Biochemistry

Biochemistry is the study of chemical processes within living organisms, focusing on the structure and function of biomolecules such as proteins, nucleic acids, carbohydrates, and lipids. Understanding biochemical processes is fundamental to comprehending cellular function, metabolism, and the molecular basis of life.

Protein Structure and Function

Primary Structure

The primary structure of a protein is its linear sequence of amino acids:

Amino Acid Properties

Amino acids have a central carbon (α-carbon) bonded to:

• Amino group (NH₃⁺ at physiological pH)
• Carboxyl group (COO⁻ at physiological pH)
• Hydrogen atom
• Side chain (R group) - varies by amino acid type

Amino Acid Classification

• Nonpolar (hydrophobic): Alanine, Valine, Leucine, Isoleucine, Proline, Phenylalanine, Tryptophan, Methionine
• Polar uncharged: Serine, Threonine, Asparagine, Glutamine, Tyrosine, Cysteine
• Acidic: Aspartate, Glutamate
• Basic: Lysine, Arginine, Histidine

Secondary Structure

α-Helix

Stabilized by hydrogen bonds between backbone carbonyl oxygen of residue $n$ and backbone amide hydrogen of residue $n+4$.

β-Sheet

• Parallel: Adjacent strands run in same direction
• Antiparallel: Adjacent strands run in opposite directions
• Stabilized by interstrand hydrogen bonds

Other Secondary Structures

• β-turn: Sharp turns (often contains Gly, Pro)
• Ω-loop: Irregular structures connecting secondary elements

Tertiary Structure

Stabilizing interactions:

• Hydrophobic interactions: Nonpolar side chains cluster internally
• Hydrogen bonds: Between polar side chains
• Ionic bonds: Between charged side chains
• Disulfide bonds: Covalent cross-links (Cys residues)
• van der Waals forces: Weak attractive forces

Quaternary Structure

Examples: Hemoglobin (α₂β₂), DNA polymerase, antibodies

Protein Folding

Thermodynamic Model

Where $\Delta G_{fold} < 0$ for spontaneous folding.

Folding Pathways

• Nucleation-condensation: Early folding nucleus formation
• Hierarchical folding: Secondary structure → domain → overall fold
• Concerted folding: All elements fold simultaneously

Enzyme Structure and Function

Enzyme Nomenclature

Enzymes are classified by the type of reaction they catalyze:

• EC 1: Oxidoreductases
• EC 2: Transferases
• EC 3: Hydrolases
• EC 4: Lyases
• EC 5: Isomerases
• EC 6: Ligases

Catalytic Mechanisms

Transition State Stabilization

Where ES† represents the transition state complex.

Catalytic Strategies

1. Acid-base catalysis: Proton transfer
2. Covalent catalysis: Formation of enzyme-substrate intermediate
3. Metal ion catalysis: Stabilization of charges or redox reactions
4. Proximity effects: Positioning of substrates

Enzyme Kinetics

Michaelis-Menten Kinetics

Where:

• $v$ = initial reaction velocity
• $V_{max}$ = maximum velocity
• $[S]$ = substrate concentration
• $K_M$ = Michaelis constant

Determination of Kinetic Parameters

Catalytic Efficiency

Where $k_{cat}$ is the turnover number (catalytic constant).

Factors Affecting Enzyme Activity

pH Effects

Temperature Effects

Substrate and Enzyme Concentrations

• At low [S]: $v \propto [S]$ (first order)
• At high [S]: $v \approx V_{max}$ (zero order)

Enzyme Regulation

Allosteric Regulation

Models of Allosteric Regulation

• MWC Model: Symmetry model (T and R states)
• KNF Model: Sequential model (induced fit)

Covalent Modification

• Phosphorylation: Most common (Ser, Thr, Tyr residues)
• Acetylation: Lysine residues
• Ubiquitination: Target for degradation
• Glycosylation: Addition of sugar groups

Isoenzymes

Example: Lactate dehydrogenase (LDH) has 5 isoenzymes (M₄, M₃H₁, M₂H₂, MH₃, H₄)

Metabolic Pathways

Overview of Major Pathways

Glycolysis

Net reaction: 1 glucose → 2 pyruvate + 2 ATP + 2 NADH

Citric Acid Cycle (TCA Cycle)

Oxidative Phosphorylation

Metabolic Regulation

Energy Charge

Phosphorylation Potential

Control of Metabolic Flux

Rate-Limiting Steps

Where $J$ is flux and $E_i$ is enzyme concentration.

