# Lecture 8: Enzyme Inhibition and Regulation ## Biochemistry --- ## Learning Objectives By the end of this lecture, students will be able to: 1. Distinguish between reversible and irreversible enzyme inhibition 2. Describe the kinetic effects of competitive, uncompetitive, and mixed/noncompetitive inhibition 3. Interpret Lineweaver-Burk plots for each type of reversible inhibition 4. Explain allosteric regulation and the concepts of cooperativity 5. Describe covalent modification (phosphorylation) as a regulatory mechanism 6. Explain the role of zymogens, isozymes, and feedback inhibition in metabolic regulation --- ## Lecture Content ### I. Reversible Inhibition Reversible inhibitors bind non-covalently to the enzyme and can dissociate. They are characterized by the inhibition constant Ki = [E][I]/[EI], where a lower Ki indicates a more potent inhibitor with higher binding affinity. #### Competitive Inhibition A competitive inhibitor binds to the **active site** of the free enzyme and competes directly with the substrate. It typically resembles the substrate structurally. The kinetic consequences are that **Km increases** (the apparent Km equals Km times (1 + [I]/Ki), meaning more substrate is needed to reach half-Vmax), while **Vmax remains unchanged** because at sufficiently high substrate concentrations, the substrate outcompetes the inhibitor. On a Lineweaver-Burk plot, competitive inhibition produces lines that intersect on the y-axis (same 1/Vmax) with increasing slopes at higher inhibitor concentrations. Clinical examples include methotrexate, which competitively inhibits dihydrofolate reductase as an anticancer drug, and statins, which competitively inhibit HMG-CoA reductase to lower cholesterol. #### Uncompetitive Inhibition An uncompetitive inhibitor binds only to the **ES complex**, not to the free enzyme. Both **Km and Vmax decrease** (each by a factor of 1 + [I]/Ki'), and the Vmax/Km ratio remains constant. On a Lineweaver-Burk plot, this produces parallel lines with the same slope but different y-intercepts. Uncompetitive inhibition is rare for single-substrate enzymes but more common in multi-substrate reactions. An example is lithium, which inhibits inositol monophosphatase uncompetitively and is used to treat bipolar disorder. #### Mixed Inhibition (includes Noncompetitive as a special case) A mixed inhibitor binds to both the **free enzyme** and the **ES complex** at an allosteric site distinct from the active site. Km may increase or decrease depending on the relative affinity for E versus ES, and **Vmax decreases** because the inhibition cannot be overcome by increasing substrate concentration. On a Lineweaver-Burk plot, lines intersect to the left of the y-axis. **Pure noncompetitive** inhibition is the special case where the inhibitor binds E and ES with equal affinity (Ki = Ki'): Km is unchanged, Vmax decreases, and lines intersect on the x-axis. Heavy metals such as lead and mercury can act as noncompetitive inhibitors by binding away from the active site. A three-panel figure showing the three types of reversible enzyme inhibition. For each type (competitive, uncompetitive, and mixed/noncompetitive): Left side shows a schematic of the enzyme with substrate and inhibitor binding (active site vs. allosteric site). Right side shows the corresponding Lineweaver-Burk plot with lines for no inhibitor and increasing inhibitor concentrations. A summary table below compares the effects on apparent Km and Vmax for each type. Color coding: enzyme in blue, substrate in green, competitive inhibitor in red, uncompetitive inhibitor in orange, mixed inhibitor in purple. ### II. Irreversible Inhibition Irreversible inhibitors form a **covalent bond** with the enzyme (or bind with extremely tight non-covalent affinity), permanently inactivating it so that the enzyme must be replaced by new synthesis. These inhibitors often react with an essential active site residue. **Aspirin** irreversibly acetylates a serine residue in cyclooxygenase (COX-1 and COX-2), blocking prostaglandin and thromboxane synthesis. **Organophosphates** (nerve agents and insecticides) phosphorylate the active site serine of acetylcholinesterase. **Penicillin** covalently modifies the active site serine of transpeptidase, disrupting bacterial cell wall synthesis. **DIPF** (diisopropylphosphofluoridate) reacts with the active site serine of serine proteases. Suicide inhibitors (mechanism-based inhibitors) are initially recognized as substrates by the enzyme. The enzyme's own catalytic mechanism converts the inhibitor into a reactive species that then covalently modifies the enzyme. Allopurinol, which inhibits xanthine oxidase and is used to treat gout, is an example. ### III. Allosteric Regulation Allosteric enzymes have regulatory sites distinct from the active site. Binding of an effector (modulator) at the allosteric site changes the enzyme's conformation and activity. A **positive effector** (activator) increases activity, while a **negative effector** (inhibitor) decreases it. Allosteric enzymes are typically multisubunit proteins that show **sigmoidal** (S-shaped) kinetics rather than the hyperbolic kinetics of Michaelis-Menten enzymes. They do not obey the Michaelis-Menten equation, and the substrate concentration at half-maximal velocity is designated K0.5 rather than Km. #### Cooperativity Cooperativity occurs when binding of substrate to one subunit affects binding at