🏔️ The Live Folding Landscape¶

Visualizing the Energy Funnel Theory of Protein Folding¶

🎯 Learning Objectives¶

In this tutorial, we explore one of the most profound concepts in structural biology: the Energy Funnel. Proteins do not fold by random searching (which would take longer than the age of the universe, known as Levinthal's Paradox). Instead, they follow a rugged energy landscape that guides them toward their most stable, "native" state.

You will learn:

🧮 How to generate a Ramachandran-style Energy Surface for a peptide
🔥 How to run Simulated Annealing using the synth-pdb physics engine
📊 How to visualize the folding trajectory on a 3D energy landscape
🎨 How canonical secondary structures (α-helix, β-sheet) appear as energy minima

💡 Scientific Context: The energy landscape theory, pioneered by Wolynes, Onuchic, and others in the 1990s, revolutionized our understanding of protein folding. It explains how proteins can fold rapidly despite astronomical conformational possibilities.

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# 🔧 Environment Detection & Setup (Works in VS Code + Google Colab)
import os
import sys

# Detect environment
IN_COLAB = 'google.colab' in sys.modules

if IN_COLAB:
    print("🌐 Running in Google Colab")

    # Install synth-pdb if not already installed
    try:
        import synth_pdb
        print("   ✅ synth-pdb already installed")
    except ImportError:
        print("   📦 Installing synth-pdb...")
        !pip install -q synth-pdb py3Dmol biotite
        print("   ✅ Installation complete")

    # Colab uses 'notebook' renderer for Plotly
    import plotly.io as pio
    pio.renderers.default = 'colab'

else:
    print("💻 Running in local Jupyter environment (VS Code/JupyterLab)")
    # Add parent directory to path for local development
    sys.path.append(os.path.abspath('../../'))

print("✅ Environment configured successfully!")
# 🔧 Environment Detection & Setup (Works in VS Code + Google Colab)
import os
import sys

# Detect environment
IN_COLAB = 'google.colab' in sys.modules

if IN_COLAB:
    print("🌐 Running in Google Colab")

    # Install synth-pdb if not already installed
    try:
        import synth_pdb
        print("   ✅ synth-pdb already installed")
    except ImportError:
        print("   📦 Installing synth-pdb...")
        !pip install -q synth-pdb py3Dmol biotite
        print("   ✅ Installation complete")

    # Colab uses 'notebook' renderer for Plotly
    import plotly.io as pio
    pio.renderers.default = 'colab'

else:
    print("💻 Running in local Jupyter environment (VS Code/JupyterLab)")
    # Add parent directory to path for local development
    sys.path.append(os.path.abspath('../../'))

print("✅ Environment configured successfully!")

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import os
import sys

import ipywidgets as widgets
import numpy as np
import plotly.graph_objects as go
import plotly.io as pio
import py3Dmol
from IPython.display import clear_output, display

# --- UNIVERSAL SETUP ---
from synth_pdb import EnergyMinimizer, PDBValidator, PeptideGenerator, PeptideResult

# Initialize variables
X, Y, Z = np.array([]), np.array([]), np.array([])
traj_phi, traj_psi, energies = np.array([]), np.array([]), []
trajectory_structs = []

# Custom color scheme for scientific visualization
ENERGY_COLORSCALE = 'Viridis'  # Perceptually uniform, colorblind-friendly
TRAJECTORY_COLOR = '#FF6B35'   # Vibrant orange for contrast

print("✅ Environment Ready | synth-pdb v1.0 | Enhanced Visualization Mode")
import os
import sys

import ipywidgets as widgets
import numpy as np
import plotly.graph_objects as go
import plotly.io as pio
import py3Dmol
from IPython.display import clear_output, display

# --- UNIVERSAL SETUP ---
from synth_pdb import EnergyMinimizer, PDBValidator, PeptideGenerator, PeptideResult

# Initialize variables
X, Y, Z = np.array([]), np.array([]), np.array([])
traj_phi, traj_psi, energies = np.array([]), np.array([]), []
trajectory_structs = []