Feed-Forward and Feedback Regulation

• Feedback inhibition: End product inhibits early enzyme
• Feed-forward activation: Substrate activates later enzyme

Carbohydrate Metabolism

Glycolysis Regulation

Key Regulatory Enzymes

1. Hexokinase: Inhibited by G6P
2. Phosphofructokinase: Allosterically regulated by ATP/AMP, citrate, fructose-2,6-bisphosphate
3. Pyruvate kinase: Regulated by F16BP (activation) and ATP (inhibition)

Gluconeogenesis

Pentose Phosphate Pathway

Major functions: NADPH production, ribose-5-phosphate synthesis

Lipid Metabolism

Fatty Acid Synthesis

Fatty Acid Oxidation (β-Oxidation)

Each cycle removes 2 carbon atoms as acetyl-CoA.

Cholesterol Metabolism

Rate-limiting step: HMG-CoA reductase

Amino Acid Metabolism

Transamination

Catalyzed by aminotransferases (require pyridoxal phosphate cofactor).

Urea Cycle

Nitrogen Balance

Bioenergetics

ATP Structure and Function

Standard Free Energy of Hydrolysis

Electron Transport and Oxidative Phosphorylation

Proton Motive Force

Where $\Delta \psi$ is membrane potential and $\Delta pH$ is pH gradient.

Signal Transduction

Receptor Types

• G-protein coupled receptors (GPCRs)
• Receptor tyrosine kinases (RTKs)
• Ion channel receptors
• Nuclear receptors

Second Messenger Systems

cAMP Pathway

Integration of Metabolism

Hormonal Control

• Insulin: Promotes glucose uptake, glycogenesis, lipogenesis
• Glucagon: Promotes glycogenolysis, gluconeogenesis
• Epinephrine: Acute energy mobilization
• Cortisol: Long-term stress response, gluconeogenesis

Tissue-Specific Metabolism

• Liver: Major site of gluconeogenesis, urea cycle, lipogenesis
• Muscle: Glucose utilization, glycogen storage
• Brain: Glucose-dependent (except during starvation)
• Adipose tissue: Fat storage and mobilization

Real-World Application: Enzyme Inhibition in Drug Design

Understanding enzyme kinetics is crucial for drug development and therapeutic applications.

Enzyme Inhibition Analysis

# Enzyme inhibition kinetics for drug development
enzyme_data = {
    'kcat': 150,          # s⁻¹ (turnover number)
    'km': 0.002,          # M (Michaelis constant)  
    'ki': 1e-7,           # M (inhibitor dissociation constant)
    'enzyme_concentration': 1e-6,  # M (total enzyme)
    'substrate_concentration': 0.005,  # M (substrate)
    'inhibitor_concentration': 1e-5,   # M (inhibitor)
    'inhibition_type': 'competitive'  # competitive, uncompetitive, noncompetitive
}

# Calculate initial velocity without inhibitor
v_max = enzyme_data['kcat'] * enzyme_data['enzyme_concentration']  # M/s
v_without_inhibitor = (v_max * enzyme_data['substrate_concentration']) / (enzyme_data['km'] + enzyme_data['substrate_concentration'])

# Calculate velocity with competitive inhibition
if enzyme_data['inhibition_type'] == 'competitive':
    km_apparent = enzyme_data['km'] * (1 + enzyme_data['inhibitor_concentration'] / enzyme_data['ki'])
    v_with_inhibitor = (v_max * enzyme_data['substrate_concentration']) / (km_apparent + enzyme_data['substrate_concentration'])
elif enzyme_data['inhibition_type'] == 'uncompetitive':
    alpha = 1 + enzyme_data['inhibitor_concentration'] / enzyme_data['ki']
    km_apparent = enzyme_data['km'] / alpha
    v_max_apparent = v_max / alpha
    v_with_inhibitor = (v_max_apparent * enzyme_data['substrate_concentration']) / (km_apparent + enzyme_data['substrate_concentration'])
else:  # noncompetitive
    alpha = 1 + enzyme_data['inhibitor_concentration'] / enzyme_data['ki']
    v_max_apparent = v_max / alpha
    v_with_inhibitor = (v_max_apparent * enzyme_data['substrate_concentration']) / (enzyme_data['km'] + enzyme_data['substrate_concentration'])