other subunits. In **positive cooperativity**, binding of one substrate molecule increases the affinity of other subunits, producing sigmoidal kinetics. In **negative cooperativity**, binding decreases affinity at other subunits. Cooperativity is quantified by the **Hill coefficient (nH)**: a value of 1 indicates no cooperativity (Michaelis-Menten behavior), values greater than 1 indicate positive cooperativity, and values less than 1 indicate negative cooperativity. #### Models of Allostery The **concerted model** (MWC model, Monod-Wyman-Changeux) proposes that the enzyme exists in two states -- T (tense, low affinity) and R (relaxed, high affinity) -- and that all subunits switch simultaneously, preserving symmetry. Substrate binds preferentially to the R state, shifting the equilibrium toward R. Activators stabilize the R state, while inhibitors stabilize the T state. The **sequential model** (KNF model, Koshland-Nemethy-Filmer) proposes that substrate binding to one subunit induces a conformational change in that subunit, which is then transmitted to adjacent subunits, though not necessarily all at once. Symmetry is not required, and hybrid states are allowed. In reality, many enzymes show features of both models. A figure comparing the concerted and sequential models of allosteric regulation. Panel A (Concerted/MWC model): Shows the enzyme existing in only two states — all subunits in T state (squares) or all in R state (circles). Substrate binding shifts the equilibrium from T to R. An activator stabilizes R (arrow toward R), and an inhibitor stabilizes T (arrow toward T). Panel B (Sequential/KNF model): Shows substrate binding to one subunit (changing its shape from square to circle) which then influences neighboring subunits one at a time, allowing mixed T/R intermediates. Panel C: A sigmoidal kinetics curve for an allosteric enzyme compared to a hyperbolic Michaelis-Menten curve, with K0.5 and Vmax labeled. Arrows show how activators shift the curve left and inhibitors shift it right. ### IV. Covalent Modification Reversible covalent modification is a major regulatory strategy, with **phosphorylation and dephosphorylation** being the most common form. Protein kinases add phosphate groups from ATP to serine, threonine, or tyrosine residues, while protein phosphatases remove them. The addition of a phosphate group introduces two negative charges that can dramatically alter protein conformation and activity. Some enzymes are activated by phosphorylation while others are inactivated -- for example, glycogen phosphorylase is activated by phosphorylation, whereas glycogen synthase is inactivated. Other regulatory covalent modifications include acetylation (of histones and metabolic enzymes), ADP-ribosylation (by bacterial toxins such as cholera toxin and pertussis toxin), and ubiquitination (targeting proteins for degradation). ### V. Zymogens (Proenzymes) Zymogens are inactive enzyme precursors that require proteolytic cleavage for activation. This activation is irreversible, functioning as a one-way switch, and is important for enzymes that would be dangerous if active in the wrong location. Digestive enzyme zymogens include pepsinogen (activated to pepsin in the stomach), trypsinogen (activated to trypsin in the small intestine by enterokinase), and chymotrypsinogen (activated to chymotrypsin). The blood clotting cascade involves sequential zymogen activation of clotting factors. Caspases in apoptosis and components of the complement system in innate immunity also follow zymogen activation cascades. Clinically, acute pancreatitis results from premature activation of digestive zymogens within the pancreas itself. ### VI. Isozymes (Isoenzymes) Isozymes are different enzymes that catalyze the same reaction but differ in amino acid sequence, kinetic properties, and regulation. They are encoded by different genes and are often tissue-specific. The classic example is **lactate dehydrogenase (LDH)**, a tetramer composed of M (muscle) and H (heart) subunits that can form five isozymes: LDH-1 (H4) through LDH-5 (M4). LDH-1 predominates in the heart, while LDH-5 predominates in skeletal muscle and liver. Serum LDH isozyme patterns are used clinically to diagnose tissue damage. Other isozyme families include hexokinase (I through IV, with IV being glucokinase) and creatine kinase (CK-MM, CK-MB, CK-BB). ### VII. Feedback Inhibition In feedback inhibition, the end product of a metabolic pathway inhibits an early enzyme in the same pathway, preventing wasteful overproduction. This typically takes the form of allosteric inhibition of the first committed step. For example, in a pathway converting A through B, C, D, to E, the final product E would inhibit the enzyme catalyzing the conversion of A to B. This is a fundamental principle of metabolic regulation. In branched pathways producing multiple end products, each product may inhibit its own branch point enzyme. A metabolic pathway diagram illustrating feedback inhibition. A linear pathway shows enzymes E1 through E4 converting substrates A through E. The end product E is shown with a dashed inhibitory arrow going back to enzyme E1 (the committed step). An allosteric site on E1 is shown binding the end product. When product E accumulates, E1 is inhibited and flux through the entire pathway decreases. A branched pathway variant is also shown where two end products each inhibit their respective branch point enzymes. ---