# Custom color scheme for scientific visualization
ENERGY_COLORSCALE = 'Viridis'  # Perceptually uniform, colorblind-friendly
TRAJECTORY_COLOR = '#FF6B35'   # Vibrant orange for contrast

print("✅ Environment Ready | synth-pdb v1.0 | Enhanced Visualization Mode")

📚 Theoretical Foundation¶

The Energy Landscape Paradigm¶

The protein folding energy landscape can be described mathematically as:

$$E(\phi, \psi) = E_{\text{bond}} + E_{\text{angle}} + E_{\text{dihedral}} + E_{\text{vdW}} + E_{\text{elec}}$$

Where:

$\phi$ (phi) = backbone dihedral angle C-N-Cα-C
$\psi$ (psi) = backbone dihedral angle N-Cα-C-N
$E_{\text{vdW}}$ = van der Waals interactions (steric clashes)
$E_{\text{elec}}$ = electrostatic interactions

Ramachandran Regions¶

Region	φ (degrees)	ψ (degrees)	Secondary Structure
α-helix	-60	-45	Right-handed helix
β-sheet	-120	+120	Extended strand
PPII	-75	+145	Polyproline II helix
Left α	+60	+45	Left-handed helix (rare)

⚠️ Note: Glycine (no side chain) can access all regions. Proline (cyclic) is restricted to φ ≈ -60°.

1️⃣ Creating the Energy Landscape with Ramachandran Overlays¶

We'll systematically scan the φ/ψ space and calculate the potential energy at each point. This creates a 2D energy surface that reveals the "allowed" and "forbidden" regions of conformational space.

🔬 Computational Details:

Grid resolution: 15×15 (225 conformations)
Force field: AMBER14
Energy calculation: Single-point (no minimization)
Expected runtime: ~30 seconds

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minimizer = EnergyMinimizer()

def get_energy_for_angles(phi, psi, sequence="ALA-ALA-ALA"):
    """Calculate energy for a given phi/psi of the central residue."""
    gen = PeptideGenerator(sequence)
    phis = [-57.0, phi, -57.0]  # Alpha helix flanking
    psis = [-47.0, psi, -47.0]

    try:
        res = gen.generate(phi_list=phis, psi_list=psis)
        energy = minimizer.calculate_energy(res)
        return energy if energy is not None else 10000.0
    except:
        return 10000.0

# Generate energy grid
res_grid = 15
phis = np.linspace(-180, 180, res_grid)
psis = np.linspace(-180, 180, res_grid)
X, Y = np.meshgrid(phis, psis)
Z = np.zeros_like(X)

print("🔄 Generating Energy Landscape...")
print("   This will sample 225 conformations across φ/ψ space")
print("   " + "="*50)

for i in range(res_grid):
    for j in range(res_grid):
        val = get_energy_for_angles(X[i,j], Y[i,j])
        Z[i,j] = min(val, 5000)  # Cap extreme energies

    # Progress indicator
    progress = (i + 1) / res_grid * 100
    bar_length = int(progress / 2)
    bar = "█" * bar_length + "░" * (50 - bar_length)
    print(f"\r   [{bar}] {progress:.0f}%", end="")

print("\n   " + "="*50)
print("✅ Energy Landscape Complete!")
print(f"   Min Energy: {Z.min():.1f} kJ/mol")
print(f"   Max Energy: {Z.max():.1f} kJ/mol")
print(f"   Energy Range: {Z.max() - Z.min():.1f} kJ/mol")
minimizer = EnergyMinimizer()

def get_energy_for_angles(phi, psi, sequence="ALA-ALA-ALA"):
    """Calculate energy for a given phi/psi of the central residue."""
    gen = PeptideGenerator(sequence)
    phis = [-57.0, phi, -57.0]  # Alpha helix flanking
    psis = [-47.0, psi, -47.0]

    try:
        res = gen.generate(phi_list=phis, psi_list=psis)
        energy = minimizer.calculate_energy(res)
        return energy if energy is not None else 10000.0
    except:
        return 10000.0

# Generate energy grid
res_grid = 15
phis = np.linspace(-180, 180, res_grid)
psis = np.linspace(-180, 180, res_grid)
X, Y = np.meshgrid(phis, psis)
Z = np.zeros_like(X)

print("🔄 Generating Energy Landscape...")
print("   This will sample 225 conformations across φ/ψ space")
print("   " + "="*50)

for i in range(res_grid):
    for j in range(res_grid):
        val = get_energy_for_angles(X[i,j], Y[i,j])
        Z[i,j] = min(val, 5000)  # Cap extreme energies

