Biochemistry: Exam 2

Flashcards covering protein binding kinetics, myoglobin and hemoglobin structure/function, oxygen affinity, enzyme mechanisms (chymotrypsin), Michaelis-Menten kinetics, inhibition types, enzyme regulation, and nucleic acid chemistry.

Dissociation Constant ($K_d$)

An equilibrium constant defined as $\frac{[P][L]}{[PL]}$; a lower numerical value corresponds to higher binding affinity, and it represents the ligand concentration at which half of the available binding sites are occupied ($Y = 0.5$).

Association Constant ($K_a$)

The equilibrium constant describing the binding reaction $P + L \rightleftharpoons PL$, defined as $\frac{[PL]}{[P][L]}$ and equal to the reciprocal of the dissociation constant ($\frac{1}{K_d}$).

Fractional Saturation ($Y$)

The fraction of total ligand-binding sites on a protein that are bound to ligand, calculated as $\frac{[PL]}{[PL] + [P]}$ or $\frac{[L]}{[L] + K_d}$.

Myoglobin

A monomeric globular hemoprotein composed of $153$ amino acid residues folded into eight $\alpha$-helices ($\text{A}-\text{H}$) with a globin fold and hydrophobic interior, specialized for oxygen storage and diffusion facilitation in muscle.

Heme

A prosthetic group consisting of a planar protoporphyrin IX ring coordinating an iron atom in the ferrous ($\text{Fe}^{2+}$) state via four in-plane pyrrole nitrogens and two perpendicular coordination sites.

Proximal Histidine

The specific residue ($\text{His F8}$ or $\text{His93}$) that coordinates directly to the ferrous ($\text{Fe}^{2+}$) iron at one of the perpendicular coordination positions of the prosthetic group.

Distal Histidine

The specific residue ($\text{His E7}$ or $\text{His64}$) located on the oxygen-binding side of the heme plane that forms a hydrogen bond with bound molecular oxygen and steric hindrance against linear carbon monoxide binding.

Protein "Breathing"

Transient, subtle conformational fluctuations of globin amino acid side chains that create temporary cavities and passages, allowing ligand molecules ($\text{O}_2$ or $\text{CO}$) to access and depart the buried prosthetic group.

Hemoglobin

A heterotetrameric oxygen-transport protein composed of two $\alpha$ and two $\beta$ subunits ($\alpha_2\beta_2$ dimer of heterodimers), containing four heme groups capable of cooperative, allosteric oxygen binding in erythrocytes.

Globin Gene Evolution

The diversification of globin genes through multiple ancestral gene duplication events over roughly $800$ million years, giving rise to specialized paralogs including neuroglobin, cytoglobin, myoglobin, and embryonic/fetal/adult hemoglobin chains.

T State

The tense, deoxygenated conformation of hemoglobin (deoxyhemoglobin) characterized by a low affinity for oxygen and stabilization via intra- and inter-subunit salt bridges and allosteric effectors.

R State

The relaxed, oxygenated conformation of hemoglobin (oxyhemoglobin) in which the planar rearrangement of the iron-porphyrin complex ruptures inter-subunit salt bridges, yielding high ligand affinity.

Homotropic Allosteric Regulator

A protein's native ligand that simultaneously acts as an allosteric modulator of its own binding behavior at other subunits, exemplified by molecular oxygen ($\text{O}_2$) binding to hemoglobin.

Hill Equation

The mathematical relationship describing cooperative ligand binding: $\log\left(\frac{Y}{1 - Y}\right) = n_H\log(pO_2) - n_H\log(P_{50})$.

Hill Coefficient ($n_H$)

A quantitative index of cooperativity among multiple binding sites: $n_H > 1$ denotes positive cooperativity, $n_H = 1$ reflects independent non-cooperative binding, and $n_H < 1$ indicates negative (anticooperative) binding.

Physiological Oxygen Binding Curves of Mb vs. Hb

Myoglobin exhibits a hyperbolic curve with high affinity ($P_{50} = 0.26\,\text{kPa}$) suited for cellular storage, whereas hemoglobin exhibits a sigmoidal curve ($P_{50} \approx 3.5\,\text{kPa}$) allowing nearly full loading at arterial lungs ($\sim 13\,\text{kPa}$) and efficient unloading in active venous tissues ($\sim 4\,\text{kPa}$).

Bohr Effect

The physiological reduction in hemoglobin's oxygen affinity triggered by elevated hydronium ion concentration (lower $\text{pH}$) and elevated partial pressure of $\text{CO}_2$, shifting the oxygen binding curve to the right to stimulate tissue release.

