README.md

Protein Folding: Generalized Master Equation

This example simulates protein folding dynamics using the Generalized Master Equation (GME) with memory kernels for non-Markovian behavior.

How to Run

cargo run -p medicine_examples --example protein_folding

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Engineering Value

Protein folding simulation is crucial for:

• Drug Discovery: Understanding protein misfolding diseases (Alzheimer's, Parkinson's)
• Bioengineering: Designing proteins with specific functions
• Computational Biology: Predicting 3D structure from sequence

The GME approach captures memory effects - proteins "remember" recent conformations.

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Physics Background

Generalized Master Equation

Standard Markov: P(t+Δt) = T · P(t)

GME adds memory: P(t+Δt) = T · P(t) + Σ K(τ) · P(t-τ)

Where:

• T: Markov transition matrix (instantaneous transitions)
• K(τ): Memory kernel (history-dependent corrections)
• P(t): Probability distribution over conformational states

Conformational States

[0] Unfolded → [1] Intermediate 1 → [2] Intermediate 2 → [3] Native (Folded)

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Causal Chain

[Init]    100% Unfolded state
             ↓
[t=1..15] Apply GME step:
             │
             ├─ Markov: T · P(t)
             │
             └─ Memory: Σ K_k · P(t-k)
             ↓
[Result]  ~65% Native state → Protein folded!

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Output Interpretation

[t= 1] Distribution:
  Unfolded:  70.00% ██████████████
  Intermed1:  30.00% ██████

Visual bars show the population flowing from Unfolded → Native over time.

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Adapting This Example

1. More states: Model detailed folding pathway with more intermediates
2. Different kinetics: Adjust transition matrix for fast/slow folders
3. Memory effects: Tune memory kernels for different physical regimes
4. Temperature dependence: Add Arrhenius-type rate modifications

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Key APIs Used

• generalized_master_equation() - Non-Markovian dynamics
• Probability - Type-safe probability values [0,1]
• CausalTensor - Transition and memory kernel matrices