Enzymes: Catalysis, Kinetics, Binding PDF

Enzymes: Catalysis, Kinetics, Binding (4 Lectures, Dr. Ford) I. II. Regulation Review Catalysis A. Thermodynamics Relationship: Activation Energy B. 1 Model + 4 Strategies C. Enzyme Anatomy: Active vs. Allosteric, Effectors, Holoenzymes D. Enzyme Diversity: 6 Biological Reactions/Enzyme Categories I...

Enzymes: Catalysis, Kinetics, Binding (4 Lectures, Dr. Ford) I. II. Regulation Review Catalysis A. Thermodynamics Relationship: Activation Energy B. 1 Model + 4 Strategies C. Enzyme Anatomy: Active vs. Allosteric, Effectors, Holoenzymes D. Enzyme Diversity: 6 Biological Reactions/Enzyme Categories III. Kinetics A. Reaction Rate B. Michaelis-Menten Catalysis Model and Equation Derivation C. Special Applications 1. More Equations/Special Situations 2. Graphing and Inhibitors 3. Substrate Binding and Cooperativity IV. Protein Case Studies A. Need for Speed: Chymotrypsin and Carbonic Anhydrase B. Cooperative Binding: Hemoglobin (with Dr. White) Lectures 8-11 General Regulatory Principles A. What is the effect on the next step of the process? Activators promote moving forward Inhibitors prevent stop forward progress A B C \ 8.1 General Regulatory Principles B. What part of the process is influenced? Substrate-level control acts on a single step in a pathway A B Feedback control targets a different step in a pathway A B C D E 8.2 Strategies to Regulate Protein Function In an on/off fashion: Availability o Synthesis vs. degradation o All pieces in the proper location Like a volume dial: Activity o Extra molecules may be required o Adding or subtracting pieces o Protein families consist of similar yet distinct proteins 8.3 Interacting with a Protein Shape and charge complementarity: 8.4 Color Coding KEY for all structures from this point onward: Blue is vitamins Pink is amino acids Green is nucleotides Purple is sugars Red is fatty acids Brown is where the chemical reaction takes place Black is for everything else 8.5 Reversible Covalent Modifications Creates nonproteinogenic amino acids by adding ≥ 1 “functional groups” to activate/inactivate the enzyme 8.6 Reversible Covalent Modifications Common additions: o Lipids Myristic Acid is a fatty acid Farnesyl is an intermediate in cholesterol synthesis 8.7 Reversible Covalent Modifications Common additions: o Nucleic Acids ADP-ribose 8.8 Reversible Covalent Modifications Common additions: o Proteins 8.9 Reversible Covalent Modifications Common additions: o Carbohydrates – the greatest source of diversity to the proteome! O- vs. N-linkages Composition of sugars Branched vs. Unbranched Length of oligosaccharide N-linked GlcNAc O-linked GalNAc 8.10 Reversible Covalent Modifications Common additions: o Small Molecules – γ-Carboxylation -Glutamyl Carboxylase glutamate -carboxyglutamate + vitamin K + O2 + CO2 + vitamin K epoxide 8.11 Reversible Covalent Modifications Common additions: o Small Molecules – Sulfation tyrosine Tyrosylprotein Sulfotransferase + + 3’,5’-Adenosine diphosphosphate PAPS = 3’-Phosphoadenosine-5’phosphosulfate 8.12 Reversible Covalent Modifications Common additions: o Small Molecules – Acetylation and Methylation Arginine: Lysine: 8.13 Reversible Covalent Modifications Common additions: o Small Molecules – Phosphorylation 8.14 Phosphorylation In Depth Kinases: ADD phosphates Phosphatases: REMOVE phosphates Vocabulary Digression: The name of a kinase indicates on which amino acid the phosphate will be added 8.15 Making Bridges: Why is phosphorylation activating? 