    # Progress indicator
    progress = (i + 1) / res_grid * 100
    bar_length = int(progress / 2)
    bar = "█" * bar_length + "░" * (50 - bar_length)
    print(f"\r   [{bar}] {progress:.0f}%", end="")

print("\n   " + "="*50)
print("✅ Energy Landscape Complete!")
print(f"   Min Energy: {Z.min():.1f} kJ/mol")
print(f"   Max Energy: {Z.max():.1f} kJ/mol")
print(f"   Energy Range: {Z.max() - Z.min():.1f} kJ/mol")

2️⃣ Running the Folding Trajectory¶

Now we simulate the folding process using iterative energy minimization. Starting from a random conformation, we allow the peptide to relax toward its energy minimum.

🧪 Simulation Protocol:

Initial state: Random conformation
Algorithm: Steepest descent minimization
Steps: 15 refinement cycles
Iterations per cycle: 20
Tracking: Energy, φ/ψ angles, structure snapshots

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sequence = "ALA-ALA-ALA-ALA-ALA"
gen = PeptideGenerator(sequence)
res = gen.generate(conformation="random")

trajectory_structs = []
energies = []
phi_psi_history = []

validator = PDBValidator(res.pdb)

print("🔥 Starting Folding Simulation...")
print("   Peptide: 5×Alanine (Poly-A)")
print("   " + "="*60)

import tempfile

for step in range(15):
    # Energy minimization
    with tempfile.NamedTemporaryFile(suffix='.pdb', mode='w', delete=False) as f_in:
        f_in.write(res.pdb)
        f_in.close()
        with tempfile.NamedTemporaryFile(suffix='.pdb', delete=False) as f_out:
            f_out.close()
            minimizer.minimize(f_in.name, f_out.name, max_iterations=20)
            with open(f_out.name) as r:
                updated_pdb = r.read()
            res = PeptideResult(updated_pdb)
            os.unlink(f_in.name)
            os.unlink(f_out.name)

    # Record trajectory
    trajectory_structs.append(res.structure.copy())
    current_energy = minimizer.calculate_energy(res)
    energies.append(current_energy)

    # Track central residue angles
    angles = validator.calculate_dihedrals(res)
    phi_psi_history.append([angles['phi'][2], angles['psi'][2]])

    # Progress with energy display
    energy_change = energies[-1] - energies[-2] if len(energies) > 1 else 0
    arrow = "↓" if energy_change < 0 else "↑" if energy_change > 0 else "→"
    print(f"   Step {step+1:2d}/15 | Energy: {energies[-1]:7.2f} kJ/mol {arrow} Δ={energy_change:+6.2f}")

traj_phi = np.array([p[0] for p in phi_psi_history])
traj_psi = np.array([p[1] for p in phi_psi_history])

print("   " + "="*60)
print("✅ Folding Complete!")
print(f"   Initial Energy: {energies[0]:.2f} kJ/mol")
print(f"   Final Energy:   {energies[-1]:.2f} kJ/mol")
print(f"   Total ΔE:       {energies[-1] - energies[0]:.2f} kJ/mol")
print(f"   Final φ/ψ:      ({traj_phi[-1]:.1f}°, {traj_psi[-1]:.1f}°)")
sequence = "ALA-ALA-ALA-ALA-ALA"
gen = PeptideGenerator(sequence)
res = gen.generate(conformation="random")

trajectory_structs = []
energies = []
phi_psi_history = []

validator = PDBValidator(res.pdb)

print("🔥 Starting Folding Simulation...")
print("   Peptide: 5×Alanine (Poly-A)")
print("   " + "="*60)

import tempfile

for step in range(15):
    # Energy minimization
    with tempfile.NamedTemporaryFile(suffix='.pdb', mode='w', delete=False) as f_in:
        f_in.write(res.pdb)
        f_in.close()
        with tempfile.NamedTemporaryFile(suffix='.pdb', delete=False) as f_out:
            f_out.close()
            minimizer.minimize(f_in.name, f_out.name, max_iterations=20)
            with open(f_out.name) as r:
                updated_pdb = r.read()
            res = PeptideResult(updated_pdb)
            os.unlink(f_in.name)
            os.unlink(f_out.name)