Haldane Effect

The physiological reduction in hemoglobin's affinity for carbon dioxide and protons upon oxygenation in the lungs, facilitating the discharge of $\text{CO}_2$ into exhaled alveolar air.

Carbamate Formation on Hemoglobin

The reversible covalent addition of $\text{CO}_2$ onto uncharged N-terminal $\alpha$-amino groups of globin chains, creating negatively charged carbamino-terminal residues that participate in salt bridges stabilizing the T state and releasing free protons.

2,3-Bisphosphoglycerate ($2,3\text{-BPG}$)

A highly anionic glycolytic intermediate present in red blood cells that functions as a negative heterotropic allosteric effector by binding to a central cavity between $\beta$-subunits and stabilizing the low-affinity T state.

Fetal Hemoglobin ($\text{HbF}$)

A tetrameric hemoglobin isoform composed of $\alpha_2\gamma_2$ chains, wherein the replacement of $\beta\text{-His143}$ with $\gamma\text{-Ser143}$ eliminates two positive charges in the central cavity, decreasing affinity for $2,3\text{-BPG}$ and providing higher oxygen affinity than maternal hemoglobin.

Sickle-Cell Hemoglobin ($\text{HbS}$)

A pathological hemoglobin variant caused by an $\text{E6V}$ point mutation (hydrophilic glutamate replaced by hydrophobic valine at position 6 of the $\beta$-chain), which creates a hydrophobic contact that induces polymerization into rigid filaments in the T state.

Hemoglobin Kansas

A clinical variant caused by an $\text{Asn102} \rightarrow \text{Thr102}$ substitution in the $\beta$-subunit that destabilizes the R state, resulting in abnormally low oxygen affinity and clinical cyanosis.

Hemoglobin Philadelphia

A clinical variant caused by a $\text{Tyr35} \rightarrow \text{Phe35}$ substitution in the $\beta$-subunit that destabilizes the quaternary tetrameric assembly, leading to hemolytic anemia.

Biological vs. Inorganic Catalysts

Enzymatic catalysts achieve substantially greater reaction rate enhancements ($10^6$ to $10^{17}$ times faster), operate under mild aqueous physiological conditions ($\sim 37^\circ\text{C}$, neutral $\text{pH}$), display high substrate specificity, and are subject to biological regulation.

Apoenzyme and Holoenzyme

An apoenzyme is the purely polypeptide, catalytically inactive form of an enzyme lacking its essential cofactor/coenzyme, whereas a holoenzyme is the complete, catalytically active complex containing the protein and all required non-protein components.

Cofactors and Coenzymes

Cofactors are inorganic chemical elements (such as $Fe^{2+}$, $Mg^{2+}$, or $Zn^{2+}$) required for catalytic activity, whereas coenzymes are complex organic or metalloorganic carrier molecules typically derived from dietary vitamins.

Seven Enzyme Commission (EC) Classes

1. Oxidoreductases (electron/hydride transfer)\n2. Transferases (functional group transfer)\n3. Hydrolases (hydrolytic cleavage)\n4. Lyases (group addition to double bonds or non-hydrolytic bond cleavage)\n5. Isomerases (intramolecular rearrangement)\n6. Ligases (bond formation coupled to ATP cleavage)\n7. Translocases (ion/molecule movement across membranes).

Activation Energy ($\Delta G^\ddagger$)

The free energy difference between the ground state of reactants and the high-energy transition state, which acts as a kinetic barrier determining reaction rate according to $k = \left(\frac{\kappa T}{h}\right)e^{-\frac{\Delta G^\ddagger}{RT}}$; catalysts accelerate reactions solely by lowering this barrier without altering $\Delta G^{\prime\circ}$.

Binding Energy ($\Delta G_B$)

The free energy released upon forming weak non-covalent interactions (hydrogen bonds, ionic pairs, hydrophobic interactions) between enzyme and substrate, reaching maximum magnitude specifically during transition state conformation.

Pauling's Principle of Transition State Complementarity

The concept that an enzyme's active site is structurally complementary to the reaction's transition state rather than the ground-state substrate; complementary binding to the transition state drives catalysis by lowering the net activation barrier, whereas high complementarity to the substrate would trap it in a thermodynamic pit.