# Calculate percent inhibition
percent_inhibition = ((v_without_inhibitor - v_with_inhibitor) / v_without_inhibitor) * 100

# Calculate IC50 (concentration for 50% inhibition)
# For competitive inhibition: IC50 = Ki * (1 + [S]/Km)
ic50 = enzyme_data['ki'] * (1 + enzyme_data['substrate_concentration'] / enzyme_data['km'])

print(f"Enzyme kinetics analysis:")
print(f"  kcat: {enzyme_data['kcat']} s⁻¹")
print(f"  Km: {enzyme_data['km']*1000:.2f} mM")
print(f"  Inhibitor Ki: {enzyme_data['ki']*1e6:.2f} μM")
print(f"  Vmax: {v_max*1e6:.2f} μM/s")
print(f"  Velocity without inhibitor: {v_without_inhibitor*1e6:.2f} μM/s")
print(f"  Velocity with inhibitor: {v_with_inhibitor*1e6:.2f} μM/s")
print(f"  Percent inhibition: {percent_inhibition:.1f}%")
print(f"  Calculated IC50: {ic50*1e6:.2f} μM")

# Therapeutic implications
if percent_inhibition > 80:
    therapeutic_assessment = "Potent inhibitor - likely therapeutic effect"
elif percent_inhibition > 50:
    therapeutic_assessment = "Moderate inhibition - may require optimization"
else:
    therapeutic_assessment = "Weak inhibition - not likely therapeutic"
    
print(f"  Therapeutic potential: {therapeutic_assessment}")

# Determine optimal dosing based on IC50
dose_recommendation = "High dose needed" if ic50 > 10e-6 else "Moderate dose effective" if ic50 > 1e-6 else "Low dose effective"
print(f"  Dose recommendation: {dose_recommendation}")

Drug Development Considerations

Factors in translating enzyme kinetics to therapeutic applications.

Your Challenge: Metabolic Control Analysis

Analyze the flux control of a metabolic pathway and determine the effects of enzyme inhibition on pathway flux.

Goal: Calculate metabolic control coefficients and analyze pathway regulation.

Pathway Data

import math

# Metabolic pathway with three consecutive enzymes
pathway_data = {
    'enzymes': [
        {'name': 'Enzyme A', 'vmax': 50, 'km': 0.1, 'concentration': 1e-6},  # μmol/min/mg
        {'name': 'Enzyme B', 'vmax': 40, 'km': 0.05, 'concentration': 1.2e-6},
        {'name': 'Enzyme C', 'vmax': 60, 'km': 0.2, 'concentration': 0.8e-6}
    ],
    'substrate_concentration': 0.1,  # mM (common substrate concentration)
    'pathway_flux': 25,              # μmol/min/mg (measured flux)
    'total_enzyme_concentration': 3e-6  # M
}

# Calculate individual enzyme velocities at given substrate concentration
enzyme_velocities = []
for enzyme in pathway_data['enzymes']:
    velocity = (enzyme['vmax'] * pathway_data['substrate_concentration']) / (enzyme['km'] + pathway_data['substrate_concentration'])
    enzyme_velocities.append(velocity)

# Calculate flux control coefficients (simplified approach)
# In a linear pathway, rate-limiting steps have higher control coefficients
relative_velocities = [v/max(enzyme_velocities) for v in enzyme_velocities]
# Estimate control coefficient based on relative velocity (inverse relationship)
control_coefficients = [1 - v for v in relative_velocities]
total_cc = sum(control_coefficients)
if total_cc > 0:
    flux_control_coefficients = [cc/total_cc * len(pathway_data['enzymes']) for cc in control_coefficients]
else:
    flux_control_coefficients = [1.0/len(pathway_data['enzymes'])] * len(pathway_data['enzymes'])

# Calculate elasticity coefficients (simplified)
elasticity_coefficients = []
for i, enzyme in enumerate(pathway_data['enzymes']):
    # Elasticity (change in rate per change in substrate) ≈ vmax / (km + [S])
    elasticity = enzyme['vmax'] / (enzyme['km'] + pathway_data['substrate_concentration'])
    elasticity_coefficients.append(elasticity)

