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Biomolecules: amino acids, peptides, proteins, nucleic acids, Table: Structures and abbreviations of the standard amino acids of proteins, and the pK values of their ionization groups _________________________________________________________________ Name Structure pK1 (COOH) pK2 (NH3+) pKR (side cahin) _________________________________________________________________ with nonpolar side chains Glycine (Gly) 2.35 9.78 Alanine (Ala) 2.35 9.87 Valine (Val) 2.29 9.74 Leucine (Leu) 2.33 9.74 Isoleucine (Ile) 2.32 9.76 Methionine (Met) 2.13 9.28 Proline (Pro) 1.95 10.64 Phenylalanine (Phe) 2.20 9.31 Tryptophan (Trp) 2.46 9.41 With uncharged polar side chains Serine (Ser) 2.19 Threonine (Thr) 2.09 Asparagine (Asn) 2.14 Glutamine (Gln) 2.17 Tyrosine (Tyr) 2.20 Cysteine (Cys) 1.92 9.21 9.10 8.72 9.13 9.21 10.70 10.46 (phenol) 8.37 (sulfhydryl) __________________________________________________________ With charged polar side chains Lysine (Lys) 2.16 9.06 10.54 (e-NH3+) Arginine (Arg) 1.82 8.99 12.48 (guanidino) Histidine (His) 1.80 9.33 6.04 (imidazole) Aspartic acid (Asp) 1.99 9.90 3.90 (b-COOH) Glutamic acid (Glu) 2.10 9.47 4.07 (g-COOH) __________________________________________________________________ HA H+ + A- (equilibrium constant is K = [H+][A-]/[HA], pK = -log K [H+] = K [HA]/[A-], so -log [H+] = -log K + log [A-]/[HA], so pH = pK + log [A-]/[HA] When pH = pK, [A-] = [HA] For a buffer, in the titration curves, when [HA] = [A-], the pH of the solution is relatively insensitive to the addition of strong base or strong acid. Proteins Biosynthesis: DNA transcription mRNA translation proteins Primary structures: sequences Secondary structures: a-helices, b-strands etc. Tertiary structures: 3-D structures Quaternary structures: compositions, such as dimer, tetreamer etc. Stabilizing interactions in macromolecules 1. Covalent bonds 2. Electrostatic interactions 3. Dipole-dipole interactions 4. Van der Waals interactions 5. Hydrogen bonds 6. Hydrophobic interactions Table: Average Dissociation Energies of Chemical Bonds ______________________________________________ Bond type Bond Energy (kJ/mol) C-H 408 C-C 342 C=C 602 C=N 606 C=O 732 O-H 458 Enzyme catalysis 1. 2. 3. 4. 5. 6. Acid-base catalysis Covalent catalysis Metal ion catalysis Electrostatic catalysis Proximity and orientation effects Preferred binding of the transition state complex 1. Acid-base catalysis CH2OH H A O O H H H OH C O H CH2OH H OH :B- H H OH H a-D-Glucose H O H-B O OH C H H :B- a-Pyridone involves the reaction OH N O N CH2OH H :A HC H H A OH b-D-Glucose - O H OH OH OH H O O H OH H OH H OH H OH linear form O H O O C H :B- H H O O C H v=k[a-pyridone][tetramethyl-a-D-glucose] The bovine pancreatic RNase A-catalyzed hydrolysis of RNA O P O CH2 O Base O H H H H NH H2O N His 12 O OH O P O CH2 O Base O HO CH2 H H O H Base H N+ H H OH O H O P O N OH O H O O P O His 119 O O P O CH2 O Base O H H H H NH H+N O O His 12 P O HO H N H O N H His 119 O P O CH2 O Base O H H H H NH N O OH His 12 O P OH H O N+ N H His 119 2. Covalent catalysis H + N H H N C OH H O H H-A :B Lys HC 2- O3PO + N N+ O CH2 C CO2 + OH- H+ O- O RNH2 OH- OHCO2 H H2C CH3 Acetone Enolate RNH2 R O H2C CH2 H2C - acetoacetate H OCH3 N C Schiff