General Acid-Base Catalysis

A mechanism accelerating reaction rates via proton donations or abstractions mediated by weak acidic or basic functional groups on amino acid side chains (e.g., His, Asp, Glu, Lys, Cys) rather than solvent hydronium ($\text{H}_3\text{O}^+$) or hydroxide ($\text{OH}^-$).

Covalent Catalysis

A mechanism in which an active-site nucleophile forms a transient covalent linkage with the substrate, introducing a modified, lower-energy pathway that is subsequently resolved to regenerate the free enzyme.

Metal Ion Catalysis

A catalytic mechanism employed by metalloenzymes wherein bound metal ions orient substrates, electrostatically shield or stabilize developing negative charges on transition states, and mediate oxidation-reduction steps.

Michaelis-Menten Equation

The fundamental mathematical expression for single-substrate hyperbolic enzyme kinetics: $V_0 = \frac{V_{\max}[S]}{K_m + [S]}$.

Steady-State Assumption

The kinetic postulate that the concentration of the enzyme-substrate complex ($[ES]$) remains virtually constant throughout the measured initial reaction velocity phase because its rate of formation equals its rate of breakdown.

Michaelis Constant ($K_m$)

The substrate concentration at which the initial reaction velocity equals half of maximal velocity ($0.5\,V_{\max}$), mechanistically defined as $\frac{k_{-1} + k_2}{k_1}$; a smaller value reflects greater substrate specificity.

Conditions Where $K_m \approx K_d$

The specific kinetic scenario where the catalytic rate constant is vastly slower than the dissociation rate constant ($k_2 \ll k_{-1}$), reducing $\frac{k_{-1} + k_2}{k_1}$ to $\frac{k_{-1}}{k_1}$.

Turnover Number ($k_{\text{cat}}$)

The first-order rate constant defining the maximum number of substrate molecules converted to product per enzyme active site per unit time at saturation, calculated as $\frac{V_{\max}}{[E_T]}$ with units of $\text{s}^{-1}$.

Specificity Constant ($k_{\text{cat}} / K_m$)

A quantitative metric of enzyme efficiency and substrate preference at low substrate concentrations ($[S] \ll K_m$); it has an upper theoretical ceiling of $10^8 - 10^9\,\text{M}^{-1}\text{s}^{-1}$ established by aqueous diffusion limits (catalytic perfection).

Lineweaver-Burk Double-Reciprocal Plot

A linearized transformation of Michaelis-Menten kinetics defined by $\frac{1}{V_0} = \left(\frac{K_m}{V_{\max}}\right)\frac{1}{[S]} + \frac{1}{V_{\max}}$, where the y-intercept is $\frac{1}{V_{\max}}$, the x-intercept is $-\frac{1}{K_m}$, and the slope is $\frac{K_m}{V_{\max}}$

Competitive Inhibitor

A reversible inhibitor that directly competes with substrate for the free enzyme's active site, increasing apparent $K_m$ ($\alpha K_m$) while leaving $V_{\max}$ unaltered; Lineweaver-Burk plots show lines intersecting at the identical y-intercept.

Uncompetitive Inhibitor

A reversible inhibitor that binds selectively to the enzyme-substrate ($ES$) complex, decreasing both apparent $V_{\max}$ ($\frac{V_{\max}}{\alpha'}$) and apparent $K_m$ ($\frac{K_m}{\alpha'}$) by the exact same proportion; Lineweaver-Burk plots yield parallel lines.

Mixed Inhibitor

A reversible inhibitor that binds to both the free enzyme ($E$) and the enzyme-substrate complex ($ES$) with differing affinities, lowering apparent $V_{\max}$ ($\frac{V_{\max}}{\alpha'}$) and altering apparent $K_m$ ($\frac{\alpha K_m}{\alpha'}$); lines intersect left of the y-axis.

Catalytic Triad Residues of Chymotrypsin

$\text{Asp102}$, $\text{His57}$, and $\text{Ser195}$; $\text{Asp102}$ forms a low-barrier hydrogen bond that polarizes $\text{His57}$, allowing it to act as a general base that abstracts a proton from $\text{Ser195}$, creating an active alkoxide nucleophile.

Oxyanion Hole in Serine Proteases

A structural pocket containing peptide backbone amide nitrogens of $\text{Gly193}$ and $\text{Ser195}$ that donate hydrogen bonds to stabilize the unstable negative formal charge on the oxygen of tetrahedral intermediates.

