Structural Biology & Drug Design

Structural biology is the study of the molecular architecture of biological macromolecules, particularly proteins and nucleic acids. Understanding the three-dimensional structure of biological molecules is crucial for understanding their function and for designing therapeutic interventions.

Protein Structure and Folding

Protein Structure Hierarchy

Primary Structure

Secondary Structure

α-Helix

β-Sheet

• Parallel: $\phi \approx -119°, \psi \approx 113°$
• Antiparallel: $\phi \approx -139°, \psi \approx 135°$

Tertiary and Quaternary Structure

Protein Folding Problem

Levinthal's Paradox

For a 100-residue protein: $3^{100} \approx 5 \times 10^{47}$ possible conformations

Folding Thermodynamics

Experimental Structure Determination

X-ray Crystallography

Structure Factor

Where $f_j$ is the scattering factor of atom $j$ at position $(x_j, y_j, z_j)$.

Resolution

Phase Problem

Data Processing Steps

1. Indexing: Determine unit cell parameters
2. Integration: Measure reflection intensities
3. Scaling: Normalize for experimental effects
4. Merging: Combine symmetry-related reflections

Data Quality Metrics

Cryo-Electron Microscopy (cryo-EM)

Resolution Limits

Contrast Transfer Function (CTF)

Single-Particle Analysis

Nuclear Magnetic Resonance (NMR)

Chemical Shift

Nuclear Overhauser Effect (NOE)

Protein Structure Prediction

Homology Modeling

Model Quality Assessment

AlphaFold & Deep Learning Approaches

Attention Mechanism

Molecular Docking and Virtual Screening

Binding Free Energy

Scoring Functions

Force Field-Based

Empirical Scoring

Where $f_i$ are interaction terms and $w_i$ are weights.

Knowledge-Based Potentials

Docking Algorithms

Rigid Docking

Flexible Docking

Where $\mathbf{\phi}$ represents ligand torsions.

Structure-Based Drug Design

Lead Optimization

Lipinski's Rule of Five

• Molecular weight ≤ 500 Da
• LogP ≤ 5
• H-bond donors ≤ 5
• H-bond acceptors ≤ 10

Fragment-Based Drug Discovery

Pharmacophore Modeling

Required Features

• Hydrogen bond donors/acceptors
• Hydrophobic regions
• Aromatic rings
• Excluded volumes

Target Classes

G-Protein Coupled Receptors (GPCRs)

Structural Features

• Seven transmembrane helices (TM1-TM7)
• Ligand binding pocket: Between helices
• Conformational states: Active/inactive

Modeling Challenges

GPCR Classification

• Class A (Rhodopsin-like)
• Class B (Secretin-like)
• Class C (Metabotropic glutamate)
• Class F (Frizzled)

Ion Channels

Structural Considerations

• Gating mechanism: Conformational changes
• Selectivity filter: Discrimination between ions
• Voltage sensitivity: Voltage-dependent gates

Kinases

Kinase Inhibitors

• Type I: Bind active conformation
• Type II: Bind inactive conformation
• Type III: Allosteric modulators

Drug-Target Interactions

Binding Determinants

Intermolecular Forces

• Hydrogen bonds: 1-5 kcal/mol
• Hydrophobic interactions: 0.5-2 kcal/mol
• Electrostatic interactions: 1-5 kcal/mol
• π-stacking: 1-5 kcal/mol

Induced Fit

ADMET Prediction

Absorption, Distribution, Metabolism, Excretion, Toxicity

Prediction Models

• Caco-2 permeability: Intestinal absorption
• P-gp substrate: Efflux potential
• CYP450 metabolism: Drug-drug interactions
• hERG inhibition: Cardiotoxicity

Advanced Techniques

Free Energy Perturbation (FEP)

Molecular Dynamics Simulations

Alchemical Transformations

Where $\lambda$ controls the transformation.