    # Record trajectory
    trajectory_structs.append(res.structure.copy())
    current_energy = minimizer.calculate_energy(res)
    energies.append(current_energy)

    # Track central residue angles
    angles = validator.calculate_dihedrals(res)
    phi_psi_history.append([angles['phi'][2], angles['psi'][2]])

    # Progress with energy display
    energy_change = energies[-1] - energies[-2] if len(energies) > 1 else 0
    arrow = "↓" if energy_change < 0 else "↑" if energy_change > 0 else "→"
    print(f"   Step {step+1:2d}/15 | Energy: {energies[-1]:7.2f} kJ/mol {arrow} Δ={energy_change:+6.2f}")

traj_phi = np.array([p[0] for p in phi_psi_history])
traj_psi = np.array([p[1] for p in phi_psi_history])

print("   " + "="*60)
print("✅ Folding Complete!")
print(f"   Initial Energy: {energies[0]:.2f} kJ/mol")
print(f"   Final Energy:   {energies[-1]:.2f} kJ/mol")
print(f"   Total ΔE:       {energies[-1] - energies[0]:.2f} kJ/mol")
print(f"   Final φ/ψ:      ({traj_phi[-1]:.1f}°, {traj_psi[-1]:.1f}°)")

3️⃣ The Interactive 3D Energy Funnel¶

This visualization combines:

🗺️ Energy surface (blue gradient) showing the conformational landscape
🎯 Folding trajectory (orange path) showing the actual folding route
📍 Ramachandran regions (annotated) showing canonical secondary structures

🎨 Interaction Tips:

Rotate: Click and drag
Zoom: Scroll or pinch
Pan: Right-click and drag
Hover: See exact φ/ψ/E values

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import os

if len(X) == 0 or len(traj_phi) == 0:
    print("⚠️  Please run the previous cells first to generate data.")
else:
    # Create figure with Ramachandran annotations
    fig = go.Figure()

    # Energy surface
    fig.add_trace(go.Surface(
        z=Z, x=X, y=Y,
        colorscale=ENERGY_COLORSCALE,
        opacity=0.85,
        name='Energy Surface',
        colorbar={
            'title': "Energy<br>(kJ/mol)",
            'tickmode': "linear",
            'tick0': Z.min(),
            'dtick': (Z.max() - Z.min()) / 5
        },
        hovertemplate='φ: %{x:.1f}°<br>ψ: %{y:.1f}°<br>E: %{z:.1f} kJ/mol<extra></extra>'
    ))

    # Folding trajectory
    fig.add_trace(go.Scatter3d(
        x=traj_phi, y=traj_psi, z=energies,
        mode='markers+lines',
        marker={
            'size': 8,
            'color': np.arange(len(energies)),
            'colorscale': 'Hot',
            'showscale': True,
            'colorbar': {
                'title': "Step",
                'x': 1.15
            },
            'line': {'color': 'white', 'width': 2}
        },
        line={'color': TRAJECTORY_COLOR, 'width': 6},
        name='Folding Path',
        hovertemplate='Step %{marker.color}<br>φ: %{x:.1f}°<br>ψ: %{y:.1f}°<br>E: %{z:.1f} kJ/mol<extra></extra>'
    ))

    # Add Ramachandran region annotations
    annotations = [
        {'x': -60, 'y': -45, 'z': Z.max()*0.3, 'text': "α-helix", 'showarrow': False,
             'font': {'size': 14, 'color': 'white'}, 'bgcolor': 'rgba(0,100,200,0.7)'},
        {'x': -120, 'y': 120, 'z': Z.max()*0.3, 'text': "β-sheet", 'showarrow': False,
             'font': {'size': 14, 'color': 'white'}, 'bgcolor': 'rgba(200,100,0,0.7)'},
        {'x': -75, 'y': 145, 'z': Z.max()*0.3, 'text': "PPII", 'showarrow': False,
             'font': {'size': 14, 'color': 'white'}, 'bgcolor': 'rgba(100,200,0,0.7)'}
    ]

