🛢️ The Oil Drop Model: Hydrophobic Burial Analysis¶

Duration: ~25 minutes | Level: ⭐⭐ Intermediate

Why do proteins fold?¶

In 1959, Walter Kauzmann proposed a deceptively simple answer: hydrophobic residues hate water. When a protein folds, it squeezes its greasy, water-fearing (hydrophobic) residues into a dry interior core — just like oil droplets coalescing in water. The polar, water-loving residues remain on the surface.

This Oil Drop Model makes a testable structural prediction:

A correctly folded protein should have its hydrophobic residues BURIED (low SASA) and its polar residues EXPOSED (high SASA).

In this tutorial we'll:

Learn what Solvent-Accessible Surface Area (SASA) measures
Generate proteins with different hydrophobic content and plot per-residue SASA
Compute the burial_ratio — a single number that tests the Oil Drop prediction
See how get_quality_report() uses this to assess biophysical plausibility

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import os
import sys

IN_COLAB = 'google.colab' in sys.modules

if IN_COLAB:
    # @title Environment Setup
    !pip install -q synth-pdb biotite matplotlib numpy scipy py3Dmol openmm
else:
    sys.path.append(os.path.abspath('../../'))

print("✅ Environment configured!")
import os
import sys

IN_COLAB = 'google.colab' in sys.modules

if IN_COLAB:
    # @title Environment Setup
    !pip install -q synth-pdb biotite matplotlib numpy scipy py3Dmol openmm
else:
    sys.path.append(os.path.abspath('../../'))

print("✅ Environment configured!")

🔧 Setup¶

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import os
import sys

try:
    import google.colab  # noqa: F401
    IN_COLAB = True
except ImportError:
    IN_COLAB = False

if IN_COLAB:
    print('🌐 Running in Google Colab — installing dependencies...')
    import subprocess
    subprocess.run(['pip', 'install', '-q', 'synth-pdb', 'biotite'], check=True)
else:
    # Local development: add the repo root to sys.path
    repo_root = os.path.abspath(os.path.join(os.path.dirname('__file__'), '..', '..'))
    if repo_root not in sys.path:
        sys.path.insert(0, repo_root)
    print(f'💻 Running locally — using repo at {repo_root}')

import matplotlib.patches as mpatches
import matplotlib.pyplot as plt

from synth_pdb.data import HYDROPHOBIC_AMINO_ACIDS
from synth_pdb.generator import generate_pdb_content
from synth_pdb.validator import PDBValidator

print('✅ All imports successful!')
print(f'   Hydrophobic residues tracked: {sorted(HYDROPHOBIC_AMINO_ACIDS)}')
import os
import sys

try:
    import google.colab  # noqa: F401
    IN_COLAB = True
except ImportError:
    IN_COLAB = False

if IN_COLAB:
    print('🌐 Running in Google Colab — installing dependencies...')
    import subprocess
    subprocess.run(['pip', 'install', '-q', 'synth-pdb', 'biotite'], check=True)
else:
    # Local development: add the repo root to sys.path
    repo_root = os.path.abspath(os.path.join(os.path.dirname('__file__'), '..', '..'))
    if repo_root not in sys.path:
        sys.path.insert(0, repo_root)
    print(f'💻 Running locally — using repo at {repo_root}')

import matplotlib.patches as mpatches
import matplotlib.pyplot as plt

from synth_pdb.data import HYDROPHOBIC_AMINO_ACIDS
from synth_pdb.generator import generate_pdb_content
from synth_pdb.validator import PDBValidator

print('✅ All imports successful!')
print(f'   Hydrophobic residues tracked: {sorted(HYDROPHOBIC_AMINO_ACIDS)}')

📐 Step 1: What is SASA?¶

Solvent-Accessible Surface Area is the area of a molecule's surface that a water molecule can touch — imagined as a 1.4 Å-radius sphere (water's radius) rolling over the protein surface.