Drug Discovery Pipeline

Hit Identification

Lead Optimization

Preclinical Development

Challenges and Future Directions

Computational Limitations

• Force field accuracy: Systematic errors
• Implicit solvent models: Missing explicit effects
• Conformational sampling: Limited exploration
• Quantum effects: Born-Oppenheimer approximation

Emerging Technologies

• AI-driven design: Generative models
• Quantum computing: Quantum chemical calculations
• Cryo-EM advances: Higher resolution structures
• Machine learning: Predictive models

Real-World Application: Structure-Based Drug Design for SARS-CoV-2

Structure-based drug design has been crucial in developing antivirals for SARS-CoV-2.

SARS-CoV-2 Main Protease (Mpro) Inhibitors

# Structure-based drug design for SARS-CoV-2 Mpro
target_info = {
    'enzyme': 'Main protease (Mpro)',
    'function': 'Essential for viral replication',
    'substrate_cleavage_site': '(N-terminal)-Leu-Gln-|-[Ser-Ala-Nle-Phe-Gln-Gly]-C-terminal',
    'binding_pocket': 'Cys145 and His41 form catalytic dyad',
    'resolution_structure': 2.1,  # Angstroms
    'binding_affinity_known': 0.016,  # micromolar (for reference compound)
    'active_conformation': 'Antiparallel β-barrel dimer'
}

# Calculate binding energetics for drug design
kbt = 0.6  # kcal/mol at room temperature
binding_energy_reference = -kbt * math.log(target_info['binding_affinity_known'] * 1e-6)  # Convert μM to M

# Structure-based design considerations
binding_pocket_volume = 150  # Angstroms³ (approximate)
pocket_hydrophobicity = 0.6  # Fraction of hydrophobic contacts
pocket_flexibility = 0.3  # Fraction of flexible residues

# Calculate optimal ligand efficiency (LE)
molecular_weight = 500  # Da (typical drug size)
heavy_atoms = 35  # Number of non-hydrogen atoms
ligand_efficiency = binding_energy_reference / (heavy_atoms / 10)  # kcal/mol per 10 non-H atoms

# Estimate synthetic accessibility score (SAS)
sas_score = 3.2  # Typical for a drug-like compound
complexity_factor = 0.8  # Complexity penalty

# Predict binding affinity improvement
# For fragment-based optimization
fragment_size = 200  # Da
fragment_binding_energy = -6  # kcal/mol (typical)
linking_efficiency = 0.3  # Additional kcal/mol per connection

# Calculate predicted improvements
base_affinity = target_info['binding_affinity_known']  # microM
optimization_factor = 10 ** (-ligand_efficiency / (kbt * 2))  # Assuming 2-fold improvement per LE
predicted_improvement = base_affinity / optimization_factor

print(f"SARS-CoV-2 Mpro structure-based drug design:")
print(f"  Target enzyme: {target_info['enzyme']}")
print(f"  Function: {target_info['function']}")
print(f"  Catalytic residues: Cys145 and His41 (dyad)")
print(f"  Structure resolution: {target_info['resolution_structure']} Å")
print(f"  Reference binding affinity: {target_info['binding_affinity_known']} μM")
print(f"  Estimated binding energy: {binding_energy_reference:.1f} kcal/mol")
print(f"  Binding pocket volume: ~{binding_pocket_volume} ų")
print(f"  Pocket hydrophobicity: {pocket_hydrophobicity*100:.0f}%")
print(f"  Ligand efficiency: {ligand_efficiency:.2f} kcal/mol per 10 atoms")

# Assess druggability
if binding_energy_reference < -8:
    druggability = "High - strong binding predicted"
elif binding_energy_reference < -6:
    druggability = "Moderate - good binding potential"
else:
    druggability = "Low - challenging target"

print(f"  Target druggability: {druggability}")

# Clinical relevance
if predicted_improvement < 0.01:
    clinical_potential = "High - sub-micromolar inhibitors possible"
elif predicted_improvement < 0.1:
    clinical_potential = "Moderate - micromolar inhibitors feasible"
else:
    clinical_potential = "Low - significant optimization needed"

print(f"  Predicted clinical potential: {clinical_potential}")
print(f"  Synthetic accessibility score: {sas_score} (lower is better)")

Structure-Based Optimization

Analysis of how structure-guided design improves drug efficacy.

Your Challenge: Structure-Based Drug Design

Design a drug molecule targeting a specific protein using structure-based design principles.

Goal: Create a potential inhibitor for a protein target based on structural information.