base (w PLP) O H2C H N+ H O CH2 C O- Schiff base (imine) R H + CH2 H N + H N H2C R H2C CH3 3. Metal ion catalysis 1. Metalloenzymes: containing tightly bound metal ions, most commonly transition metal ions such as Fe2+, Fe3+, Cu2+, Zn2+, Mn2+, or Co3+ 2. Metal-activated enzymes: loosely bind metal ions from solution, usually the alkaline earth metal ions Na+, K+, Mg2+, or Ca2+ Three major roles: 1. By binding to substrates so as to orient them properly for reaction 2. By mediating oxidation-reduction reactions through reversible changes in the metal ion’s oxidation state. 3. By electrostatically stabilizing or shielding negative charges Mn+ O CH3 OC O Mn+ C C CH3 C - O O Im Im O- O- O 2+ CH3 - C CH3 Zn O C Im H O O O Im H O C O- Im O Mg2+ O O- Adenine Ribose O P O P O P OO O CH3 O Zn2+ Im - CH3 C CH O - O O + Mn+ 4. Electrostatic catalysis The pK’s of amino acid side chains in proteins may vary by several units from their nominal values 5. Proximity and orientation effects a. Proximity alone contributes relatively little to catalysis b. Properly orienting reactants and arresting their relative motions can result in large catalytic rate enhancement O H3C O NO2 k1 N k2 = 24 x k1[imidazole] NH O H2 C O NO2 k2 N NH R R' R'' Y- R' R R' R'' R R'' Y- Y 6. Preferred binding of the transition state complex Transition state analogues are competitive inhibitors proline racemase - COO C N H H C H + + H N H H planar TS COO- D-proline L-proline C- COON H COON H N+ H pyrrole-2-carboxylate competitive inhibitors COO- D-1-pyrroline-2-carboxylate Lysozyme A. Enzyme structure: E + (NAG)3 poor substrate (NAG)6 is a good substrate, 2-fold smaller kcat than (NAG-NAM)3 Modeling suggested that the fourth NAG needs to be distorted to change to half-chair form Asp52 and Glu35 are close to the cut. For non-enzymatic reaction, oxonium ion can be formed. OR' H C OR' OR' H C O R" R H + +H R R"OH acetal R' O+ C H R R' OR' H C OH O C+ H R Hemiacetal R oxonium ion (resonance-stabilized) When the reaction was run in 18O water, 18O O was incorporated. NAM RO CH2OH C O+ O H3C N H O - OH H O C Glu35 O NAG HO O H3C C Asp52 - O C O O N H O Possible covalent catalysis (need proof) CH2OH H O O O O C CH2 H OR H H NHCOCH3 Asp52 covalent catalysis H Intermediate can be trapped by speeding up its formation and slowing down its decomposition. CH2OH CH2OH O H H OH OH H H O O H H OH NHCOCH3 H H H F H (good leaving group) - O O C CH2-Asp52 F (stabilize the negative charge) MASS and crystal structure showed unambiguously the intermediate formation Serine protease Burst kinetics assay chymotrypsin O H3C O NO2 p-nitrophenyl acetate fast rapid O H3C Enzyme acy-enzyme intermediate + - O NO2 450 nm slow O H3C O- Burst kinetics: A rapid release of p-nitrophenylacetate followed by a slow release of acetate Asp-His-Ser catalytic triad and oxyanion hole to facilitate tetrahedral intermediate The tetrahedral intermediate is mimicked in a complex of Trypsin with Trypsin inhibitor 1013 M-1 Trypsin-BPTI (bovine pancreatic trypsin inhibitor) The side-chain oxygen of Ser95 is in closer than van der Waals contact with the pyramidally distorted carbonyl carbon of BPTI’s scissile peptide KA = Ser195 H Ala 16I O Ca O C N Ca Lys 15I H Asp102 His57 H2C C O O- Asp102 Ser195 