Q: Effectiveness factor η for immobilized enzymes: how do we quantify the extent to which diffusion slows the reaction rate relative to the intrinsic (no-diffusion-limit) rate?

Introduction: The effectiveness factor η captures how internal and external mass transfer resistances depress the observable reaction rate below the intrinsic kinetic potential. It is widely used with porous catalysts and immobilized enzymes to indicate whether pore diffusion or film limitations are significant. Given Data / Assumptions: Intrinsic rate refers to the rate at uniform surface/interior concentration equal to bulk (no diffusion limitation). Actual rate is the measured volumetric rate under operating conditions, including transport resistances. η is dimensionless and bounded 0 < η ≤ 1 in classical definitions. Concept / Approach: By definition, η = (actual rate) / (rate if not slowed by diffusion). Values much less than 1 indicate significant diffusion limitation; values close to 1 indicate kinetic control. Engineers use η to decide whether to decrease particle size, increase temperature (raising diffusivity), or change support porosity. Step-by-Step Solution: Step 1: Determine the intrinsic kinetic expression (e.g., Michaelis–Menten or power-law) at the relevant C_s.Step 2: Measure or compute the observed rate under the same bulk conditions.Step 3: Take the ratio η = r_actual / r_intrinsic.Step 4: Interpret η to guide process changes to mitigate diffusion effects. Verification / Alternative check: Thiele modulus and effectiveness factor relationships for porous catalysts provide analytical connections between η and internal diffusion severity, supporting the above definition. Why Other Options Are Wrong: Inverted ratios correspond to 1/η, not η itself. Mass transfer rate over reaction rate is a different diagnostic, not the standard η definition. Common Pitfalls: Comparing rates at different bulk concentrations or temperatures; η must compare under identical intrinsic driving forces to be meaningful. Final Answer: actual reaction rate/ rate if not slowed by diffusion

Question 1

Immobilized enzymes—properties: which statement below is not incorrect about how immobilization can alter enzyme behavior and microenvironment?

Accepted Answer

Introduction: Immobilization anchors enzymes onto or within insoluble supports through adsorption, entrapment, covalent linkage, or ionic interactions. This often changes microenvironmental conditions, stability, and transport around the active site. The question probes recognition that many reported changes (chemical and physical property shifts or mimicry of native-like microenvironments) are common and not incorrect statements. Given Data / Assumptions: Immobilization can modify apparent pH optimum, temperature tolerance, and inhibitor sensitivity. Supports and matrices create local microenvironments (e.g., charged gels, hydrophobic pores). Some immobilization modes reduce conformational mobility; others protect from denaturation. Concept / Approach: Reports in biocatalysis literature show altered catalytic constants (k_cat, K_m, apparent), improved thermal or solvent stability, and changes in diffusional accessibility after immobilization. Entrapment within biopolymers and synthetic matrices can approximate aspects of the crowded cellular milieu, hence it is not incorrect to say immobilization may simulate a more realistic environment than dilute aqueous buffers for certain enzymes. Step-by-Step Discussion: Step 1: Evaluate chemical property changes: microenvironmental pH shifts or local ionic strength can alter ionization states near the active site.Step 2: Evaluate physical property changes: mechanical stabilization or altered diffusion can change apparent activity profiles.Step 3: Consider natural-like environments: entrapment in biopolymers (e.g., alginate, collagen) can mimic crowding and protect structure.Step 4: Conclude that options (a)–(c) are acceptable statements; thus “None of the above” is correct to the prompt “Which is not the correct answer?”. Verification / Alternative check: Case studies show immobilized lipases with shifted solvent stability and immobilized glucose isomerase with extended thermal life, illustrating altered properties consistent with the statements. Why Other Options Are Wrong: Stating that immobilized enzyme always loses activity is false; activity may decrease, remain similar, or even increase depending on orientation and support. Common Pitfalls: Interpreting “simulate natural environment” too literally; immobilization mimics some aspects (crowding, local polarity) but not full cellular complexity. Also, do not assume immobilization invariably improves every performance metric. Final Answer: None of the above

Question 2

Immobilization techniques—physical methods: which option best characterizes the bonding responsible for physical immobilization modes such as adsorption, entrapment, and encapsulation?

Accepted Answer

Introduction: Immobilization strategies are broadly divided into physical methods (adsorption, entrapment, encapsulation) and chemical methods (covalent binding, crosslinking). Recognizing the type of interactions involved guides selection of supports and operating conditions, especially when reversible immobilization or mild processing is desired. Given Data / Assumptions: Physical methods aim to retain the enzyme without forming covalent bonds to the matrix. Typical interactions include hydrophobic forces, van der Waals forces, hydrogen bonding, and electrostatic attraction. Entrapment confines enzymes within gels or membranes without direct bonding to the matrix. Concept / Approach: Because physical immobilization avoids covalent reactions with the protein backbone, it is generally simpler, reversible, and gentle, preserving activity for sensitive enzymes. However, it can be more prone to enzyme leaching under changing pH/ionic strength. Chemical methods, in contrast, create covalent linkages that improve retention but require careful control to avoid active-site modification. Step-by-Step Solution: Step 1: List physical modes: adsorption on solids, entrapment in gels, encapsulation in microcapsules.Step 2: Identify the forces: non-covalent interactions or steric confinement.Step 3: Exclude covalent/crosslinking mechanisms used in chemical immobilization.Step 4: Select the option stating non-covalent dependence. Verification / Alternative check: Standard bioprocess references categorize adsorption/entrapment as non-covalent or physical retention techniques, confirming the answer. Why Other Options Are Wrong: Covalent/ionic bond options describe chemical immobilization modes or specific ion-exchange attachment, not general physical methods. Exclusive self-crosslinking (e.g., CLEAs) is chemical and not a physical mode. Common Pitfalls: Assuming ionic binding is always non-covalent “physical”: while ionic is non-covalent, ion-exchange attachment is typically treated as a specific chemical interaction category, not entrapment/encapsulation. Final Answer: non-covalent bond formation dependent

Question 3

Covalent immobilization—supports: which water-insoluble supports are commonly employed for covalent attachment of enzymes?