SASA	Meaning
High SASA (> 100 Å²)	Residue is surface-exposed, touching water
Low SASA (< 25 Å²)	Residue is buried in the protein core

The Oil Drop prediction in numbers¶

Hydrophobic residues (ALA, VAL, ILE, LEU, MET, PHE, TRP, TYR): low SASA ← buried
Polar residues (SER, THR, ASN, GLN, LYS, ARG, ASP, GLU, HIS): high SASA ← exposed

We measure this with the burial_ratio:

$$\text{burial\_ratio} = \frac{\overline{\text{SASA}_{\text{polar}}}}{\overline{\text{SASA}_{\text{hydrophobic}}} + 10^{-6}}$$

A burial_ratio ≥ 0.8 means the polar mean SASA is at least 80% of the hydrophobic mean SASA — consistent with hydrophobic burial. This is the threshold used in get_quality_report().

🧬 Step 2: Generate Three Test Proteins¶

We'll compare three structures designed to test different burial regimes:

Structure	Sequence design	Expected burial_ratio
Amphipathic helix	Alternating Lys/Leu — polar one face, hydrophobic the other	≥ 0.8 (plausible)
Hydrophobic-only peptide	All Val — no polar surface possible	< 0.1 (implausible)
Random-coil decoy	Scrambled amphipathic, no minimization	Variable

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# ── Amphipathic helix: alternating polar/hydrophobic faces ──────────────
# AAKLLLAAKLLLAAK  →  Ala/Leu hydrophobic face, Lys/Ala polar face
SEQ_HELIX  = 'AAKLLLAAKLLLAAK'
SEQ_HYDRO  = 'VIVVIVVIVVI'       # All hydrophobic — should FAIL burial check
SEQ_RANDOM = 'LKLALAKLLAKA'      # Scrambled — may or may not pass

print('🧬 Generating structures (seed=42 for reproducibility)...')

pdb_helix  = generate_pdb_content(
    sequence_str=SEQ_HELIX, structure=f'1-{len(SEQ_HELIX)}:alpha',
    minimize_energy=True, seed=42
)

pdb_hydro  = generate_pdb_content(
    sequence_str=SEQ_HYDRO, structure=f'1-{len(SEQ_HYDRO)}:beta',
    minimize_energy=False, seed=42
)

pdb_random = generate_pdb_content(
    sequence_str=SEQ_RANDOM, structure=f'1-{len(SEQ_RANDOM)}:random',
    minimize_energy=False, seed=42
)

print('✅ All three structures generated!')
print(f'   Amphipathic helix:     {len(SEQ_HELIX)} residues')
print(f'   Hydrophobic-only:      {len(SEQ_HYDRO)} residues')
print(f'   Random-coil decoy:     {len(SEQ_RANDOM)} residues')
# ── Amphipathic helix: alternating polar/hydrophobic faces ──────────────
# AAKLLLAAKLLLAAK  →  Ala/Leu hydrophobic face, Lys/Ala polar face
SEQ_HELIX  = 'AAKLLLAAKLLLAAK'
SEQ_HYDRO  = 'VIVVIVVIVVI'       # All hydrophobic — should FAIL burial check
SEQ_RANDOM = 'LKLALAKLLAKA'      # Scrambled — may or may not pass

print('🧬 Generating structures (seed=42 for reproducibility)...')

pdb_helix  = generate_pdb_content(
    sequence_str=SEQ_HELIX, structure=f'1-{len(SEQ_HELIX)}:alpha',
    minimize_energy=True, seed=42
)

pdb_hydro  = generate_pdb_content(
    sequence_str=SEQ_HYDRO, structure=f'1-{len(SEQ_HYDRO)}:beta',
    minimize_energy=False, seed=42
)

pdb_random = generate_pdb_content(
    sequence_str=SEQ_RANDOM, structure=f'1-{len(SEQ_RANDOM)}:random',
    minimize_energy=False, seed=42
)

print('✅ All three structures generated!')
print(f'   Amphipathic helix:     {len(SEQ_HELIX)} residues')
print(f'   Hydrophobic-only:      {len(SEQ_HYDRO)} residues')
print(f'   Random-coil decoy:     {len(SEQ_RANDOM)} residues')

📊 Step 3: Compute Per-Residue SASA¶

PDBValidator.calculate_residue_sasa() returns:

SASA: a dict mapping {res_id → SASA_in_Å²} for every residue
mean_hydrophobic_sasa / mean_polar_sasa: group averages
burial_ratio: the Oil Drop metric

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def compute_sasa(pdb_content, sequence):
    """Compute and return SASA data for a PDB string."""
    v = PDBValidator(pdb_content)
    sasa_data = v.calculate_residue_sasa()