1. Thermodynamics: ATP hydrolysis can drive unfavorable reactions (ΔG ≈ -50 kJ/mol) 2. Kinetics: physiological processes dictate reaction rate (msec – hrs/rxn) 3. Cell processes: ATP amounts dictated by metabolism (energy charge) Signal transduction amplification (catalytic turnover) 4. Shape and Charge Complementarity: each phosphate adds (-2) charge and (3+) H-bonds 8.16 Magnitude of Catalysis 8.17 Catalysis Overview What do enzymes do? Lower the activation energy Stabilize the transition state What do enzymes NOT do? Change the DG of the reaction Irreversibly change shape A catalyst is something that increases the rate (speed) of a reaction but does not undergo any permanent chemical change as a result 8.18 Speed vs. Stability Measures From a thermodynamics perspective, can we determine reaction rate? 8.19 Speed vs. Stability Measures How do we speed up a reaction? How many molecules can overcome the Activation Energy barrier (ΔG°‡)? Option #1: Increase the energy of all molecules by raising temperature 8.20 Speed vs. Stability Measures How do we speed up a reaction? How many molecules can overcome the Activation Energy barrier (ΔG°‡)? Option #2: Lower the energy barrier by decreasing the energy of the transition state 8.21 Speed vs. Stability Measures How do we speed up a reaction? How many molecules can overcome the Activation Energy barrier (ΔG°‡)? Option #2: Lower the energy barrier by decreasing the energy of the transition state 8.22 The Active Site… 1. Is only a few residues out of the protein 2. Is a 3-D cleft/crevice/pocket, creating a unique microenvironment 3. Determines substrate specificity by size and charge complementarity 4. Contacts with the substrate through noncovalent interactions 8.23 Catalysis Model In the Induced Fit model, when a substrate binds, the enzyme changes shape so that the substrate is forced into the transition state 8.24 Catalysis Model Catalysis is achieved through: Substrate orientation Straining substrate bonds Creating a favorable microenvironment Covalent and/or noncovalent interactions between enzyme and substrate 8.25 Catalysis Strategy #1 – Covalent Catalysis Enzyme covalently binds the transition state (electrons transfer) 8.26 Catalysis Strategy #2 – Acid-Base Catalysis Partial proton transfer to the substrate 8.27 Catalysis Strategy #3 – Approximation Remember, binding occurs in three dimensions….. If electrons and/or protons must be exchanged, proper spatial orientation and close contact (proximity) of the reactant molecules must occur If both pieces of the puzzle are “captured” and held in the proper orientation right next to each other, they are more likely to react with one and other…. But wait! We can also call this “entropy reduction”! 8.28 Catalysis Strategy #4 – Electrostatic Catalysis Stabilization of unfavorable charges on the transition state by polarizable side chains in the enzyme and/or metal ions 8.29 Allosteric Binding…. 