# Calculate pathway response to 50% inhibition of each enzyme
inhibition_effects = []
for i, velocity in enumerate(enzyme_velocities):
    # If an enzyme is 50% inhibited, its effective rate becomes 0.5 * original
    # Simplified model: pathway flux is proportional to minimum velocity
    modified_velocities = enzyme_velocities.copy()
    modified_velocities[i] = velocity * 0.5
    # Assume overall flux is proportional to minimum of all velocities
    new_flux = min(modified_velocities)  # Simplified model
    effect = (new_flux - pathway_data['pathway_flux']) / pathway_data['pathway_flux']
    inhibition_effects.append(effect)

# Calculate metabolic control summation
# The sum of control coefficients should equal 1 (flux control) or 0 (concentration control)
flux_control_sum = sum(flux_control_coefficients)

Analyze the metabolic pathway to determine rate-limiting steps and control patterns.

Hint:

• Calculate enzyme velocities at given substrate concentration
• Estimate flux control coefficients using relative velocities
• Consider how inhibition of each enzyme affects overall pathway flux
• Evaluate the relationship between enzyme kinetic parameters and pathway control

# TODO: Calculate metabolic control parameters
rate_limiting_step = ""  # Name of most rate-limiting enzyme
flux_control_coefficients = [0, 0, 0]  # Control coefficients for each enzyme
elasticity_coefficients = [0, 0, 0]  # Elasticity coefficients for each enzyme
inhibition_sensitivity = [0, 0, 0]  # Sensitivity to 50% inhibition
flux_response = 0  # Overall pathway flux response

# Calculate velocities for each enzyme
for i, enzyme in enumerate(pathway_data['enzymes']):
    velocity = (enzyme['vmax'] * pathway_data['substrate_concentration']) / (enzyme['km'] + pathway_data['substrate_concentration'])
    enzyme_velocities[i] = velocity

# Calculate flux control coefficients (simplified approach based on relative rates)
max_velocity = max(enzyme_velocities)
relative_rates = [v/max_velocity for v in enzyme_velocities]
rate_limiting_step_idx = enzyme_velocities.index(min(enzyme_velocities))
rate_limiting_step = pathway_data['enzymes'][rate_limiting_step_idx]['name']

# Calculate elasticity coefficients: dV/d[S] at the working point
for i, enzyme in enumerate(pathway_data['enzymes']):
    # dV/d[S] = Vmax*Km / (Km + [S])²
    elasticity = (enzyme['vmax'] * enzyme['km']) / (enzyme['km'] + pathway_data['substrate_concentration'])**2
    elasticity_coefficients[i] = elasticity

# Calculate response to 50% inhibition
for i in range(len(pathway_data['enzymes'])):
    # Simplified: the pathway flux is limited by the slowest step
    modified_rates = [r if j != i else r*0.5 for j, r in enumerate(enzyme_velocities)]
    new_flux = min(modified_rates)
    inhibition_sensitivity[i] = (new_flux - min(enzyme_velocities)) / min(enzyme_velocities)

# Calculate flux control coefficients based on sensitivity analysis
# Using the concept that control coefficient = fractional change in flux / fractional change in enzyme activity
for i in range(len(pathway_data['enzymes'])):
    flux_control_coefficients[i] = inhibition_sensitivity[i] / -0.5  # -0.5 because 50% inhibition

# Print results
print(f"Rate-limiting enzyme: {rate_limiting_step}")
print(f"Enzyme velocities: {enzyme_velocities}")
print(f"Flux control coefficients: {flux_control_coefficients}")
print(f"Elasticity coefficients: {elasticity_coefficients}")
print(f"Inhibition sensitivity: {inhibition_sensitivity}")

# Pathway characterization
if max(flux_control_coefficients) > 0.6:
    pathway_type = "Single rate-limiting step"
elif max(flux_control_coefficients) > 0.3:
    pathway_type = "Distributed control with dominant step"
else:
    pathway_type = "Distributed control"
    
print(f"Pathway control type: {pathway_type}")

How would the control analysis change if substrate concentration increased significantly in the pathway?