    # Layout
    fig.update_layout(
        title={
            'text': '🏔️ Protein Folding Energy Landscape<br><sub>Ramachandran Space with Folding Trajectory</sub>',
            'x': 0.5,
            'xanchor': 'center',
            'font': {'size': 20}
        },
        scene={
            'xaxis': {'title': 'Phi φ (degrees)', 'backgroundcolor': 'rgb(20,20,20)', 'gridcolor': 'rgb(50,50,50)'},
            'yaxis': {'title': 'Psi ψ (degrees)', 'backgroundcolor': 'rgb(20,20,20)', 'gridcolor': 'rgb(50,50,50)'},
            'zaxis': {'title': 'Potential Energy (kJ/mol)', 'backgroundcolor': 'rgb(20,20,20)', 'gridcolor': 'rgb(50,50,50)'},
            'camera': {
                'eye': {'x': 1.5, 'y': 1.5, 'z': 1.3}
            }
        },
        width=1000,
        height=800,
        template='plotly_dark',
        showlegend=True,
        legend={
            'x': 0.02,
            'y': 0.98,
            'bgcolor': 'rgba(0,0,0,0.5)'
        }
    )

    fig.show(renderer='json' if os.getenv('CI') else None)
import os

if len(X) == 0 or len(traj_phi) == 0:
    print("⚠️  Please run the previous cells first to generate data.")
else:
    # Create figure with Ramachandran annotations
    fig = go.Figure()

    # Energy surface
    fig.add_trace(go.Surface(
        z=Z, x=X, y=Y,
        colorscale=ENERGY_COLORSCALE,
        opacity=0.85,
        name='Energy Surface',
        colorbar={
            'title': "Energy
(kJ/mol)",
            'tickmode': "linear",
            'tick0': Z.min(),
            'dtick': (Z.max() - Z.min()) / 5
        },
        hovertemplate='φ: %{x:.1f}°
ψ: %{y:.1f}°
E: %{z:.1f} kJ/mol'
    ))

    # Folding trajectory
    fig.add_trace(go.Scatter3d(
        x=traj_phi, y=traj_psi, z=energies,
        mode='markers+lines',
        marker={
            'size': 8,
            'color': np.arange(len(energies)),
            'colorscale': 'Hot',
            'showscale': True,
            'colorbar': {
                'title': "Step",
                'x': 1.15
            },
            'line': {'color': 'white', 'width': 2}
        },
        line={'color': TRAJECTORY_COLOR, 'width': 6},
        name='Folding Path',
        hovertemplate='Step %{marker.color}
φ: %{x:.1f}°
ψ: %{y:.1f}°
E: %{z:.1f} kJ/mol'
    ))

    # Add Ramachandran region annotations
    annotations = [
        {'x': -60, 'y': -45, 'z': Z.max()*0.3, 'text': "α-helix", 'showarrow': False,
             'font': {'size': 14, 'color': 'white'}, 'bgcolor': 'rgba(0,100,200,0.7)'},
        {'x': -120, 'y': 120, 'z': Z.max()*0.3, 'text': "β-sheet", 'showarrow': False,
             'font': {'size': 14, 'color': 'white'}, 'bgcolor': 'rgba(200,100,0,0.7)'},
        {'x': -75, 'y': 145, 'z': Z.max()*0.3, 'text': "PPII", 'showarrow': False,
             'font': {'size': 14, 'color': 'white'}, 'bgcolor': 'rgba(100,200,0,0.7)'}
    ]