1. Does NOT occur at the active site, but follows the same interaction rules as an active site 2. Involves a second substrate, which can be an activator or an inhibitor 8.30 Effector Binding (Heteroallostery) 8.31 Effector Binding (Heteroallostery) 8.32 Heteroallostery Example Role of ATCase in metabolism: 8.33 Heteroallostery Example Binding of CTP prefers the T/inactive state Binding of ATP prefers the R/active state T = “tense” R = “relaxed” 8.34 Helping Hands Apoenzymes: Incomplete Inactive Lack cofactor/coenzyme Holoenzymes: Whole Active Contain cofactor/coenzyme 8.35 More “Helping” Hands? Zymogens: Inactive Require proteolytic activation Secondary Structure Primary Structure 8.36 Enzyme Diversity 8.37 “Better” Metabolic Chemistry Reactions 1 2 3 4 5 Reaction Nucleophilic Substitution Nucleophilic Addition Carbonyl Condensation Elimination Oxidation-Reduction Result Swap functional groups Add functional groups Change # of carbons Change (increase) bond order Move electrons 8.38 Enzyme Diversity 1. Oxidoreductases Move electrons (Redox Reactions) Activated Carriers/Coenzymes: NADH, NADPH, FADH2, FMNH2 ❑ ❑ ❑ ❑ Nicotinamide Adenine Dinucleotide (Phosphate) Building Blocks: Vitamin B3 and Adenine Carry a single electron (follow the H) Metabolism notes: In Catabolic reactions, Dehydrogenases oxidize their substrate and use NAD+ In Anabolic reactions, Reductases reduce their substrate and use NADPH Adenosine Monophosphate Vitamin B3 (Niacin/Nicotinic Acid) Vitamin B3 (Niacinamide/Nicotinamide) 8.39 NAD+ NADH Nicotinamide Adenosine Monophosphate 8.40 Enzyme Diversity 1. Oxidoreductases Move electrons (Redox Reactions) Activated Carriers/Coenzymes: NADH, NADPH, FADH2, FMNH2 ❑ ❑ ❑ ❑ Flavin Mononucleotide and Flavin Adenine Dinucleotide Building Blocks: Vitamin B2 (and Adenine) Carry two electrons (follow the H’s) Structure note: Ribitol is a reduced form of Ribose Adenosine Monophosphate ribose ribitol Vitamin B2 (Riboflavin) 8.41 FMN FMNH2 FAD Vitamin B2 (Riboflavin) Adenosine Monophosphate FADH2 8.42 Enzyme Diversity Transfer PHOSPHATE group 2. Transferases Move a functional group (group transfer) Activated Carriers/Coenzymes: ATP, pyridoxal phosphate (B6), SAM, Tetrahydrofolate (B9), 5’-deoxyadenosylcobalamin (B12) ❑ Adenosine Triphosphate ❑ Structure note: Usually the -phosphate is removed, but the β+ phosphates can be removed as pyrophosphate (PPi)  β ❑ Vitamin B6 collectively refers to 6 molecules: pyridoxine, pyridoxal and pyridoxamine; plus their phosphate derivatives α ATP Vitamin B6 (pyridoxine) Pyridoxal phosphate 8.43 Enzyme Diversity Transfer METHYL group 2. Transferases Move a functional group (group transfer) Activated Carriers/Coenzymes: ATP, pyridoxal phosphate (B6), SAM, Tetrahydrofolate (B9), 5’-deoxyadenosylcobalamin (B12) ❑ S-Adenosylmethionine ❑ Building Blocks: Methionine and Adenine ❑ Biology note: SAM is the primary methyl donor in cells SAM Methionine Adenosine 8.44 ❑ Vitamin B9 is a glutamate derivative ❑ Forms of interest: Sold as Folic Acid Bioavailable after reduction, as Tetrahydrofolate Donates a methyl from Methyltetrahydrofolate Glutamate Tetrahydrofolate Vitamin B9 (Folic acid) Transfer METHYL group Methyltetrahydrofolate 8.45 ❑ Vitamin B12 also can take many forms: Sold as Cyanocobalamin Metabolically active as 5’-Deoxyadenosylcobalamin or Methylcobalamin ❑ Unusual because contains a metal (Cobalt) Methylcobalamin Vitamin B12 (Cyanocobalamin) Transfer METHYL group Adenosine 5’-Deoxyadenosylcobalamin 8.46 Enzyme Diversity 3. Isomerases Rearrange order of atoms in a molecule (isomerization) 8.47 Enzyme Diversity +/- ALDEHYDE group (-COH) 4. Hydrolases Break a chemical bond by adding water across it (hydrolysis) 5. Lyases Break a chemical bond without using water 6. Ligases Paste two pieces together (make a chemical bond), uses ATP Activated Carriers/Coenzymes: TPP, CoASH, lipoamide, biotin ❑ Thiamine Pyrophosphate ❑ Building Blocks: Vitamin B1 + 2 phosphates ❑ Uses redox chemistry (also can help oxidize substrates) Vitamin B1 (Thiamine) TPP 8.48 Enzyme Diversity +/- ACYL group (-COR) 4. Hydrolases Break a chemical bond by adding water across it (hydrolysis) 5. Lyases Break a chemical bond without using water 6. Ligases Paste two pieces together (make a chemical bond), uses ATP Activated Carriers/Coenzymes: TPP, CoASH, lipoamide, biotin ❑ Common theme = Sulfur (and sulfur = redox chemistry!) ❑ Coenzyme A Building Blocks: Vitamin B5 + Adenine ❑ Lipoamide Building Blocks: a fatty acid derivative + Lysine Adenosine Monophosphate Octanoic acid Vitamin B5 Lysine 8.49 +/- ACYL group (-COR) CoASH Lipoamide (Lipoyllysine) Octanoic acid Vitamin B5 Lipoic acid Lysine Adenosine Monophosphate 8.50 Enzyme Diversity +/- CO2 group 4. Hydrolases Break a chemical bond by adding water across it (hydrolysis) 5. Lyases Break a chemical bond without using water 6. Ligases Paste two pieces together (make a chemical bond), uses ATP Activated Carriers/Coenzymes: TPP, CoASH, lipoamide, biotin ❑ Biotin is Vitamin B7 ❑ Biocytin (biotin + lysine) is the version found in enzymes ❑ Fun fact: The biotin-streptavidin interaction is the strongest natural noncovalent interaction Biocytin Vitamin B7 (Biotin) Lysine 8.51 Before we dive into the kinetics portion…. 3 kinetics trends are possible: 2. Hyperbolic 3. Sigmoidal 𝜈=𝑘 𝑆 𝜈0 = 𝜈= 𝜈𝑚𝑎𝑥 𝑆 𝐾𝑚 + 𝑆 𝑆𝑛 𝐾𝐷 + 𝑆 𝑛 Reaction Rate (ν) 1. Linear [S] 8.52 Reaction Rate For an IRREVERSIBLE reaction: 𝜈= Δ𝑆 − Δ𝑇 = Δ𝑃 Δ𝑇 =𝑘 𝑆 S→P 𝑛 Where n indicates how many molecules are in play (reaction order) 8.53 Reaction Order S 1/[S] [S] time P A: Graph your data 3 ways! Linear line is the winner. k is the slope of that line ln [S] How do I know the reaction order? enzyme time time 8.54 Reaction Order 1 1/[S] [S] time P =𝑘 𝑆 ln [S] First order kinetics: 𝜈 = 𝑘 𝑆 1S enzyme time time 8.55 Reaction Order 2S enzyme SA + SB 2 P 1/[S] [S] time enzyme or 𝑘 𝑆𝐴 𝑆𝐵 ln [S] Second order kinetics: 𝜈 = 𝑘 𝑆 P time time 8.56 Reaction Order S enzyme P time 1/[S] [S] ln [S] Zero order kinetics: 𝜈 = 𝑘 𝑆 0 = 𝑘 Substrate-independent Interpretations: A) Unimolecular reaction B) Enzyme is saturated time time 8.57 Reaction Rate For a REVERSIBLE reaction: 𝜈= Δ𝑆 − Δ𝑇 = Δ𝑃 Δ𝑇 k1 S⇌P k-1 = 𝑘1 𝑆 𝑛 − 𝑘−1 𝑃 𝑚 In other words: the substrate is being both used and created 8.58 Reaction Rate For a REVERSIBLE reaction: k1 S⇌P k-1 At EQUILIBRIUM, by definition, the forward rate = the reverse rate 𝜈= Δ𝑆 − Δ𝑇 = Δ𝑃 Δ𝑇 = 𝑘1 𝑆 − 𝑘−1 𝑃 = 0 𝑘1 𝑆 = 𝑘−1 𝑃 8.59 Reaction Rate For a REVERSIBLE reaction at equilibrium: k1 S⇌ P k -1 𝑘1 𝑆 = 𝑘−1 𝑃 We now can define 2 important equilibrium constants: 𝐾𝐴 = 𝑃 𝑆 𝐾𝐷 = 𝑆 𝑃 = 