H2C H2C C O O- 1 H N CH2 N His57 H N H O N C H O R R' O H CH2 N+ R R' Ser195 H2C N C O- H Tetrahedral intermediate Asp102 H2C C His57 O O- Asp102 Ser195 H2C H2O H N CH2 N H2C C O O- His57 H N CH2 N H O R'NH2 R O Ser195 H2C C R N O H H O R' C O H Acyl-enzyme intermediate Asp102 H2C C O O- Asp102 His57 Ser195 H2C H N CH2 + N H2C C O O- His57 Ser195 H2C H N CH2 N H O H O R O H R C O- O H C O Thermodynamics and Kinetics in Biology Thermodynamics (Greek: therme, heat + dynamis, power) A. The First Law of Thermodynamics: Energy Is Conserved A system is defined as the part of universe that is of interest, such as a reaction vessel or an organism; the rest of the universal is known as the surroundings. H (enthalpy) = U (energy) + PV At constant pressure, DH = DU + PDV = qp – w + PDV = qp – PDV + PDV = qp (heat change) B. The Second Law of Thermodynamics: Entropy Tends to Increase The degree of randomness of a system is indicated by its entropy (S). S = kB ln W (KB = Boltzmann constant; W = the number of energetically equivalent ways) DS universe > 0 C. Free Energy DS > qp/T = DH/T, thus DH – TDS < 0 In 1878, by J. Willard Gibbs, he defined the Gibbs free energy, G = H – TS Spontaneous processes at constant temperature and pressure have DG = DH – TDS < 0 (exergonic) When DG = DH – TDS > 0 (endergonic); DG = DH – TDS = 0 (equilibrium) Table: Variation of reaction spontaneity (sign of DG with signs of DH and DS _____________________________________________________________ DH DS DG = DH-TDS _____________________________________________________________ + The reaction is both enthalpically favored (exothermic) and entropically favored. The reaction is enthalpically favored (exothermic) and entropically opposed. + + The reaction is both enthalpically opposed (endothermic) and entropically favored. + The reaction is both enthalpically and entropically opposed. _____________________________________________________________ D. Chemical Equilibrium and the Standard State For a reaction aA + bB cC + dD DG = cGC + dGD –aGA –bGB DGo = cGCo + dGDo –aGAo –bGBo (reactants and products are in their standard states) DG = DGo + RT ln ([C]c[D]d/[A]a[B]b) At equilibrium DG = 0, so DGo = -RT ln Keq Keq = exp (-DGo/RT) Keq depends on Temperature ln Keq = -DHo/R(1/T) + DSo/R, the plot of ln Keq versus 1/T is known as a van’t Hoff plot. Standard State: 1. Temperature at 25 oC, at neutral pH =7, pressure at 1 atm 2. Consider [H2O] = 1 Elementary Reactions A I 1 I2 P (I: intermediates) P (A: reactant, P: product) k aA + bB + …….+zZ P Rate = k [A]a[B]b…..[Z]z order: a+b+…+z A A P A+B v = d[A]/d[t] = k[A] (first-order reaction, k = s-1) P v = d[A]/d[t] = d[B]/d[t] = k{A][B] (second-order reaction, k= M-1s-1) For first-order Rx: d[A]/[A] = -k d[t] For second-order Rx A+A P ln[A] = ln[A]o - kt d[A]/[A]2 = k d[t] [A] = [A]oe-kt t1/2 = ln2/k 1/[A] = 1/[A]o + kt Transition state theory of enzyme Catalysis Activation energy profile of a reaction. (a) Activation energy (DGo╪) , free energy change (DGo) (b) A comparison of activation energy profiles for catalyzed and uncatalyzed reactions. For a reaction A + B P Rate = -DA/Dt = -DB/Dt = DP/Dt = k+[A][B] – k-[P] k = (kT/h) exp (-DG ╪ /RT) k=Boltzmann constant, h=Planck constant R: gas constant) DGo = -RT