sp-fitting-models
超分子ポリマーのフィッティングモデルライブラリ
A Python library for fitting supramolecular polymerization data with various thermodynamic models.
概要 / Overview
このライブラリは、超分子ポリマー形成データを解析するための数理モデルを提供します。特に温度依存的な会合挙動を定量的に解析し、熱力学パラメータ（エンタルピー、エントロピー）を推定することができます。
This library provides mathematical models for analyzing supramolecular polymerization data. It enables quantitative analysis of temperature-dependent aggregation behavior and estimation of thermodynamic parameters (enthalpy, entropy).
特徴 / Features
-
複数のモデルに対応
- Isodesmicモデル: すべての会合定数が等しい単純な会合モデル
- Cooperativeモデル: 核形成と伸長で異なる定数を持つ協同的会合モデル
- Mixedモデル: IsodesmicとCooperativeの2経路が競合するモデル
-
温度依存性の解析
- van't Hoff式に基づく温度依存的な会合定数の計算
- ΔH（エンタルピー変化）とΔS（エントロピー変化）の推定
-
フィッティング機能
- lmfitライブラリを使用した実験データへのフィッティング
- 複数濃度データの同時フィッティング(グローバルフィット)に対応
インストール / Installation
uv add https://github.com/IndigoCarmine/sp_fitting_models.git
使用方法 / Usage
基本的な使用例
import numpy as np
import matplotlib.pyplot as plt
from sp_fitting_models.models import temp_cooperative_model
# Temperature range
temps = np.linspace(280, 400, 200) # 280-400 K
# Thermodynamic parameters
deltaH = -96000 # Enthalpy change (J/mol)
deltaS = -180 # Entropy change (J/(mol·K))
deltaHnuc = 100000 # Nucleation penalty (J/mol)
c_tot = 5e-6 # Total concentration (M)
# Calculate aggregation
agg = temp_cooperative_model(
Temp=temps,
deltaH=deltaH,
deltaS=deltaS,
deltaHnuc=deltaHnuc,
c_tot=c_tot,
scaler=1.0
)
# Plot
plt.plot(temps - 273.15, agg)
plt.xlabel('Temperature (°C)')
plt.ylabel('Aggregation')
plt.show()
データフィッティング
import lmfit as lm
from sp_fitting_models.data import TempVsAggData
from sp_fitting_models.fitting import objective_temp_cooperative
# Prepare your experimental data
data_list = [
TempVsAggData(temp=temps1, agg=agg1, concentration=c1),
TempVsAggData(temp=temps2, agg=agg2, concentration=c2),
]
# Set up parameters
params = lm.Parameters()
params.add('deltaH', value=-100000, min=-200000, max=0)
params.add('deltaS', value=-180, min=-400, max=0)
params.add('deltaHnuc', value=50000, min=0, max=200000)
params.add('scaler', value=1.0, min=0.5, max=1.5)
# Fit
minner = lm.Minimizer(objective_temp_cooperative, params, fcn_args=(data_list,))
result = minner.minimize()
print(lm.fit_report(result))
インタラクティブな可視化
# Run the interactive mixed model example
python examples/interactive_mixed.py
スライダーを使用してパラメータを変更し、リアルタイムで会合曲線の変化を観察できます。
Windowsアプリとしてビルド (uv + PyInstaller)
examples/interactive_mixed.py をコンソールなしの Windows GUI アプリとしてビルドできます。
./scripts/build_interactive_mixed.ps1
または cmd.exe から:
build_interactive_mixed.bat
生成物:
dist/interactive_mixed/interactive_mixed.exe
このスクリプトは次を自動で行います。
uv syncで依存関係とローカルパッケージを同期uv run --with pyinstaller ...で GUI アプリをビルド
プロジェクト構造 / Project Structure
sp_fitting_models/
├── src/
│ └── sp_fitting_models/
│ ├── __init__.py
│ ├── data.py # Data structures
│ ├── models/ # Model implementations
│ │ ├── __init__.py
│ │ ├── isodesmic.py # Isodesmic models
│ │ ├── cooperative.py # Cooperative models
│ │ ├── mixed.py # Mixed models
│ │ └── utils.py # Utility functions
│ └── fitting/ # Fitting utilities
│ ├── __init__.py
│ └── objective.py # Objective functions for lmfit
├── tests/ # Test files
│ ├── test_isodesmic.py
│ ├── test_cooperative.py
│ ├── test_mixed.py
│ └── test_fitting.py
├── examples/ # Example scripts
│ ├── basic_usage.py
│ └── interactive_mixed.py
├── pyproject.toml
└── README.md
モデルの説明 / Model Description
Isodesmicモデル
すべての会合ステップが同じ平衡定数Kを持つモデルです。シグモイド型の会合曲線を示します。
$$K = \exp\left(-\frac{\Delta H}{RT} + \frac{\Delta S}{R}\right)$$
次のような平衡状態です。 供給されるモノマーは省略してあります。： $$M \stackrel{K}{\rightleftarrows} M_2\stackrel{K}{\rightleftarrows} M_3 \stackrel{K}{\rightleftarrows} ...$$
Cooperativeモデル
核形成と伸長で異なる平衡定数を持つモデルです。非シグモイド型の会合曲線を示します。核形成ペナルティσにより協同性が表現されます。
$$\sigma = \exp\left(-\frac{\Delta H_{nuc}}{RT}\right)$$
$$ K = \exp\left(-\frac{\Delta H}{RT} + \frac{\Delta S}{R}\right)$$
$$ K_{nuc} = \sigma K $$ 次のような平衡状態です。 $$M \stackrel{K_{nuc}}{\rightleftarrows} M_2\stackrel{K}{\rightleftarrows} M_3 \stackrel{K}{\rightleftarrows} ...$$
Mixedモデル
IsodesmicとCooperativeの2つの経路が同じモノマープールを共有して競合するモデルです。実験系で複数の会合機構が同時に起こる場合に適用できます。
次のような平衡状態を考えています。 $$M \stackrel{K_{nuc}}{\rightleftarrows} M_2\stackrel{K}{\rightleftarrows} M_3 \stackrel{K}{\rightleftarrows} ...$$ $$ \searrow \nwarrow^{K_{iso}} M_2\stackrel{K_{iso}}{\rightleftarrows} M_3 \stackrel{K_{iso}}{\rightleftarrows} ...$$ （MDではこれ以上きれいに書けませんでした...）
テスト / Testing
# Run all tests
python -m pytest tests/
# Run specific test
python tests/test_cooperative.py
サンプル / Examples
# Basic usage examples
python examples/basic_usage.py
# Interactive mixed model visualization
python examples/interactive_mixed.py
uvでの実行
uv run --with maturin maturin develop --release
uv run pytest
依存関係 / Dependencies
- Python >= 3.13
- numpy >= 2.4.2
- numba >= 0.64.0
- lmfit >= 1.3.4
- matplotlib >= 3.10.8
引用 /Citation
書いていただけるなら嬉しいですが、必ずしも論文で言及する必要はありません。 ご自由にお使いください。
I would be grateful if you could cite this library in your publications, but it is not mandatory. Please feel free to use it as you see fit.
作成者 / Author
山田悠平 (Yuhei Yamada, Orcid: 0009-0003-9780-4135, google scholar: Yuhei Yamada)
1 maintainer
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