𝑘1 𝑘−1 = 𝑘−1 𝑘1 Association Constant (make P) = 1 𝐾𝐴 Dissociation Constant (un-make P) 8.60 Reaction Rate and Catalysis Michaelis-Menten enzymes follow first-order kinetics, BUT No matter what, catalysis is not a first order reaction. At worst, we can express catalysis as: k1 k2 k3 k-1 k-2 k-3 E + S ⇌ E·S ⇌ E·P ⇌ E + P 8.61 Reaction Rate and Catalysis Michaelis-Menten enzymes follow first-order kinetics, BUT No matter what, catalysis is not a first order reaction. At worst, we can express catalysis as: k1 k2 k3 k-1 k-2 k-3 E + S ⇌ E·S ⇌ E·P ⇌ E + P By making an assumption, we can simplify to: E + S ⇌ E·S → E + P k1 k2 k-1 8.62 Reaction Rate Simplification If we measure the initial rate of reaction (ν0) Not much P is present, so we can ignore k-3 Whatever P is present is released instantly, so [E·P] ≈ 0 (k3 >> k-2) Moreover, the changes in concentration will be LINEAR 8.63 Reaction Rate Simplification If we measure the initial rate of reaction (ν0) Not much P is present, so we can ignore k-3 Whatever P is present is released instantly, so [E·P] ≈ 0 (k3 >> k-2) Moreover, the changes in concentration will be LINEAR 8.64 Reaction Rate Model k1 We call the reaction E + S ⇌ E·S k the Michaelis-Menten kinetics model -1 →E+P k2 We can now define some equations and variables that follow from this model… 8.65 Variable definitions (non-math) Variable Km νmax kcat Ks kcat/Km Name Definition Michaelis [S] where reaction rate is half maximal OR Constant half of the active sites are full Maximum Maximum rate possible for a given concentration velocity of enzyme Turnover Number of substrate molecules converted per number active site per time (first order rate constant) N/A A dissociation constant for substrate binding Specificity A measure of enzyme performance that predicts constant the fate of E·S 8.66 Toward Michaelis-Menten FIRST: Assuming that binding of the substrate is at equilibrium, We can define an equilibrium constant for this reaction (KS = KD) 𝐸 𝑆 𝑘−1 𝐾𝑆 = = 𝐸·𝑆 𝑘1 Great – just one problem….. We cannot measure [E] (free enzyme)! The solution: know how much enzyme you added to the reaction ([E]T) 𝐸 𝑇 = 𝐸 + 𝐸·𝑆 or 𝐸 = 𝐸 𝑇 − 𝐸·𝑆 8.67 Reaction Rate Simplification SECOND: The steady state assumption, when [S] >> [E], ΔS ≈ 0 Formation of the E·S complex occurs at the same rate as its loss (in either direction). Mathematically, we can say, Δ𝐸·𝑆 = 𝑘1 𝐸 𝑆 − 𝑘−1 𝐸·𝑆 − 𝑘2 𝐸·𝑆 = 0 and, Δ𝑇 𝑘1 𝐸 𝑆 = 𝑘−1 + 𝑘2 𝐸·𝑆 Moreover, we can define a special equilibrium constant, Km 𝐾𝑚 = 𝐸 𝑆 𝐸·𝑆 = 𝑘−1 +𝑘2 𝑘1 Since k2 is the rate-determining step, we say that the rate of product formation is, Δ𝑃 𝜈0 = = 𝑘2 𝐸·𝑆 = 𝑘𝑐𝑎𝑡 𝐸·𝑆 Δ𝑇 Great – just one more problem….. We cannot measure [E·S] either! The solution: more ALGEBRA 8.68 Toward Michaelis-Menten OK, let’s put some pieces together: 𝐸 = 𝐸 𝑇 − 𝐸·𝑆 and 𝐾𝑆 = 𝐸 𝑆 , or 𝐾𝑆 𝐸 ·𝑆 ∗ 𝐸·𝑆 = 𝐸 𝑆 Plug in for [E] and solve for [E·S]: 𝐾𝑆 ∗ 𝐾𝑆 ∗ 𝐾𝑆 ∗ 𝐾𝑆 ∗ 𝐸·𝑆 𝐸·𝑆 = 𝐸 𝑆 𝐸·𝑆 = 𝐸 𝑇 − 𝐸·𝑆 𝑆 𝐸·𝑆 = 𝐸 𝑇 𝑆 − 𝐸·𝑆 𝑆 𝐸·𝑆 + 𝐸·𝑆 𝑆 = 𝐸 𝑇 𝑆 𝐾𝑆 + 𝑆 = 𝐸 𝑇 𝑆 𝑬·𝑺 = 𝑬𝑻𝑺 𝑲𝑺 + 𝑺 original equation definition of [E] factor add 𝐸·𝑆 𝑆 to both sides factor divide both sides by 𝐾𝑆 + 𝑆 8.69 Toward Michaelis-Menten Still going… Plug into the rate equation: 𝜈0 = 𝑘𝑐𝑎𝑡 𝐸·𝑆 and 𝐸·𝑆 = 𝐸𝑇𝑆 𝐾𝑆 + 𝑆 𝒌𝒄𝒂𝒕 𝑬 𝑻 𝑺 𝝂𝟎 = 𝑲𝑺 + 𝑺 8.70 Toward Michaelis-Menten