lnKeq (Keq = [P]/[A][B]) Keq = k+ / k- (forward reaction rate constant / reverse reaction rate constant ) Steady-state Enzyme Kinetics (simplified scheme) E+S k1 ES k2 E+P k-1 If [S] >> [E], d[ES]/dt = 0 Rate = k2[ES] d[ES]/dt =0 is called steadystate condition. d[ES]/dt = k1[E][S] – k-1[ES] + k2 [ES] = 0 k1[E][S] = k-1[ES] + k2 [ES] k1([E]T – [ES]) [S] = k-1[ES] + k2 [ES] ([E]T – [ES]) [S] / [ES] = (k-1 + k2) / k1 = KM [E]T [S] – [ES] [S] = KM [ES] [E]T [S] = [ES] (KM + [S]) [ES] = [E]T [S] / (KM + [S]) V = [ES] k2 Vmax = [E]T k2 V = Vmax [S] / (KM + [S]) Michaelis-Menten equation when [S] = KM, V = ½ Vmax Km = (k-1 + k2) / k1 , when k-1 >> k2 (rapid equilibrium), KM = KES = k-1/ k1 In the case of k-1 is comparable to k2 (Briggs-Haldane kinetics), KM = KES + k2 / k1 Lineweaver-Burk double reciprocal plot Vmax / [E]T = turnover number = kcat kcat indicates catalytic efficiency (kcat is larger, reaction is faster) KM indicates substrate binding affinity (KM is smaller, binding is tighter) kcat/Km is a measure of catalytic efficiency vo = kcat[E]T[S] when [S]<<Km, little ES is formed, so [E] ~ [E]T ,vo = (kcat/Km) [E][S] Km + [S] kcat/Km is apparent second-order rate constant for an enzyme reaction, It is smaller than diffusion-controlled limit 108~1010 M-1s-1 fK P V max m [P]eq The Haldane Relationship: Keq = = VmaxrKmS [S]eq k1 The one-intermediate Model Vmaxf = k2[E]T Vmaxr = k-1[E]T Competitive inhibitor k1 k2 ES E+S k-1 + I KI EI + S E+S No reaction k-1 k2 EX KMS = E+P k-2 k-1 + k2 k1 E+P Vo = k2[E]T[S] KM (1+ [I] ) + [S] KI KMP = K2 + k-1 K-2 Uncompetitive inhibitor E+S k1 k-1 KI’ ES + I k2 ESI E+P Vmax[S] Vo = KM + (1+ No reaction Mixed or Noncompetitive inhibitor k2 k1 E+S ES E+P k-1 + + I I KI KI’ No reaction ESI EI [I] KI’ )[S] Vmax[S] Vo = (1+ [I] [I] )KM + (1+ )[S] KI’ KI pH dependence of simple Michaelis-Menten Enzymes E- ES- EH + S KE1 H+ k1 k-1 ESH KES1 EH2+ Vo = H+ KES2 H+ KE2 k2 EH + P H+ ESH2+ Vmax’[S] KM’ + [S] Vmax’ = Vmax/f2 KM’ = KM(f1/f2) [H+] k f1 = + 1 + E2+ kE1 [H ] f2 = [H+] +1+ kES1 kES2 [H+] Bi-substrate Reactions A+B E P+Q E Transfer Reaction P-X + B P + B-X Terminology: 1. Substrates are designated by the letters A, B, C, and D in the order that they add to the enzyme. 2. Products are designated P, Q, R, and S in the order that leave the enzyme. 3. Stable enzyme forms are designated E, F, and G with E being the free enzyme. 4. The numbers of reactants and products in a given reaction are specified, in order, by the terms Uni (one), Bi (two), Ter (three), and Quad (four). Types of Bi Bi reaction: 1. Sequential reactions (single-displacement), can be subclassifieid into an Ordered mechanism (left) , and a Random mechanism (right). A E A B k1 k-1 k2 k-2 EA P k3 EAB k-3 EPQ P B Q Q k4 k-4 k5 k-5 EQ E E EAB-EPQ E B A Q P 2. Ping Pong Reactions Ping Pong Bi Bi: double displacement P A E EA-FP Q B F FB-EQ E Rate equations Ordered Bi Bi KSAKSB 1 1 KMA KMB + = + + Vo Vmax Vmax[A] Vmax[B] Vmax[A][B] Rapid-equilibrium random Bi Bi Ping Pong Bi Bi 1 1 = Vo Vmax + KSAKMB VmaxKS B[A] 1 1 KMA KMB + = + Vo Vmax Vmax[A] Vmax[B] + KMB Vmax[B] + KSAKMB Vmax[A][B] slope = KMA/Vmax Diagnostic plot for Ping Pong Bi Bi 1/vo increasing constant [B] slope = KM A intercept = 1/Vmax + KMB/Vmax[B] KSAKMB + [B] 1/[A] Vmax double-reciprocal plots for a Ping Pong Bi Bi mechanism 1/vo increasing constant [B] intercept = 1 + KMB/[B] Vmax Diagnostic plot for sequential Bi Bi 1/[A] double-reciprocal plots for a Sequential Bi Bi mechanism Differentiating random and ordered sequential mechanisms 1. Product inhibition: 2. isotope exchange Enzyme reaction is complicated 1. Calculation of net rate constant k1 A k2 B k-1 k3 C k-2 k4 D k-3 k5 E k-4 F The net rate constant for D -> E, k4’ = k4k5/(k-4 + k5) The net rate constant for C -> D, k3’ = k3k4’/(k-3 + k4’) …….etc kP k1’ P A F The partitioning of A to F vs. P =k1’/kP 2. Use of transit times instead of rate constant k1 k2 k3 k4 kn-1 EP1 EP2 EP3 EP4 ….. EPn The total time from P1 to Pn, 1/k, is given by the sum of the transit times for each step 1/k = 1/k1 + 1/k2 + 1/k3 + 1/k4 + …. + 1/kn-1 As an example E + A EA E+P The binding step is reduced to k1[A]k2 / (k-1 + k2) [E]o/V = 1/k = (k-1 + k2) / k1[A]k2 + 1/k2 1/V = (k-1 + k2) / k1[A]Vmax + 1/Vmax 1/V = KM / [A] Vmax + 1/Vmax Pre-steady-state kinetics vs steady-state kinetics 1. The order of binding of substrates and release of product serves to define the reactants present at the active site during catalysis: it does not establish the kinetically preferred order of substrate addition and product release or allow conclusions pertaining to the events occurring between substrate binding and product release. 2. The value of kcat sets a lower limit on each of the first-order rate constants governing the conversion of substrate to product following the initial collision of substrate with enzyme. These include conformational changes in the enzymeSubstrate complex, chemical reactions (including the formation and breakdown of intermediates), and conformational changes that limit the rate of product release. 3. The value of kcat/KM defines the apparent second-order rate constant for substrate binding and sets a lower limit on the second-order rate constant for substrate binding. The term kcat/KM is less than the true rate constant by a factor defined by the kinetic partitioning of the E-S to dissociate or go forward in the reaction. The goal of pre-steady-state kinetics to to establish the complete kinetic pathway Including substrate binding, chemical reaction (substrate through intermediates to product), and product release. k2 k3 k4 k1 E+ S ES EX EP E+P k-1 k-2 k-3 k-4 Fast kinetics •Product release step is slow so the steady-state rate = product release rate •To measure the rate of chemical step where the product release is much slower, a single-turnover condition needs to be employed. •Under single-turnover condition where [E] >[S], product release needs not to be considered. •Under multiple-turnover condition where [S] = 4 x [E], a burst kinetics (a fast phase followed by a steady-state phase of product formation) can be observed for a reaction with slower post-chemical step. •A special tool Quench-Flow, needs to be used for single-turnover experiment in msec time scale. •A Stopped-Flow instrument allows the measurements of ligand interaction and chemical steps. Rapid-Quench fast kinetics instrument Measure the real rate of chemical step (single turnover, [E]>[S]) Measure the product formation burst (multiple turnover, [S] = 