    # Build a list of (res_id, one_letter, sasa, is_hydrophobic)
    residues = []
    aa_3to1 = {
        'ALA':'A','ARG':'R','ASN':'N','ASP':'D','CYS':'C','GLN':'Q','GLU':'E',
        'GLY':'G','HIS':'H','ILE':'I','LEU':'L','LYS':'K','MET':'M','PHE':'F',
        'PRO':'P','SER':'S','THR':'T','TRP':'W','TYR':'Y','VAL':'V',
    }
    # Map from sequence index to 3-letter
    aa_1to3 = {v: k for k, v in aa_3to1.items()}

    for i, (res_id, sasa_val) in enumerate(sorted(sasa_data['SASA'].items())):
        aa1 = sequence[i] if i < len(sequence) else '?'
        aa3 = aa_1to3.get(aa1, 'UNK')
        is_hydro = aa3 in HYDROPHOBIC_AMINO_ACIDS
        residues.append({'res_id': res_id, 'aa': aa1, 'sasa': sasa_val, 'hydrophobic': is_hydro})

    return residues, sasa_data

residues_helix,  sasa_helix  = compute_sasa(pdb_helix,  SEQ_HELIX)
residues_hydro,  sasa_hydro  = compute_sasa(pdb_hydro,  SEQ_HYDRO)
residues_random, sasa_random = compute_sasa(pdb_random, SEQ_RANDOM)

for label, sasa_data in [('Amphipathic helix', sasa_helix),
                          ('Hydrophobic-only',  sasa_hydro),
                          ('Random-coil decoy', sasa_random)]:
    print(f'{label}:')
    print(f'   mean_hydrophobic_sasa = {sasa_data["mean_hydrophobic_sasa"]:7.1f} Å²')
    print(f'   mean_polar_sasa       = {sasa_data["mean_polar_sasa"]:7.1f} Å²')
    print(f'   burial_ratio          = {sasa_data["burial_ratio"]:7.3f}')
    print()
def compute_sasa(pdb_content, sequence):
    """Compute and return SASA data for a PDB string."""
    v = PDBValidator(pdb_content)
    sasa_data = v.calculate_residue_sasa()

    # Build a list of (res_id, one_letter, sasa, is_hydrophobic)
    residues = []
    aa_3to1 = {
        'ALA':'A','ARG':'R','ASN':'N','ASP':'D','CYS':'C','GLN':'Q','GLU':'E',
        'GLY':'G','HIS':'H','ILE':'I','LEU':'L','LYS':'K','MET':'M','PHE':'F',
        'PRO':'P','SER':'S','THR':'T','TRP':'W','TYR':'Y','VAL':'V',
    }
    # Map from sequence index to 3-letter
    aa_1to3 = {v: k for k, v in aa_3to1.items()}

    for i, (res_id, sasa_val) in enumerate(sorted(sasa_data['SASA'].items())):
        aa1 = sequence[i] if i < len(sequence) else '?'
        aa3 = aa_1to3.get(aa1, 'UNK')
        is_hydro = aa3 in HYDROPHOBIC_AMINO_ACIDS
        residues.append({'res_id': res_id, 'aa': aa1, 'sasa': sasa_val, 'hydrophobic': is_hydro})

    return residues, sasa_data

residues_helix,  sasa_helix  = compute_sasa(pdb_helix,  SEQ_HELIX)
residues_hydro,  sasa_hydro  = compute_sasa(pdb_hydro,  SEQ_HYDRO)
residues_random, sasa_random = compute_sasa(pdb_random, SEQ_RANDOM)

for label, sasa_data in [('Amphipathic helix', sasa_helix),
                          ('Hydrophobic-only',  sasa_hydro),
                          ('Random-coil decoy', sasa_random)]:
    print(f'{label}:')
    print(f'   mean_hydrophobic_sasa = {sasa_data["mean_hydrophobic_sasa"]:7.1f} Å²')
    print(f'   mean_polar_sasa       = {sasa_data["mean_polar_sasa"]:7.1f} Å²')
    print(f'   burial_ratio          = {sasa_data["burial_ratio"]:7.3f}')
    print()

📈 Step 4: Per-Residue SASA Bar Chart¶

Each bar is coloured by residue type:

🟠 Orange = hydrophobic (should be SHORT → buried)
🟢 Green = polar (should be TALL → exposed)

In a well-folded protein, orange bars are below green bars everywhere.