Another variable: νmax is reached when the enzyme is fully saturated, meaning we can say that [E·S]=[E]T AND our rate equation 𝜈0 = 𝑘𝑐𝑎𝑡 𝐸·𝑆 becomes: 𝝂𝒎𝒂𝒙 = 𝒌𝒄𝒂𝒕 𝑬 𝑻 8.71 Toward Michaelis-Menten Note also, we can relate Km to νmax: 8.72 Toward Michaelis-Menten Let’s simplify our initial rate equation again by using νmax: 𝜈0 = 𝑘𝑐𝑎𝑡 𝐸 𝑇 𝑆 𝐾𝑆 + 𝑆 and 𝜈𝑚𝑎𝑥 = 𝑘𝑐𝑎𝑡 𝐸 𝑇 , means 𝝂𝒎𝒂𝒙 𝑺 𝝂𝟎 = 𝑲𝑺 + 𝑺 8.73 Toward Michaelis-Menten If k2 is the rate-limiting step, meaning that k2 is small, we can say: 𝐾𝑚 = 𝑘−1 +𝑘2 𝑘1 ≈ 𝑘−1 𝑘1 ≈ 𝐾𝑆 Now we FINALLY can see the Michaelis-Menten Equation in its most familiar form: 𝝂𝒎𝒂𝒙 𝑺 𝝂𝟎 = 𝑲𝒎 + 𝑺 8.74 Special Applications Some very important (laboratory) shortcuts to remember: 𝜈0 ≈ 𝜈𝑚𝑎𝑥 𝐾𝑚 2. [S] = Km 𝜈0 = 𝜈𝑚𝑎𝑥 2 3. [S] >> Km 𝜈0 = 𝜈𝑚𝑎𝑥 1. [S] > k-1, and 𝑘𝑐𝑎𝑡 𝐾𝑚 ≈ 𝑘1 2. A poor enzyme would have kcat > k-1 𝑘𝑐𝑎𝑡 𝐾𝑚 𝑘𝑐𝑎𝑡 𝐾𝑚 𝑘𝑐𝑎𝑡 𝐾𝑚 = = 𝑘𝑐𝑎𝑡 𝑘 𝑘−1 + 𝑘𝑐𝑎𝑡 1 𝑘𝑐𝑎𝑡 𝑘 𝑘𝑐𝑎𝑡 1 = 𝑘1 original equation simplification: kcat is dominant (remove k-1) kcat/kcat = 1 Poor Enzyme: kcat 1 binding site Sites are ALL equivalent AND independent >1 binding site Sites are EITHER equivalent OR independent Difficulty Binding analyses get very messy, very quickly….. >1 binding site Sites are NEITHER equivalent NOR independent All emojis downloaded from https://hdsmileys.com/big-smileys/animated-smileys-for-facebook/ 8.89 Toward the Hill Equation Remember our general definitions: 𝐾𝐴 = 𝐸∙𝑆 𝐸 𝑆 = 1 𝐾𝐷 “affinity” or “association” constant -- Coming together 𝐾𝐷 = 𝐸 𝑆 𝐸∙𝑆 = 1 𝐾𝐴 “dissociation” constant -- Breaking apart Some additional definitions of KD to keep in mind for today: A. Dissociation constant for E·Sn complexes B. Equal to the concentration of ligand where ½ the available binding sites are full C. When the receptor is half-saturated 8.90 Toward the Hill Equation Let’s start with the simplest scenario: n = 1 We can define a term, Y or “Fractional Saturation”: The fraction of total protein molecules that contain ligand 𝑌= 𝐸∙𝑆 𝐸 + 𝐸∙𝑆 We want to write this equation in terms of 𝐾𝐷 …. 8.91 Toward the Hill Equation The Algebra: Given that 𝑌 = 𝑌= 𝐸∙𝑆 𝐸 + 𝐸∙𝑆 𝐸 𝑆 𝑌= 𝑌= 𝒀= 𝐸+ 𝐷 𝐸 𝑆 𝐸∙𝑆 or 𝐸 ∙ 𝑆 = 𝐸 𝑆 𝐾𝐷 ൗ𝐾 substituting in for both 𝐸·𝑆 terms 𝐷 𝐸 𝑆 𝐸 𝐾𝐷 + 𝐸 𝑆 𝑺 𝑲𝑫 + 𝑺 and 𝐾𝐷 = original equation ൗ𝐾 𝐸 𝑆 𝐸∙𝑆 𝐸 + 𝐸∙𝑆 multiply numerator and denominator terms by 𝐾𝐷 remove cancelling [E] terms 8.92 Toward the Hill Equation Some conclusions about the simplest scenario: n = 1 Possible values for Y: 0 < Y < 1 o 0 means no ligand bound o 1 means receptor is saturated o 0.5 means receptor is half-saturated Y Note that for Y = 0.5, by definition [S] = KD Plotting Y vs. [S] gives a hyperbolic curve: [S] 8.93 Toward the Hill Equation For the scenario n = 1 𝐸·𝑆 1 𝐸 𝑇 =− 𝐸·𝑆 + 𝑆 𝐾𝐷 𝐾𝐷 The slope = 1 − 𝐾𝐷 The y-intercept = [E·S]/[S] To make a LINEAR plot (Scatchard Plot), use the equation: [E·S] 1 𝐾𝐷 The x-intercept = 𝐸 𝑇 8.94 Toward the Hill Equation Here’s where it starts to get hairy, for n > 1: Fractional Saturation becomes θ, BUT may also go by ν or b or “degree of binding” or even remain as Y…. θ still means “The fraction of protein molecules that contain ligand” BUT now we need multiple species of 𝐸·𝑆 to describe this situation…. AND our binding sites may or may not be independent and/or equivalent…. So, for our purposes, we will just consider the case of Cooperativity…. 