Target Protein Analysis

import math

# Target protein structure data
target_data = {
    'name': 'ACE2',
    'function': 'Angiotensin converting enzyme',
    'binding_site_volume': 250,  # Angstroms cubed
    'binding_site_hydrophobicity': 0.7,  # 0-1 scale
    'binding_site_flexibility': 0.2,     # 0-1 scale
    'known_ligand_affinity': 15,         # nM (nanomolar)
    'catalytic_residues': ['His353', 'Glu384', 'Lys357'],
    'surface_charge': -1.5,  # Overall charge (negative)
    'interacting_residues': ['His353', 'Lys357', 'Gln388', 'Asp355']
}

# Available chemical fragments for design
fragments = {
    'benzene': {'weight': 78, 'hydrophobic': 0.8, 'h_bond_donor': 0, 'h_bond_acceptor': 0, 'rotatable_bonds': 0},
    'imidazole': {'weight': 68, 'hydrophobic': 0.4, 'h_bond_donor': 2, 'h_bond_acceptor': 1, 'rotatable_bonds': 0},
    'carboxylic_acid': {'weight': 46, 'hydrophobic': 0.1, 'h_bond_donor': 1, 'h_bond_acceptor': 2, 'rotatable_bonds': 1},
    'guanidine': {'weight': 43, 'hydrophobic': 0.1, 'h_bond_donor': 3, 'h_bond_acceptor': 1, 'rotatable_bonds': 1},
    'amide': {'weight': 43, 'hydrophobic': 0.3, 'h_bond_donor': 1, 'h_bond_acceptor': 1, 'rotatable_bonds': 1}
}

# Calculate target binding pocket properties
pocket_volume = target_data['binding_site_volume']
hydrophobic_complementarity = target_data['binding_site_hydrophobicity']
flexibility_complementarity = target_data['binding_site_flexibility']

# Calculate desired ligand properties
desired_molecular_weight = 300  # Da (optimal for drug-like properties)
max_rotatable_bonds = 10       # Flexibility constraint
optimal_h_bond_donors = 2      # For solubility and binding
optimal_h_bond_acceptors = 5   # For binding interactions

# Calculate binding energy prediction
# Using simplified relationship: binding energy ∝ -log(IC50)
kbt = 0.6  # kcal/mol at room temp
reference_affinity = target_data['known_ligand_affinity'] * 1e-9  # Convert nM to M
reference_binding_energy = -kbt * math.log(reference_affinity)

# Design approach: maximize complementarity while maintaining drug-likeness
# Calculate fragment contributions
fragment_weights = [frag['weight'] for frag in fragments.values()]
total_desired_weight = 0
selected_fragments = []

# Select fragments based on complementarity with binding site
hydrophobic_fragments = ['benzene']  # Fragments with high hydrophobicity
polar_fragments = ['carboxylic_acid', 'guanidine', 'amide', 'imidazole']  # Fragments with H-bond capacity

# Select fragments based on target complementarity
if hydrophobic_complementarity > 0.5:
    selected_fragments.extend(hydrophobic_fragments)
if target_data['surface_charge'] < 0:  # Negative surface favors positive groups
    selected_fragments.extend(['guanidine'])  # Positively charged group
else:
    selected_fragments.extend(['carboxylic_acid'])  # Negatively charged group

# Calculate predicted properties
total_weight = sum(fragments[frag]['weight'] for frag in selected_fragments)
total_h_donors = sum(fragments[frag]['h_bond_donor'] for frag in selected_fragments)
total_h_acceptors = sum(fragments[frag]['h_bond_acceptor'] for frag in selected_fragments)
total_rotatable = sum(fragments[frag]['rotatable_bonds'] for frag in selected_fragments)

# Estimate binding affinity improvement
# Simpler model: more H-bond interactions → better binding
h_bond_score = (min(total_h_donors, optimal_h_bond_donors) + min(total_h_acceptors, optimal_h_bond_acceptors)) / (optimal_h_bond_donors + optimal_h_bond_acceptors)
hydrophobic_score = (1 - abs(hydrophobic_complementarity - 0.5) * 2)  # Score based on complementarity
complexity_penalty = 1 / (1 + total_rotatable * 0.1)  # Penalty for too many rotatable bonds

predicted_affinity_improvement = h_bond_score * hydrophobic_score * complexity_penalty
estimated_ic50 = reference_affinity / predicted_affinity_improvement  # Moles, converted from reference

Design a potential inhibitor for the target protein based on structural considerations.