4x[E]) UPPs (undeca-prenyl pyrophosphate synthase) reaction UPPs catalyzes sequential addition of eight IPP to an FPP molecule, forming an undeca-prenyl pyrophosphate with 55 carbons and newly formed cis double bonds. UPPs synthesizes lipid carrier for bacterial cell wall assembly Dolichyl pyrophosphate synthase catalyzes the lipid carrier for Glycoprotein syntehsis Enzyme single turnover rate is the same with or without triton 10 mM E, 1 mM FPP, 50 mM [14C]IPP (With triton) (Without triton) kcat is 0.013 s-1 in the absence of triton and 190-fold higher (2.5 s-1) in the presence of triton. However, the rate 2.5 s-1 under enzyme single turnover is the same with or without triton Pan et al., (2000) Biochemistry 10936-10942 UPPs single-turnover reaction time courses 10 mM UPPs, 1 mM FPP, 50 mM [14C]IPP Y axis represents the sum of [14C]IPP incorporated 10 Concentration (uM) 8 6 4 2 0 0 2 4 Time (sec) 6 8 10 1.2 The data represent the time courses of C20 (●), C25 (○), C30 (■), C35 (□), C40 (◆), C45 (◊), C50 (▲), and C55 (△). Concentration (uM) 1 0.8 0.6 0.4 0.2 0 -0.2 0 1 2 3 Time (sec) 4 5 6 The rate constants for IPP condensation determined from single-turnover fast E + FPP 30 s -1 -1 IPP 2 mM s 2.5 s-1 E-C20 E-FPP-IPP E-FPP -1 IPP E-C30 3.5 s-1 E-C25-IPP IPP 2.5 s-1 E-C30-IPP E-C25 IPP 2 s-1 IPP E-C35 E-C35-IPP E-C20-IPP 3 s-1 E-C40 IPP E-C50 3.5 s-1 3.5 s-1 E-C45-IPP IPP IPP E-C50-IPP E-C45 3 s-1 fast (with triton) E-C55 E + C55 fast E-C40-IPP UPPs multiple-turnover reaction 0.75 mM enzyme, 6 mM FPP and 50 mM [14C]IPP without Triton The data indicate formation of C55 (△), C60 (●), C 65 (■), C70 (◆) and C75 (▲) 0.5 10 0.4 Concentration (uM) Concentration (uM) 8 6 4 2 0.3 0.2 0.1 0 -0.1 0 0 20 40 60 80 Time (sec) 100 120 140 160 0 20 40 60 80 Time (sec) 100 120 140 160 Product dissociation is partially rate limiting and protein conformational change is rate determining 0.001 s-1 E* + C55 E 0.4 s-1 E-C55 IPP (without triton) E-C55-IPP 0.001 s -1 -1 0.4 s E-C60 E* + C60 E 0.5 s-1 IPP E-C60-IPP -1 E 0.001 s E* + C65 -1 0.4 s 0.1 s-1 E-C65 IPP E-C65-IPP 0.02 s-1 E-C70 0.001 s-1 E + C70 + C75 Substrate binding kinetics E k1[S] ES Rate = d[E]/dt = -k1[S][E] d[E]/[E] = -k1[S]dt ln([E]t / [E]o) = -k1[S]t [E]t = [E]o exp (-k1[S]t) [ES] = [E]o-[E]t = [E]o(1-exp (-k1[S]t)) kobs = k1 [S] k1[S] E ES kobs = k1[S] + k-1 k-1 The slope of kobs vs [S] gives kon and intercept gives koff Stopped-flow for measurements of protein-protein and protein-small molecule interaction B A Absorbance Signal Light Flow Cell Fluorescence Signal Stop Syringe W91 has altered fluorescence upon FPP and IPP binding: Use this property to measure kon UPPs-FsPP + IPP 1 phase in 0.2 sec Binding rates vs. [IPP] gives IPP kon = 2 mM-1 s-1 Competition experiments to measure koff of FPP using fluorescent substrate analog OPP O PPO O PPO O OPP OPP CF3 Chen et al., (2002) J. Am. Chem. Soc. 124, 15217-15224 Substrate and product release rate FPP is released at 30 s-1 fast E + FPP E-C25 E-C45 30 s-1 3.5 s-1 3.5 s-1 UPP is released at 0.5 s-1 -1 -1 IPP 2 mM s 2 s-1 2.5 s-1 E-C20 E-FPP-IPP E-FPP E-C30 E-C50 2.5 s-1 3 s-1 E-C35 E-C55 3 s-1 0.5 s-1 3.5 s-1 E-C40 E + C55 Can this method apply to drug-targeted prenyltransferases to find non-competitive inhibitor?