydrogen between atoms shortens their optimum distance Atom--atom l/0pt / kJ rnol-1 ropt / nm rmin/nm He-- •He 0.05 0.28 0.25 -H-- •H- 0.50 0.24 0.20 -C-- •C- 0.50 0.34 0.30 -N-- •N- 0.85 0.31 0.27 -NH- •N- 0.31 -0-. •0- 0.95 0.30 0.27 -OH- • •0- 0.28 l/(H-bond)= 20 kJ/mol Lukáš Žídek C6215 54/146 void space less than in ice Lukáš Zídek C6215 57/146 AG = 0 Lukáš Žídek C6215 59/146 AG = -12kJ/mol Lukáš Žídek C6215 60/146 Hydrophobic cyclohexane: O.IMPagas AH=-30 kJ/mol TAS = -12kJ/mol AG = - 18 kJ/mol AH=-30kJ/mol TAS = -40kJ/mol AG = + 10 kJ/mol AH= OkJ/mol 7AS = - 28 kJ/mol AG = + 28 kJ/mol 9 entropy AH= -3kJ/mol 7AS= -3kJ/mol AG = 0 kJ/mol crystal 000 ooo 1M solution AH= +3kJ/mol ľAS = -25kJ/mol AG = + 28 kJ/mol □ r5P Lukáš Zídek C6215 61/146 _2Q 1_1_1_1_1_1 O 20 40 60 80 100 T/°C Lukáš Žídek C6215 62/146 • orientation of solvent molecules • to maximize energy (enthalpy) of their hydrogen bonds at the cost of lowering entropy Lukáš Zídek C6215 63/146 6 possible orientations: entropie contribution -FľTln6 = -15kJ/mol <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 64/146 3 possible orientations: entropie contribution -FľTln3 = -7.5kJ/mol <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 65/146 • packing nonpolar sidechains reduces entropy cost (less water molecules with restricted orientation) • the most important contribution to -AG Ala: 2.5kJ/mol, Leu: 8kJ/mol, Phe: 12kJ/mol • no specificity Lukáš Žídek C6215 66/146 Loss of compactness = /* volume V during denaturation High cooperativity (sharp drop of AG) Packed side chains in compact folded proteins No side chain rotation possible 1 side chain orientation: entropic contribution -RT\n 1 = 0 Less compact protein ("molten globule") Reduced dispersion energy (less -H AH > 0) but side chain rotation possible ( S - TAS 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 82/146 I 4 III 02 Intensity Distribution of Diffracted Light Figure 2 sin 0 Higher Diffracted Orders -3k -2k -k! Ik 2k 3k ■ ■ ■ ■ ' Uli l+U 2X -2X -X d d d Diffracted Light Intensity Maximum Intensity _^ 2X 3X d d d U O o era Detector Screen 6 p 9 73 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 85/146 Lukáš Zídek C6215 86/146 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 87/146 Lukáš Žídek C6215 88/146 Lukáš Žídek C6215 89/146 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 90/146 Lukáš Žídek C6215 91/146 Lukáš Žídek C6215 92/146 Lukáš Žídek C6215 93/146 (1) Scattered wave is added to the original wave: A cos (t- I)) +/If cos (t- |) - 0) = /\cosa + /\fcos(a - 0) Scattered amplitude is a small fraction (f) of the original one (2) We know that wave interacting weakly with molecules is apparently slightly retarded (c' = c/n, n = refractive index) Original wave: Acos (t - |)) = /Acosa Retarded wave: /A'cos(^ (t - f)) =/\/cos(^ (t - § - ^z)) = /\7 cos (a — 5) = /\7 cos 5 cos a + /A' sin S sin a « A' cos a + /A'£ sin a because n is only slightly > 1 n - 1 small =4> 5 is small (we use arc lenght to measure angle and for a small angle S, cos S « 1, sin S « 5) (3) /A cos a + /Af cos(a -(/)) = Af cos a + Ä5 sin a if /A = Ä, f = ô, (j) = 7r/2 (because sin a = cos(a - tt/2)) Lukáš Žídek C6215 94/146 5» 2« • 2 •• •• I ••• i m • •••• • »• • ! • A'* *.•! S líTI •/!• •Vili* / V V ! Lukáš Zídek C6215 95/146 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Žídek C6215 96/146 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 100/146 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 102/146 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 103/146 Lukáš Žídek C6215 104/146 • a Perfect lens in focus provide contrast in intensity of scattered vs. original wave if the scattered wave is absorbed by the sample o b Perfect lens in focus provide no contrast in intensity of scattered vs. original wave if the scattered wave is not absorbed by the sample, but only phase-shifted by 90° • c Imperfect and defocused lens provide contrast in intensity of scattered vs. original wave if the scattered wave is absorbed by the sample • d Defocus and spherical aberration of lens provide contrast in intensity of scattered vs. original wave if the scattered wave is not absorbed by the sample, but only phase-shifted by 90°. Defocus and spherical aberration introduce another phase shift scattered have oposite phase and cancel each other. Lukáš Žídek C6215 105/146 Photons scatter as waves =4> limited resolution resolution < 0.61 X/n (A = wavelegth, n = refractive index =4> A « 0.1 nm (distances of atoms in molecules), X-rays Lens are not available for X-rays (A ^ 0.1 nm) no material has sufficient refractive index SOLUTIONS: o Microscopy with electrically charged waves electrons scatter as waves electron beams are bent in electromagnetic field =4> Electron microscopy • Analysis of diffraction patterns intensity enhanced if molecules are aligned in crystals =4> X-ray crystallography applicable also to