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def plot_sasa_bars(ax, residues, title, burial_ratio, plausible):
    """Draw per-residue SASA coloured by residue type."""
    ids   = [r['res_id'] for r in residues]
    vals  = [r['sasa']   for r in residues]
    colors = ['#e67e22' if r['hydrophobic'] else '#27ae60' for r in residues]
    labels = [r['aa']    for r in residues]

    ax.bar(range(len(ids)), vals, color=colors, edgecolor='white', linewidth=0.5)
    ax.set_xticks(range(len(ids)))
    ax.set_xticklabels(labels, fontsize=9)
    ax.set_ylabel('SASA (Å²)', fontsize=10)
    ax.set_ylim(0, max(vals) * 1.25 if vals else 200)

    verdict = 'PASS: Plausible' if plausible else 'FAIL: Not plausible'
    ax.set_title(
        f'{title}\nburial_ratio = {burial_ratio:.3f}  |  {verdict}',
        fontsize=11, fontweight='bold'
    )

    # Threshold line at 25 Å² (canonical buried cutoff)
    ax.axhline(25, color='#95a5a6', linestyle='--', linewidth=0.8, alpha=0.7)
    ax.text(len(ids) - 0.5, 27, 'buried < 25 Å²', ha='right', fontsize=7.5,
            color='#7f8c8d', style='italic')


fig, axes = plt.subplots(3, 1, figsize=(11, 10))
fig.suptitle('Per-Residue SASA: The Oil Drop Test', fontsize=14, fontweight='bold', y=1.01)

plot_sasa_bars(axes[0], residues_helix,
               'Amphipathic Helix (AAKLLLAAKLLLAAK)',
               sasa_helix['burial_ratio'],
               sasa_helix['burial_ratio'] >= 0.8)

plot_sasa_bars(axes[1], residues_hydro,
               'Hydrophobic-Only Strand (VIVVIVVIVVI)',
               sasa_hydro['burial_ratio'],
               sasa_hydro['burial_ratio'] >= 0.8)

plot_sasa_bars(axes[2], residues_random,
               'Random-Coil Decoy (LKLALAKLLAKA)',
               sasa_random['burial_ratio'],
               sasa_random['burial_ratio'] >= 0.8)

# Shared legend
legend_patches = [
    mpatches.Patch(color='#e67e22', label='Hydrophobic residue'),
    mpatches.Patch(color='#27ae60', label='Polar residue'),
]
fig.legend(handles=legend_patches, loc='upper right', fontsize=9, framealpha=0.9)

plt.tight_layout()
plt.show()
def plot_sasa_bars(ax, residues, title, burial_ratio, plausible):
    """Draw per-residue SASA coloured by residue type."""
    ids   = [r['res_id'] for r in residues]
    vals  = [r['sasa']   for r in residues]
    colors = ['#e67e22' if r['hydrophobic'] else '#27ae60' for r in residues]
    labels = [r['aa']    for r in residues]

    ax.bar(range(len(ids)), vals, color=colors, edgecolor='white', linewidth=0.5)
    ax.set_xticks(range(len(ids)))
    ax.set_xticklabels(labels, fontsize=9)
    ax.set_ylabel('SASA (Å²)', fontsize=10)
    ax.set_ylim(0, max(vals) * 1.25 if vals else 200)

    verdict = 'PASS: Plausible' if plausible else 'FAIL: Not plausible'
    ax.set_title(
        f'{title}\nburial_ratio = {burial_ratio:.3f}  |  {verdict}',
        fontsize=11, fontweight='bold'
    )

