Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Physical Chemistry → Chemical kinetics ↓


Enzyme Kinetics


Enzyme kinetics is an important part of biochemistry and physical chemistry that deals with the study of chemical reactions mediated by enzymes. Enzymes are biological catalysts—their presence accelerates reaction rates without being consumed in the process. By understanding enzyme kinetics, scientists can not only understand the mechanisms of enzyme reactions but also develop insights into how to manipulate or control such reactions in a variety of applications ranging from industrial processes to disease treatment.

Basics of enzyme kinetics

Enzymes work by lowering the activation energy required for a chemical reaction to occur. This usually involves the formation of an enzyme-substrate complex, which is subsequently broken down to release the product and regenerate the enzyme. The basic equation governing enzyme kinetics is the Michaelis-Menten equation.

v = (V_max [s]) / (K_m + [s])

Where:

  • v is the rate of the reaction.
  • [S] is the substrate concentration.
  • V_max is the maximum rate achieved by the system at saturated substrate concentration.
  • K_M is the Michaelis constant - a measure of the affinity of the enzyme for its substrate.

Visual example of Michaelis-Menten kinetics

Rate of reaction (v) [S]

Deriving the Michaelis-Menten equation

The derivation of the Michaelis–Menten equation begins with the construction of the enzyme–substrate complex:

E + S ⇌ ES → E + P

Where E represents the enzyme, S the substrate, ES the enzyme-substrate complex and P the product. The first step is an equilibrium reaction marked by the rate constants k_1 and k_-1, while the second step has the rate constant k_2.

The rate of product formation can be described as:

rate = k_2 [ES]

In the steady state, the formation of [ES] remains constant, resulting in:

k_1[E][S] = (k_-1 + k_2)[Es]

From this, we replace [E] in terms of the total enzyme concentration [E]_0:

[E] = [E]_0 - [ES]

Inserting this into the previous equation gives the steady-state concentration of [ES], which ultimately simplifies the Michaelis–Menten equation.

Key parameters in enzyme kinetics

It is important to understand key parameters such as the Michaelis constant (K_M) and the maximum rate (V_max):

  • Michaelis constant (K_M): It represents the concentration of substrate required to reach half of V_max. Low K_M indicates high affinity between the enzyme and substrate.
  • Maximum rate (V_max): This is the rate observed when the enzyme is saturated with substrate.

Lineweaver–Burk and Eadie–Hofstee plots

Another method used to analyze enzyme kinetics is the Lineweaver-Burk plot. It is the double reciprocal of the Michaelis-Menten equation:

1/v = (K_M/V_max)(1/[S]) + 1/V_max

The plot of 1/v vs 1/[S] gives a straight line that can be used to obtain both K_M and V_max.

1/V 1/[S]

Another powerful method is the Eadie-Hofstee plot:

v = V_max - K_M (v/[S])

This is plotted with v on the y-axis and v/[S] on the x-axis. The slope gives the K_M value, and the intercept on the y-axis gives V_max.

Inhibition of enzyme kinetics

Enzyme activity can be inhibited, and understanding these effects is important for manipulating enzyme behavior. Inhibitors are molecules that reduce enzyme activity. There are several types of inhibition:

  • Competitive inhibition: The inhibitor competes with the substrate for the active site.
  • Non-competitive inhibition: The inhibitor binds to another part of the enzyme, changing its shape.
  • Noncompetitive inhibition: The inhibitor binds to the enzyme-substrate complex.

Competitive inhibition

In competitive inhibition, the presence of the inhibitor increases K_M but does not change V_max. The formula is represented as:

v = (V_max [S]) / (αK_M + [S])

where α is the factor by which the original K_M is increased.

Non-competitive inhibition

Non-competitive inhibitors reduce the total number of active enzyme molecules, thereby decreasing V_max, but having no effect K_M.

v = (V_max [S]) / (K_M + α[S])

Non-compete prohibition

Uncompetitive inhibitors bind only to the enzyme-substrate complex, resulting in lower V_max and K_M values. This binding makes the complex more stable and less likely to release product:

v = (V_max [S]) / (K_M + [S]/α')

Applications of enzyme kinetics

Enzyme kinetics has many practical applications, ranging from pharmaceuticals to the fermentation industry. Here are some examples:

  • Drug design: Understanding how drugs interact with enzymes and developing competitive inhibitors as drugs.
  • Enzyme replacement therapy: Used to treat diseases caused by enzyme deficiency by supplying enzyme replacement.
  • Biotechnology: Development of biocatalysts for industrial processes involving chemical reactions.

Conclusion

Enzyme kinetics provides important information about the function and behavior of enzymes in different environments and conditions. This scientific discipline combines aspects of chemistry and biology, leading to great advances in both theoretical and practical applications. By using graphs and equations such as the Michaelis-Menten equation, the Lineweaver-Burk plot, and by dealing with inhibition types, we deepen our understanding of how reactions are catalyzed in biological systems.


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Enzyme Kinetics

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