Advanced biochemistry and its methods Lecture 4 Lukáš Žídek lzidek@chemi.muni.cz Finkelstein and Ptitsyn: Protein Physics, Academic Press 2002 Daune: Molecular Biophysics, Molecular Biophysics, Oxford University Press 1999 Žídek: Strukturní biochemie (skripta k přednášce C9530), kapitoly 2, 6, A □ ť3? - = Lukáš Zídek C6215 1/73 Amino acids connected by peptide bonds Protein structure = conformation defined by torsion angles (0, ^ X1 , • • •) Lukáš Zídek C6215 2/73 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 — \^—052H52 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 3/73 Amino acid sequence SAKIIHLTDDSFDTDVLKAILVDFW AEWCGPCKMIAPILDEIADEYQGKL TAPKYGIRGIPTLLLFKNGEVAATK VGALSKGQLKEFLDANLA Lukáš Žídek C6215 4/73 Conformation of protein backbone regular universal repetitive motifs o-helix antiparallel /3-sheet parallel /3-sheet Lukáš Žídek C6215 5/73 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 9/73 Boltzmann's law: numbers of molecules in states 1 and 2 of the most probable macrostate (with the highest number of microstates): Ol = e-(^-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 Chemistry: electromagnetic force only Coulomb's law: F = 1 QiQt 4-K60 ŕ U = j Fúr' rref = / Far' = QAQ2 [ 1 47Te0 ■ôŕ = 1 QiCk oo oo 47ľe0 Force is a vector: F = -r—^S2- • 47reo unit vector _ 1 Q r ^ Electric intensity: E - r • W = itr9^ if expressed in kJ/mol Lukáš Zídek C6215 11/73 Quantum mechanics O Oa reference energy lower energy q^q higher energy <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 12/73 1000 o -1000 h o bond 0.2 r / nm 0.4 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 13/73 • 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 tap IMPOSSIBLE ! Lukáš Zídek C6215 15/73 les 0.1 0 -0.1 0 0.2 r / nm rmin ropt 0.4 Lukáš Zídek C6215 16/73 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 17/73 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 18/73 Lukáš Žídek C6215 19/73 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 20/73 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 21/73 Repulsion of backbone C and N only (|> Lukáš Žídek C6215 22/73 Repulsion including backbone amide H and O Repulsion including Repulsion including side chains (all, olar molecules .Charged molecules (ions) . Neutral polar molecules Lukáš Zídek C6215 26/73 Charged groups (ions): F = 1 Q^Q2 4ire0 U = 1 0^2 47re0 AG = 460 kJ/mol for charges 0.3 nm appart Lukáš Zídek C6215 27/73 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 28/73 Polar molecules Permanent electric dipoles: zero net charge but partial charges ±q separated by distance d polar groups in molecules Lukáš Žídek C6215 29/73 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 30/73 I F I Q e I Q ® Ar Ar 2Ar =-d cos (7C-9) 2Ar = c/cose F= F d « r Lukáš Zídek C6215 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O 31/73 Charge Q - permanent dipóle q d Charge and permanent dipóle in the same molecule u=_LS?í!coeí 47re0 r r Charge and permanent dipole in different molecules w = --^-(-^-^)2 x ' 3RT \4neo r r J Derived in Žídek: Strukturní biochemie, dodatek A Lukáš Zídek C6215 32/73 Permanent dipole qr1 - c/i — permanent dipole q2 d2 Permanent dipoles in the same molecule U = _L^l*^L^k fs\nd Sin02cos(0i - fa) - 2 cos ^ cos#2) 47re0 r r r Permanent dipoles in different molecules (U) = - 1 Qi Q2 Cf| Cfe 3f?7 V 47re0 r r r Derived in Žídek: Strukturní biochemie, dodatek A Lukáš Zídek C6215 34/73 induced dipóle is proportional to inducing force: qd = aeQE Charge Q- induced dipóle ae0E = _^0/vA 1 \2Q2 47re0 / r2 Permanent dipóle q d - induced dipóle ae0E W = -^W4f^-)2íí(1+3cos^) 47ľe0 r2 r2 induced dipóle ae0E - induced dipóle ae0E (dispersion forces) 3hvNA í ae0 \ 1 4 V47ľ6o / r6 Derived in Žídek: Strukturní biochemie, dodatek A Lukáš Zídek C6215 35/73 teins backbone (C=0, N-H =4> dipole of a-helices) sidechains (nonpolar/polar/charged) WATER □ rS1 Lukáš Zídek C6215 36/73 Interaction of charges with water dipoles greatly reduces interaction between charges Lukáš Zídek C6215 37/73 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 = 460 kJ/mol 6 kJ/mol for charges 0.3 nm appart Lukáš Zídek C6215 38/73 Effect of orientation of water molecules, water does not need to be between charges □ rS1 Lukáš Žídek C6215 39/73 water *9 A A □ S - = Lukáš Zídek C6215 40/73 water Lukáš Žídek C6215 41/73 ein sufrace □ rSP - = Lukáš Zídek C6215 42/73 Lukáš Žídek C6215 43/73 protein Lukáš Žídek C6215 45/73 0.30 nm v 0.18 nm 4 >\ 0.28 nm Lukáš Žídek C6215 46/73 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 47/73 void space less than in ice Lukáš Zídek C6215 50/73 AG = 0 <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 52/73 AG = -12 kJ/mol (entropy of water) Lukáš Žídek C6215 53/73 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 54/73 _2Q 1_1_1_1_1_1 O 20 40 60 80 100 T/°C Lukáš Žídek C6215 55/73 • orientation of solvent molecules • to maximize energy (enthalpy) of their hydrogen bonds at the cost of lowering entropy 6 possible orientations: entropie contribution -FľTln6 = -15kJ/mol <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 57/73 3 possible orientations: entropie contribution -FľTln3 = -7.5kJ/mol <□► 4 ^ > 4 = t 4 = > = ^0 Q, O Lukáš Zídek C6215 58/73 • 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 59/73 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