electron and neutron waves Lukáš Žídek C6215 106/146 Transmission Electron Microscope Electron source: Thermal emission from heated cathode Focussing: Electro-magnetic Lenses Detection: Phosphor screen or CCD camera (former times: negative) Vacuum! Lukáš Žídek C6215 107/146 Proteins in vitrous ice, can reach atomic resolution Lukáš Žídek C6215 108/146 Amplitude vs. phase objects Macromolecules in water / vitreous ice are phase objects Undisturbed . „ ()„ Wavelength Refractive Ampmude ^ ,ndex(R., = n ( Rl = n L" Amplitude Specimen [ Phase Specimen J- ' 1 and Phase Specimen [ *<-180 Object Lens Image O o O" cd" o < cd Lukáš Zídek C6215 109/146 Signal to noise ratio Lukáš Žídek C6215 110/146 Images contain diffrent views of possibly different molecules Classification and averaging (principal component analysis) Lukáš Žídek C6215 112/146 Iterative process: 2D projections are calculated from a 3D model alignment and classification are improved iteratively Lukáš Žídek C6215 113/146 Lukáš Žídek C6215 115/146 stals Lukáš Žídek C6215 117/146 Lukáš Žídek C6215 120/146 Lukáš Žídek C6215 121/146 Lukáš Žídek C6215 122/146 Lukáš Žídek C6215 123/146 Real space cat Circular rainbow scale of phases i i i Fourier transform Linear intensity scale of amplitude size Fourier amplitudes and phases F(hkl) = V J J J p (x y z) exp[2^i(hx + ky + lz)} d x dy d z x=0y=0 z=0 Observed amplitudes <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 124/146 Lukáš Žídek C6215 125/146 Electron density equation & PHASE PROBLEM Lukáš Žídek C6215 126/146 • Direct interpretation of amplitudes mutual positions of atoms calculated from amplitudes for simple molecules (Patterson function/map) a Using heavy atoms • Molecular replacement Diffraction back-calculated from a known structure similar to the studied proteins Orientation and position of the molecule in the crystal obtained by searching for the match of diffraction patterns (measured vs. back-calculated) Calculated phases used for the unknown molecule Lukáš Žídek C6215 127/146 o o o o o o Lukáš Žídek C6215 128/146 Known structure Manx cat Fourier transforn, try different orientations Observed amplitudes Phases unknown! Fourier cat Calculated amplitudes and phases FT of Manx cat Wrong orientation! Lukáš Zídek C6215 129/146 Observed amplitudes (tailed cat), calculated pha es (Manx cat) Inverted Fourier transform Even the tail becomes visible! Lukáš Zídek C6215 130/146 Model building & resolution Lukáš Žídek C6215 131/146 Model building & refinement Lukáš Žídek C6215 132/146 R-factor, Rf factor Film X-ray tube X-ray beam Diffracted x-rays Observed reflections Model 1 1 1 ^_ F 1— * • • 1 1 Fr i ^ • i 1 ' » • / Calculated diffraction pattern R = R-factor ^ H^bsl -fcl^cafcll AM l^obsl Rfree faCt0r 5^ ligotal -tlFcaidl fifree = hklcJ hklcJ Lukáš Zídek C6215 133/146 UV/VIS spectrophotometry absorption, transition of electrons to higher orbitals concentration, content of aromatic amino acids, heme, prosthetic groups CD spectroscopy absorption differences of polarized light by chiral molecules overall content of secondary structures IR spectroscopy absorption, transition of nuclei to higher vibration states y structure Random coil o-helix /3-sheet 80 j- 70 -60 - _50 _1_1_1_1_1_1_1_ 170 180 190 200 210 220 230 240 250 A / nm Lukáš Žídek C6215 135/146 • NMR spectroscopy precession of magnetic moments of nuclei in magnetic field magnetic moments are slightly aligned in a static magnet axis of alignment is tilted by electromagnetic (radio) waves aligned magnetic moments precess about the static field resulting oscillating magnetic field is measured we do not observe the applied electromagnetic waves interactions of magnetic moments (mutual, with electrons) resolution, structural information atomic resolution structure determination, dynamics, interactions • molecule /* magnetic moment S 10"97 rads-1T"1 % e~ 1/2 -182.000 100 1H 1/2 0.277 99.98 13C 1/2 0.067 1.1 14N 1 0.019 99.6 15N 1/2 -0.027 0.4 170 5/2 -0.036 0.04 19F 1/2 0.252 100 31 p 1/2 0.108 100 129Xe 1/2 -0.075 24.4 quadrupolar (relax fast) rare isotopes (enrichment) Lukáš Žídek C6215 137/146 in equilibrium (spherical symmetry) Lukáš Žídek C6215 138/146 jl-B Boltzmann distribution: P(0) oc e kzT = e^7" Precession (angular momentum in afield): ú u - njIb_ - V3kBT -7B Lukáš Zídek C6215 139/146 x reproduced from M. H. Levitt: Spin Dynamics Lukáš Žídek C6215 142/146 nd electrons NOESY spectra Nuclear Overhauser effect: result of dipole-dipole interactions Peak intensities are proportional to nuclear Overhauser effect 9.0 0.5H 1.0H E 1-5H Q. Q. 2.0^ 2.5^ 3.0H 8 5 O Ji Ô 8.0 7.5 7.0 6.5 0 o O o o 9.0 8.5 0 o ň 8 0 o Q h0.5 M.o H .5 h2.0 h2.5 h3.0 8.0 7.5 C02 - 1H (ppm) 7.0 6.5 □ ť3? - = Lukáš Zídek C6215 144/146 user effect Nuclear Overhauser effect proportional to 1 /d6 {d = distance) Lukáš Zídek C6215 145/146 lation Model of the protein built from known distances