    # Layout
    fig.update_layout(
        title={
            'text': '🏔️ Protein Folding Energy Landscape
Ramachandran Space with Folding Trajectory',
            'x': 0.5,
            'xanchor': 'center',
            'font': {'size': 20}
        },
        scene={
            'xaxis': {'title': 'Phi φ (degrees)', 'backgroundcolor': 'rgb(20,20,20)', 'gridcolor': 'rgb(50,50,50)'},
            'yaxis': {'title': 'Psi ψ (degrees)', 'backgroundcolor': 'rgb(20,20,20)', 'gridcolor': 'rgb(50,50,50)'},
            'zaxis': {'title': 'Potential Energy (kJ/mol)', 'backgroundcolor': 'rgb(20,20,20)', 'gridcolor': 'rgb(50,50,50)'},
            'camera': {
                'eye': {'x': 1.5, 'y': 1.5, 'z': 1.3}
            }
        },
        width=1000,
        height=800,
        template='plotly_dark',
        showlegend=True,
        legend={
            'x': 0.02,
            'y': 0.98,
            'bgcolor': 'rgba(0,0,0,0.5)'
        }
    )

    fig.show(renderer='json' if os.getenv('CI') else None)

4️⃣ Molecular Structure Viewer¶

Browse through the folding trajectory snapshots to see the backbone actually condensing into its stable form.

🔍 Visualization Features:

Stick representation with spectrum coloring (N→C terminus: blue→red)
Sphere representation for atoms
Interactive rotation and zoom
Real-time energy display

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import os

IN_CI = bool(os.getenv("CI"))

if not IN_CI:
    import io

    import py3Dmol
    from biotite.structure.io.pdb import PDBFile

    viewer_output = widgets.Output()
    info_label = widgets.HTML(
        "<div style='background: linear-gradient(135deg, #667eea 0%, #764ba2 100%); "
        "color: white; padding: 15px; border-radius: 10px; font-family: sans-serif; "
        "box-shadow: 0 4px 6px rgba(0,0,0,0.3);'>"
        "<b>🧬 Select a snapshot to begin</b></div>"
    )

    def display_molecule(index):
        """Render structure using py3Dmol with enhanced styling."""
        if len(trajectory_structs) == 0:
            return

        # Update info panel
        energy_delta = energies[index] - energies[0] if index > 0 else 0
        info_label.value = f"""
        <div style='background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
                    color: white; padding: 15px; border-radius: 10px;
                    font-family: sans-serif; box-shadow: 0 4px 6px rgba(0,0,0,0.3);'>
            <b>📸 Snapshot {index}</b> |
            Energy: <span style='color: #FFD700;'>{energies[index]:.1f} kJ/mol</span> |
            ΔE: <span style='color: {'#00FF00' if energy_delta < 0 else '#FF6B6B'};'>{energy_delta:+.1f} kJ/mol</span> |
            φ/ψ: <span style='color: #87CEEB;'>({traj_phi[index]:.1f}°, {traj_psi[index]:.1f}°)</span>
        </div>
        """

        with viewer_output:
            clear_output(wait=True)

            # Get PDB string
            pdb_file = PDBFile()
            pdb_file.set_structure(trajectory_structs[index])
            sink = io.StringIO()
            pdb_file.write(sink)
            pdb_str = sink.getvalue()

            # Create viewer
            view = py3Dmol.view(width=600, height=450)
            view.addModel(pdb_str, 'pdb')

            # Enhanced styling
            view.setStyle({
                'stick': {'colorscheme': 'chainHetatm', 'radius': 0.15},
                'sphere': {'scale': 0.25, 'colorscheme': 'chainHetatm'}
            })

            view.setBackgroundColor('#1a1a1a')
            view.zoomTo()
            view_widget = view.show()
            display(view_widget)

    def on_slider_change(change):
        display_molecule(change['new'])

    # Create slider with custom styling
    slider = widgets.IntSlider(
        value=0,
        min=0,
        max=max(0, len(trajectory_structs)-1),
        step=1,
        description='Snapshot:',
        continuous_update=False,
        layout=widgets.Layout(width='600px'),
        style={'description_width': '80px'}
    )
    slider.observe(on_slider_change, names='value')

    # Display
    display(widgets.VBox([
        info_label,
        slider,
        viewer_output
    ]))

    # 3Dmol.js initializes asynchronously in the browser. Calling view.show()
    # at kernel execution time races with the library bootstrap and produces
    # the 'failed to load' error. Show a placeholder instead; the first
    # slider drag fires display_molecule() after 3Dmol.js is fully ready.
    with viewer_output:
        from IPython.display import HTML as _HTML
        from IPython.display import display as _disp
        _disp(_HTML(
            '<div style="text-align:center;padding:40px;color:#aaa;'
            'border:1px dashed #555;border-radius:8px;'
            'font-style:italic;background:#1a1a1a;">'
            '&#128260; Move the slider above to load the 3D structure'
            '</div>'
        ))
# (Widget output skipped in CI)
import os