Chymotrypsin Acylation Phase

The first catalytic stage wherein nucleophilic $O^\gamma$ of $\text{Ser195}$ attacks the substrate carbonyl carbon, forming a tetrahedral intermediate that collapses into an ester-linked acyl-enzyme intermediate while $\text{His57}$ donates a proton to eject the C-terminal peptide fragment.

Chymotrypsin Deacylation Phase

The second catalytic stage wherein an incoming water molecule is deprotonated by $\text{His57}$ acting as a general base to form hydroxide, attacking the acyl-enzyme ester to yield a second tetrahedral intermediate that collapses to release the carboxylate product and regenerate free enzyme.

pH-Dependence of Chymotrypsin

At acidic $\text{pH}$, $\text{His57}$ is protonated and cannot serve as a general base (reducing $k_{\text{cat}}$), while at alkaline $\text{pH}$, the $\text{Ile16}$ $\alpha$-amino group deprotonates, abolishing its salt bridge with $\text{Asp194}$ and collapsing the substrate-binding pocket (increasing $K_m$).

Specificity Pockets of Chymotrypsin, Trypsin, and Elastase

Chymotrypsin features a deep, nonpolar pocket accommodating aromatic side chains (Phe, Trp, Tyr); Trypsin possesses an $\text{Asp189}$ residue at its base that binds positively charged basic residues (Arg, Lys); Elastase contains bulky $\text{Val190}$ and $\text{Val216}$ side chains that restrict entry to small residues (Ala, Gly).

Effect of Temperature on Enzyme Velocity

Reaction velocity rises with temperature due to increased kinetic energy and collision frequency until reaching an optimum ($\sim 40^\circ\text{C}$), beyond which thermal denaturation unfolds tertiary protein structure and causes a steep drop in activity.

Aspartate Transcarbamoylase (ATCase) Structure

A regulatory allosteric transferase composed of $12$ total subunits organized into two catalytic trimers ($2 \times c_3$) and three regulatory dimers ($3 \times r_2$), catalyzing the committing step in pyrimidine biosynthesis.

Allosteric Modulators of ATCase

$\text{ATP}$ (a purine) acts as a positive heterotropic activator that stabilizes the R state and decreases $K_{0.5}$; $\text{CTP}$ (a pyrimidine end-product) acts as a negative heterotropic feedback inhibitor that stabilizes the T state and increases $K_{0.5}$.

Zymogen

An inactive enzymatic precursor (proenzyme) requiring irreversible, site-specific proteolytic cleavage of one or more peptide bonds to acquire conformational activation (e.g., trypsinogen converted to active trypsin).

Protein Kinases and Phosphatases

Protein kinases covalently attach a phosphoryl group from the $\gamma$-position of $\text{ATP}$ to specific hydroxyl groups (Ser, Thr, Tyr) or His side chains, whereas phosphoprotein phosphatases hydrolytically cleave and remove attached phosphoryl groups.

Nucleoside vs. Nucleotide

A nucleoside consists solely of a nitrogenous base joined to a five-carbon pentose sugar via an N-glycosidic bond, whereas a nucleotide consists of a nucleoside esterified to one or more phosphate groups at the ribose hydroxyl positions.

Purine vs. Pyrimidine Bases

Purines are planar bicyclic structures containing fused five- and six-membered rings (adenine and guanine), while pyrimidines are monocyclic planar six-membered rings (cytosine, thymine, and uracil).

Phosphodiester Bond

The covalent linkage connecting adjacent nucleotides in nucleic acid polymers, formed between the $5'\text{-phosphate}$ group of one pentose sugar and the $3'\text{-hydroxyl}$ group of the adjoining pentose sugar.

Structural Features of B-DNA

A right-handed antiparallel double helix with a hydrophilic sugar-phosphate backbone on the exterior, aromatic bases stacked perpendicularly inside, major and minor grooves, and $10.5$ base pairs per helical repeat.

Alkaline Hydrolysis of RNA

The rapid cleavage of the phosphodiester backbone of $\text{RNA}$ under basic conditions, driven by deprotonation of the ribose $2'\text{-OH}$ group which initiates an intramolecular nucleophilic attack on the adjacent phosphorus to produce a $2',3'\text{-cyclic monophosphate}$ intermediate.

Non-Genomic Cellular Roles of Nucleotides

Serving as cellular energy currency through phosphoanhydride hydrolysis of $\text{ATP}$, functioning as structural scaffolds in metabolic coenzymes ($\text{NAD}^+$, $\text{FAD}$, $\text{CoA}$), and acting as secondary intracellular messengers ($\text{cAMP}$, $\text{cGMP}$).