8.95 Toward the Hill Equation Cooperativity: Binding of each subsequent ligand influences the affinity (strength of interaction) of the next ligand to bind an active site → Binding sites are equivalent but not independent Vocabulary Reminder: Allostery Heteroallostery Effector binds at allosteric site Homoallostery Cooperativity https://www.merriam-webster.com/dictionary/cooperate?src=search-dict-hed 8.96 Toward the Hill Equation Remember that for one binding site (n = 1) we had: 𝑆 𝑌= 𝐾𝐷 + 𝑆 For the case of a perfectly cooperative binder (where n > 1), we can approximate θ: θ= 𝑆𝑛 𝐾𝐷 + 𝑆 𝑛 Where n = the number of binding sites also called 𝑛𝐻 or 𝛼𝐻 , the Hill Coefficient 8.97 The Hill Equation To make a LINEAR plot (Hill Plot), use the Hill Equation: 𝜃 1 𝑙𝑜𝑔 = 𝑙𝑜𝑔 + 𝑛𝐻 𝑙𝑜𝑔 𝑆 1−𝜃 𝐾𝐷 The slope = nH Log (θ/1-θ) For a cooperative binder where n > 1 Log [S] The y-intercept = log (1/KD) 8.98 The Hill Equation In terms of cooperativity, we interpret Hill Coefficients in the following way: nH = 1 means no cooperativity (sites are independent) nH > 1 means positive cooperativity (affinity increases) 0 < nH < 1 means negative cooperativity (affinity decreases) Log (θ/1-θ) Sadly, cooperativity is never perfect… … and Hill Plots are not really linear (except when n = 1!) For example, a Hill Plot of Hemoglobin looks more like this: nH = 1 nH = 2.8 nH = 1 Log [S] - - Reference Slope – Hemoglobin 8.99 Back to Michaelis-Menten Remember, Michaelis-Menten kinetics requires first order enzymes. Noncooperative Enzyme Cooperative Enzyme Reaction rate Reaction rate But, multiple binding site enzymes CAN follow Michaelis-Mentin kinetics, as long as they are NONCOOPERATIVE… [Substrate] [Substrate] 8.100 A Tale of Two Catalysts: A need for speed Serine Proteases/Chymotrypsin Carbonic Anhydrases Problem faced (uncat) Reaction is too slow Reaction is not fast enough Reaction substrate(s) Polypeptide/Peptide bond CO2/HCO3– Reaction product(s) Shorter polypeptides HCO3–/CO2 Type of enzyme Hydrolase Hydrolase Type of reaction Hydrolysis Hydrolysis years seconds milliseconds microseconds Active site Catalytic triad + oxyanion hole 3 His + Zn++-OH Specificity Hydrophobic specificity pocket (size of entryway) Covalent catalysis Acid-base catalysis (Approximation) Acid-base catalysis Approximation Electrostatic catalysis Reaction time (uncat) Reaction time (cat) Catalytic strategies 8.101 Example Enzyme: Chymotrypsin Why do we need proteases? Recycling Regulation Defense 8.102 Example Enzyme: Chymotrypsin The active site is an example of a catalytic triad: o Serine (S195) = a nucleophile o Histidine (H57) = a base (proton acceptor) o Aspartic Acid (D102) = an acid (proton donor) 8.103 Active Site Digression #1: Naming Other classes of proteases also are named for their active sites: Papain From papayas Used as a meat tenderizer Classic example Papain Human Examples Calpains and Caspases Calpains and Caspases Require Ca++ as a cofactor Cell death pathway proteins Found in Eukaryotes and Eubacteria, but not Archaea! Calpains split the active site residues over a heterodimer 8.104 Active Site Digression #1: Naming Other classes of proteases also are named for their active sites: HIV Protease Cleave precursor proteins