IN_CI = bool(os.getenv("CI"))

if not IN_CI:
    import io

    import py3Dmol
    from biotite.structure.io.pdb import PDBFile

    viewer_output = widgets.Output()
    info_label = widgets.HTML(
        ""
        "🧬 Select a snapshot to begin
"
    )

    def display_molecule(index):
        """Render structure using py3Dmol with enhanced styling."""
        if len(trajectory_structs) == 0:
            return

        # Update info panel
        energy_delta = energies[index] - energies[0] if index > 0 else 0
        info_label.value = f"""
        
📸 Snapshot {index} |
            Energy: {energies[index]:.1f} kJ/mol |
            ΔE: {energy_delta:+.1f} kJ/mol |
            φ/ψ: ({traj_phi[index]:.1f}°, {traj_psi[index]:.1f}°)

        """

        with viewer_output:
            clear_output(wait=True)

            # Get PDB string
            pdb_file = PDBFile()
            pdb_file.set_structure(trajectory_structs[index])
            sink = io.StringIO()
            pdb_file.write(sink)
            pdb_str = sink.getvalue()

            # Create viewer
            view = py3Dmol.view(width=600, height=450)
            view.addModel(pdb_str, 'pdb')

            # Enhanced styling
            view.setStyle({
                'stick': {'colorscheme': 'chainHetatm', 'radius': 0.15},
                'sphere': {'scale': 0.25, 'colorscheme': 'chainHetatm'}
            })

            view.setBackgroundColor('#1a1a1a')
            view.zoomTo()
            view_widget = view.show()
            display(view_widget)

    def on_slider_change(change):
        display_molecule(change['new'])

    # Create slider with custom styling
    slider = widgets.IntSlider(
        value=0,
        min=0,
        max=max(0, len(trajectory_structs)-1),
        step=1,
        description='Snapshot:',
        continuous_update=False,
        layout=widgets.Layout(width='600px'),
        style={'description_width': '80px'}
    )
    slider.observe(on_slider_change, names='value')

    # Display
    display(widgets.VBox([
        info_label,
        slider,
        viewer_output
    ]))

    # 3Dmol.js initializes asynchronously in the browser. Calling view.show()
    # at kernel execution time races with the library bootstrap and produces
    # the 'failed to load' error. Show a placeholder instead; the first
    # slider drag fires display_molecule() after 3Dmol.js is fully ready.
    with viewer_output:
        from IPython.display import HTML as _HTML
        from IPython.display import display as _disp
        _disp(_HTML(
            ''
            '🔄 Move the slider above to load the 3D structure'
            '
'
        ))
# (Widget output skipped in CI)

🎓 Key Takeaways¶

Energy Landscapes are Rugged: The folding pathway navigates through multiple local minima
Ramachandran Constraints: Only certain φ/ψ combinations are sterically allowed
Funnel Topology: Proteins fold via a funnel-shaped landscape, not a single pathway
Secondary Structure Stability: α-helices and β-sheets occupy deep energy wells

📖 Further Reading¶

Dill & MacCallum (2012). "The Protein-Folding Problem, 50 Years On." Science 338:1042-1046. DOI: 10.1126/science.1219021
Onuchic et al. (1997). "Theory of protein folding: the energy landscape perspective." Annu Rev Phys Chem 48:545-600. DOI: 10.1146/annurev.physchem.48.1.545
Ramachandran et al. (1963). "Stereochemistry of polypeptide chain configurations." J Mol Biol 7:95-99. DOI: 10.1016/S0022-2836(63)80023-6

🚀 Next Steps¶

Try modifying the code to:

Use different amino acid sequences (e.g., GLY-ALA-GLY to see glycine flexibility)
Increase grid resolution for smoother landscapes
Compare different force fields
Analyze multi-domain proteins

🎉 Tutorial Complete!

You've successfully visualized the protein folding energy landscape using synth-pdb

Continue exploring the other interactive tutorials to learn more!