    # Threshold line at 25 Å² (canonical buried cutoff)
    ax.axhline(25, color='#95a5a6', linestyle='--', linewidth=0.8, alpha=0.7)
    ax.text(len(ids) - 0.5, 27, 'buried < 25 Å²', ha='right', fontsize=7.5,
            color='#7f8c8d', style='italic')


fig, axes = plt.subplots(3, 1, figsize=(11, 10))
fig.suptitle('Per-Residue SASA: The Oil Drop Test', fontsize=14, fontweight='bold', y=1.01)

plot_sasa_bars(axes[0], residues_helix,
               'Amphipathic Helix (AAKLLLAAKLLLAAK)',
               sasa_helix['burial_ratio'],
               sasa_helix['burial_ratio'] >= 0.8)

plot_sasa_bars(axes[1], residues_hydro,
               'Hydrophobic-Only Strand (VIVVIVVIVVI)',
               sasa_hydro['burial_ratio'],
               sasa_hydro['burial_ratio'] >= 0.8)

plot_sasa_bars(axes[2], residues_random,
               'Random-Coil Decoy (LKLALAKLLAKA)',
               sasa_random['burial_ratio'],
               sasa_random['burial_ratio'] >= 0.8)

# Shared legend
legend_patches = [
    mpatches.Patch(color='#e67e22', label='Hydrophobic residue'),
    mpatches.Patch(color='#27ae60', label='Polar residue'),
]
fig.legend(handles=legend_patches, loc='upper right', fontsize=9, framealpha=0.9)

plt.tight_layout()
plt.show()

📊 Step 5: Comparing burial_ratio Across Structures¶

The Oil Drop threshold is burial_ratio ≥ 0.8. Let's see how our three structures score:

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fig, ax = plt.subplots(figsize=(8, 4))

labels  = ['Amphipathic\nHelix', 'Hydrophobic\nOnly', 'Random\nCoil Decoy']
ratios  = [sasa_helix['burial_ratio'],
            sasa_hydro['burial_ratio'],
            sasa_random['burial_ratio']]
colors  = ['#2ecc71' if r >= 0.8 else '#e74c3c' for r in ratios]

bars = ax.bar(labels, ratios, color=colors, alpha=0.85, edgecolor='white', linewidth=0.5)

# Value labels
for bar, ratio in zip(bars, ratios, strict=False):
    ax.text(bar.get_x() + bar.get_width() / 2,
            min(bar.get_height(), 2.0) + 0.05,
            f'{ratio:.3f}', ha='center', va='bottom', fontsize=10, fontweight='bold')

# Threshold line
ax.axhline(0.8, color='#2c3e50', linestyle='--', linewidth=1.2, alpha=0.7, label='Threshold (0.8)')
ax.set_ylim(0, max(max(ratios) * 1.2, 1.1))
ax.set_ylabel('burial_ratio  (polar SASA / hydrophobic SASA)', fontsize=10)
ax.set_title('Oil Drop Test: Which structure passes?', fontsize=12, fontweight='bold')
ax.legend(fontsize=9)

for _i, (bar, label) in enumerate(zip(bars, ['PASS', 'FAIL', '?' ], strict=False)):
    col = '#27ae60' if 'PASS' in label else ('#e74c3c' if 'FAIL' in label else '#7f8c8d')
    ax.text(bar.get_x() + bar.get_width() / 2, 0.04, label,
            ha='center', va='bottom', fontsize=12, color=col, fontweight='bold')

plt.tight_layout()
plt.show()
fig, ax = plt.subplots(figsize=(8, 4))

labels  = ['Amphipathic\nHelix', 'Hydrophobic\nOnly', 'Random\nCoil Decoy']
ratios  = [sasa_helix['burial_ratio'],
            sasa_hydro['burial_ratio'],
            sasa_random['burial_ratio']]
colors  = ['#2ecc71' if r >= 0.8 else '#e74c3c' for r in ratios]

bars = ax.bar(labels, ratios, color=colors, alpha=0.85, edgecolor='white', linewidth=0.5)

# Value labels
for bar, ratio in zip(bars, ratios, strict=False):
    ax.text(bar.get_x() + bar.get_width() / 2,
            min(bar.get_height(), 2.0) + 0.05,
            f'{ratio:.3f}', ha='center', va='bottom', fontsize=10, fontweight='bold')

# Threshold line
ax.axhline(0.8, color='#2c3e50', linestyle='--', linewidth=1.2, alpha=0.7, label='Threshold (0.8)')
ax.set_ylim(0, max(max(ratios) * 1.2, 1.1))
ax.set_ylabel('burial_ratio  (polar SASA / hydrophobic SASA)', fontsize=10)
ax.set_title('Oil Drop Test: Which structure passes?', fontsize=12, fontweight='bold')
ax.legend(fontsize=9)

for _i, (bar, label) in enumerate(zip(bars, ['PASS', 'FAIL', '?' ], strict=False)):
    col = '#27ae60' if 'PASS' in label else ('#e74c3c' if 'FAIL' in label else '#7f8c8d')
    ax.text(bar.get_x() + bar.get_width() / 2, 0.04, label,
            ha='center', va='bottom', fontsize=12, color=col, fontweight='bold')

plt.tight_layout()
plt.show()