Homodimer with 1 active site Asp per subunit Renin Secreted from kidneys Helps increase blood pressure and retain water/salt Classic example HIV protease Human Examples Renin 8.105 Active Site Digression #1: Naming Other classes of proteases also are named for their active sites: Thermolysin Active site is His-His-Glu with Zn and another Glu holds H2O Secreted from Gram+ bacteria Bacillus thermoproteolyticus MMPs Active site is His-His-His-Glu Degrade the extracellular matrix Classic example Thermolysin Human Examples Matrix Metalloproteinases and Alcohol Dehydrogenase ADH Active site is His-Cys-Cys-H2O In the liver, ADH uses NAD+ to convert alcohols to acetaldehyde 8.106 Active Site Digression #2: Coenzymes NAD+ resides in the active site of ADH: To explore this structure more, go to https://pdb101.rcsb.org/motm/13 8.107 Example Enzyme: Chymotrypsin The active site is an example of a catalytic triad Oxyanion hole stabilizes the tetrahedral intermediate (transition state) o Serine (S195) o Glycine (G193) Note: Interactions are with amines in backbone not side chains! 8.108 Example Enzyme: Chymotrypsin The active site is an example of a catalytic triad Oxyanion hole stabilizes the tetrahedral intermediate (transition state) Specificity (S1)pocket determines placement of cut 8.109 Specificity Pocket Digression Specificity is determined by “protrusions” into the Specificity Pocket Remember Dr. Ford’s favorite words: Shape and Charge Complementarity 8.110 Example Enzyme: Chymotrypsin Can you find examples of: Covalent Catalysis Acid-Base Catalysis Approximation 8.111 Example Enzyme: Carbonic Anhydrases How do we use CA? Physiology Relevance – pH regulation Enzyme pathway regulation Medical Application – Artificial lungs Industrial Application – CO2 scrubbers to decrease greenhouse gas emissions Plants use CA for carbon fixation 8.112 Example Enzyme: Carbonic Anhydrases The active site contains a Zn++ ion: o Coordinated to 3 Histidines and a water To explore these structures more, go to https://pdb101.rcsb.org/motm/49 8.113 Active Site Digression #3: Evolution A little preview of Molecular Evolution: Carbonic anhydrases are an example of CONVERGENT evolution Currently 8 families of carbonic anhydrases have been discovered Family Prevalence Metal ion used α Universal Zn β Bacteria, plants, fungi Zn  Bacteria, archaea, plants, fungi Zn or Fe or Co δ Marine diatoms Co ζ Marine diatoms Cd or Zn η Plasmodium parasites Zn θ Marine diatoms Zn ι Marine diatoms and bacteria Mn Humans produce ≥ 15 splice variations 8.114 Example Enzyme: Carbonic Anhydrases The active site contains a Zn++ ion H2O facilitates the transition state o Must be deprotonated o Catalytic strategy of Approximation 8.115 Example Enzyme: Carbonic Anhydrases Reaction Mechanism: 1. Water binds to Zn++, lowering its pKa. At physiological pH, water loses a proton 2. Catalytic strategy of approximation as substrate enters active site 3. Nucleophilic addition (adds functional group to CO2) 4. Release of product and regeneration of enzyme (histidine proton shuttle) 8.116 Example Enzyme: Carbonic Anhydrases The active site contains a Zn++ ion H2O facilitates the transition state Entry Channel determines size of substrate o CO2 is small and weakly polar… 8.117