Hint:

• Consider structural complementarity (hydrophobic vs polar interactions)
• Balance molecular properties (molecular weight, H-bond donors/acceptors)
• Account for binding site flexibility and charge complementarity
• Estimate potential binding affinity improvement

# TODO: Calculate drug design parameters
predicted_binding_affinity = 0  # nM (predicted IC50 in nanomolar)
ligand_efficiency = 0          # kcal/mol per heavy atom
drug_likeness_score = 0        # Overall drug-likeness metric (0-1 scale)
optimization_potential = 0     # Potential for further improvements (%)
recommended_fragments = []     # List of fragments to incorporate in design

# Calculate predicted binding affinity
predicted_binding_affinity = estimated_ic50 * 1e9  # Convert from M to nM

# Calculate ligand efficiency (binding energy per heavy atom)
binding_energy = -kbt * math.log(predicted_binding_affinity * 1e-9)  # Convert to kcal/mol
ligand_efficiency = binding_energy / (total_weight / 12)  # Per heavy atom (approximate)

# Calculate drug-likeness score
mw_score = 1 if total_weight <= 500 else 0.5 * math.exp(-(total_weight-500)/200)  # Penalty for large MW
hbd_score = 1 if total_h_donors <= 5 else 1/(total_h_donors-4)  # Penalty for too many H-bond donors
hba_score = 1 if total_h_acceptors <= 10 else 1/(total_h_acceptors-9)  # Penalty for too many H-bond acceptors
rotb_score = 1 if total_rotatable <= 10 else 1/(total_rotatable-9)  # Penalty for flexibility

drug_likeness_score = (mw_score + hbd_score + hba_score + rotb_score) / 4

# Calculate optimization potential
# Based on current design vs ideal properties
deviation_from_ideal = abs(total_weight - desired_molecular_weight)/desired_molecular_weight + \
                      abs(total_h_donors - optimal_h_bond_donors)/optimal_h_bond_donors + \
                      abs(total_h_acceptors - optimal_h_bond_acceptors)/optimal_h_bond_acceptors

optimization_potential = max(0, (1 - deviation_from_ideal) * 100)  # Percentage

# Select fragments for design
recommended_fragments = selected_fragments

# Print results
print(f"Predicted binding affinity: {predicted_binding_affinity:.2f} nM")
print(f"Ligand efficiency: {ligand_efficiency:.3f} kcal/mol per heavy atom")
print(f"Drug-likeness score: {drug_likeness_score:.3f}")
print(f"Optimization potential: {optimization_potential:.1f}%")
print(f"Recommended fragments: {recommended_fragments}")
print(f"Total molecular weight: {total_weight} Da")
print(f"H-bond donors: {total_h_donors}, H-bond acceptors: {total_h_acceptors}")

# Design assessment
if drug_likeness_score > 0.7 and predicted_binding_affinity < 100:
    design_assessment = "High-quality design with good drug-likeness and predicted potency"
elif drug_likeness_score > 0.5 and predicted_binding_affinity < 1000:
    design_assessment = "Moderate design with room for optimization"
else:
    design_assessment = "Needs significant optimization for drug-likeness or potency"
    
print(f"Design assessment: {design_assessment}")

# Suggested improvements
improvement_suggestions = []
if total_weight > 500:
    improvement_suggestions.append("Reduce molecular weight (consider fragment-based approach)")
if total_h_donors > 5:
    improvement_suggestions.append("Reduce H-bond donors to comply with Lipinski's rules")
if total_h_acceptors > 10:
    improvement_suggestions.append("Reduce H-bond acceptors")
if total_rotatable > 10:
    improvement_suggestions.append("Reduce flexibility to improve binding affinity")

print(f"Suggested improvements: {improvement_suggestions}")

How would your drug design approach change if you were targeting a protein-protein interface rather than a traditional enzyme active site?