🏅 Step 6: The Oil Drop Check Inside `get_quality_report()`¶

burial_ratio is one of the five criteria in the Scientific Defensibility Scorecard. Let's see it in context:

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def show_burial_in_report(label, pdb_content):
    v = PDBValidator(pdb_content)
    report = v.get_quality_report()

    br    = report['hydrophobic_burial_ratio']
    bio   = report['is_biophysically_plausible']
    defns = report['is_overall_scientifically_defensible']
    def tick(b):
        return 'PASS' if b else 'FAIL'

    print(f'{label}')
    print(f'   burial_ratio            = {br:.3f}  ({tick(bio)} Oil Drop test)')
    print(f'   is_biophysically_plausible = {bio}')
    print(f'   is_overall_defensible      = {defns}')
    print()

show_burial_in_report('Amphipathic Helix', pdb_helix)
show_burial_in_report('Hydrophobic-Only Strand', pdb_hydro)
show_burial_in_report('Random-Coil Decoy', pdb_random)
def show_burial_in_report(label, pdb_content):
    v = PDBValidator(pdb_content)
    report = v.get_quality_report()

    br    = report['hydrophobic_burial_ratio']
    bio   = report['is_biophysically_plausible']
    defns = report['is_overall_scientifically_defensible']
    def tick(b):
        return 'PASS' if b else 'FAIL'

    print(f'{label}')
    print(f'   burial_ratio            = {br:.3f}  ({tick(bio)} Oil Drop test)')
    print(f'   is_biophysically_plausible = {bio}')
    print(f'   is_overall_defensible      = {defns}')
    print()

show_burial_in_report('Amphipathic Helix', pdb_helix)
show_burial_in_report('Hydrophobic-Only Strand', pdb_hydro)
show_burial_in_report('Random-Coil Decoy', pdb_random)

🎓 Key Takeaways¶

What the Oil Drop Model predicts¶

Residue type	Surface area	Why
Hydrophobic (ALA, VAL, LEU…)	Low SASA → buried	Water contact is thermodynamically unfavourable
Polar (LYS, ASP, SER…)	High SASA → exposed	Hydrogen bonding to water is stabilising

What burial_ratio measures¶

burial_ratio ≥ 0.8 → polar residues are as exposed as (or more than) hydrophobic ones ✅
burial_ratio < 0.1 → nearly all surface area belongs to hydrophobic residues ❌
Extreme sequences (all-hydrophobic, all-polar) can saturate the metric — always interpret alongside the per-residue bar chart.

Why this matters¶

Protein design: sequences that fail the Oil Drop check are unlikely to fold stably
Structure validation: misfolded decoys often expose hydrophobic patches
AI structure assessment: AlphaFold predictions with low burial_ratio in low-pLDDT regions are likely disordered, not misfolded

What to try next¶

Run generate_pdb_content with minimize_energy=True on the hydrophobic-only strand. Does minimization improve the burial_ratio?
Extend the analysis to the Structure Defensibility Dashboard for all five criteria.
Try sequences from real IDPs (e.g. Alpha-synuclein N-terminal: MDVFMKGLSKAKEGVVAA).

🛢️ The Oil Drop Model: Hydrophobic Burial Analysis¶

Why do proteins fold?¶

🔧 Setup¶

📐 Step 1: What is SASA?¶

The Oil Drop prediction in numbers¶

🧬 Step 2: Generate Three Test Proteins¶

📊 Step 3: Compute Per-Residue SASA¶

📈 Step 4: Per-Residue SASA Bar Chart¶

📊 Step 5: Comparing burial_ratio Across Structures¶

🏅 Step 6: The Oil Drop Check Inside get_quality_report()¶

🎓 Key Takeaways¶

What the Oil Drop Model predicts¶

What burial_ratio measures¶

Why this matters¶

What to try next¶

🏅 Step 6: The Oil Drop Check Inside `get_quality_report()`¶