Accepted Answer

Introduction: Choosing a support for covalent immobilization balances mechanical strength, chemical functionality, hydrophilicity, and biocompatibility. A wide range of organic and biopolymeric matrices have been used successfully to anchor enzymes via functional groups while maintaining activity and stability. Given Data / Assumptions: Acrylamide-based polymers (e.g., polyacrylamide) can be functionalized for coupling. Polypeptide or proteinaceous matrices (e.g., collagen, gelatins) can provide reactive groups for mild coupling. Dextran (e.g., Sephadex derivatives) is a classic hydrophilic support easily activated (e.g., CNBr, epoxy). Concept / Approach: All listed materials have precedents as enzyme carriers after activation to introduce reactive handles (e.g., aldehyde, epoxy, carbodiimide-activated carboxyls). The choice depends on pH/solvent compatibility, pore structure, and targeted orientation to minimize active-site modification. Step-by-Step Solution: Step 1: Assess each material for water-insolubility and functionalizability.Step 2: Confirm literature usage for covalent immobilization.Step 3: Select the inclusive option covering all three support families. Verification / Alternative check: Handbooks on immobilized enzymes list activated dextrans, polyacrylamide gels, and protein-based matrices among standard carriers. Why Other Options Are Wrong: Each single material alone is incomplete as an answer. Silica only: Silica is also common, but restricting to silica ignores the many polymer supports used widely. Common Pitfalls: Overlooking activation chemistry requirements; unactivated polymers may not couple efficiently without prior functionalization. Final Answer: all of these

Question 4

Steady-state concept check: for a system at steady state with respect to substrate concentration, what is the time derivative dCs/dt?

Accepted Answer

Introduction: Steady state is a foundational concept in reactor engineering and transport phenomena. It means that macroscopic state variables do not change with time, even though microscopic processes (reactions, flows) continue. Recognizing what steady state implies for time derivatives helps in setting balances and solving design equations. Given Data / Assumptions: We focus on substrate concentration C_s as the variable of interest. Conditions are steady in time (startup transients have died out). Spatial variations may exist (e.g., gradients), but temporal derivative is zero at each point considered for a steady-state analysis. Concept / Approach: By definition, steady state implies d(any state variable)/dt = 0. In a CSTR at steady state, inlet and outlet flows and reaction exactly balance to maintain constant compositions inside the reactor. In plug flow at steady state, compositions vary with position but not with time at a fixed position, so local time derivatives are still zero. Step-by-Step Solution: Step 1: Write the general transient species balance including accumulation term.Step 2: Apply the steady-state condition: accumulation term = 0.Step 3: Conclude dC_s/dt = 0 for steady operation.Step 4: Use this to simplify reactor design equations (e.g., algebraic rather than differential forms for CSTRs). Verification / Alternative check: Textbook formulations explicitly set time derivatives to zero at steady state, leaving only convective, diffusive, and reaction terms in the balance. Why Other Options Are Wrong: Numerical values (1, >1, <1) do not represent a derivative at steady state. Dependence on reactor volume is irrelevant to whether the time derivative vanishes. Common Pitfalls: Confusing steady state with equilibrium; at steady state, reactions can proceed with non-zero rates as long as influx equals consumption plus outflow. Final Answer: zero

Question 5

Effectiveness factor η for immobilized enzymes: how do we quantify the extent to which diffusion slows the reaction rate relative to the intrinsic (no-diffusion-limit) rate?

Accepted Answer

Introduction: The effectiveness factor η captures how internal and external mass transfer resistances depress the observable reaction rate below the intrinsic kinetic potential. It is widely used with porous catalysts and immobilized enzymes to indicate whether pore diffusion or film limitations are significant. Given Data / Assumptions: Intrinsic rate refers to the rate at uniform surface/interior concentration equal to bulk (no diffusion limitation). Actual rate is the measured volumetric rate under operating conditions, including transport resistances. η is dimensionless and bounded 0 < η ≤ 1 in classical definitions. Concept / Approach: By definition, η = (actual rate) / (rate if not slowed by diffusion). Values much less than 1 indicate significant diffusion limitation; values close to 1 indicate kinetic control. Engineers use η to decide whether to decrease particle size, increase temperature (raising diffusivity), or change support porosity. Step-by-Step Solution: Step 1: Determine the intrinsic kinetic expression (e.g., Michaelis–Menten or power-law) at the relevant C_s.Step 2: Measure or compute the observed rate under the same bulk conditions.Step 3: Take the ratio η = r_actual / r_intrinsic.Step 4: Interpret η to guide process changes to mitigate diffusion effects. Verification / Alternative check: Thiele modulus and effectiveness factor relationships for porous catalysts provide analytical connections between η and internal diffusion severity, supporting the above definition. Why Other Options Are Wrong: Inverted ratios correspond to 1/η, not η itself. Mass transfer rate over reaction rate is a different diagnostic, not the standard η definition. Common Pitfalls: Comparing rates at different bulk concentrations or temperatures; η must compare under identical intrinsic driving forces to be meaningful. Final Answer: actual reaction rate/ rate if not slowed by diffusion

Immobilized Enzyme Questions