| Name | llrq JSON |
| Version |
0.0.3
JSON |
| download |
| home_page | None |
| Summary | Log-Linear Reaction Quotient Dynamics: Tractable framework for chemical reaction networks |
| upload_time | 2025-09-08 01:54:30 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.8 |
| license | Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/
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reaction quotient
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# LLRQ - Log-Linear Reaction Quotient Dynamics
A Python package for analyzing chemical reaction networks using the log-linear reaction quotient dynamics framework described in Diamond (2025) "Log-Linear Reaction Quotient Dynamics" ([arXiv:2508.18523](https://arxiv.org/pdf/2508.18523)).
## Overview
This framework introduces a novel approach to modeling chemical reaction networks where reaction quotients (Q) evolve exponentially toward equilibrium when viewed on a logarithmic scale. Unlike traditional mass action kinetics, this yields analytically tractable linear dynamics in log-space.
### Key Equation
For reaction networks, the dynamics follow:
```
d/dt ln Q = -K ln(Q/Keq) + u(t)
```
Where:
- **Q**: Vector of reaction quotients measuring distance from equilibrium
- **Keq**: Vector of equilibrium constants
- **K**: Relaxation rate matrix
- **u(t)**: External drive vector (e.g., ATP/ADP ratios)
## Framework Advantages
1. **Analytical Solutions**: Exact solutions exist for arbitrary network topologies
2. **Thermodynamic Integration**: Automatic incorporation of constraints via ΔG = RT ln(Q/Keq)
3. **Decoupled Dynamics**: Conservation laws separate from reaction quotient evolution
4. **Linear Control**: External energy sources couple linearly to dynamics
5. **Tractable Analysis**: Decades of linear systems theory become applicable
## Installation
### From PyPI (when available)
```bash
pip install llrq
```
### From source
```bash
git clone <repository-url>
cd llrq
pip install -e .
```
### Requirements
- Python ≥3.8
- numpy ≥1.20.0
- scipy ≥1.7.0
- matplotlib ≥3.3.0
- python-libsbml ≥5.19.0
- tellurium ≥2.2.0
- cvxpy ≥1.7.2
## Quick Start
### Simple Reaction Example
```python
import llrq
import numpy as np
# Create a simple A ⇌ B reaction
network, dynamics, solver, visualizer = llrq.simple_reaction(
reactant_species="A",
product_species="B",
equilibrium_constant=2.0,
relaxation_rate=1.0,
initial_concentrations={"A": 1.0, "B": 0.1}
)
# Solve the dynamics
solution = solver.solve(
initial_conditions={"A": 1.0, "B": 0.1},
t_span=(0, 10),
method='analytical'
)
# Visualize results
fig = visualizer.plot_dynamics(solution)
```
### SBML Model Example
```python
import llrq
# Load SBML model
network, dynamics, solver, visualizer = llrq.from_sbml(
'model.xml',
equilibrium_constants=np.array([2.0, 1.5, 0.8]), # Keq for each reaction
relaxation_matrix=np.diag([1.0, 0.5, 1.2]) # K matrix (diagonal)
)
# Solve with external drive
def atp_drive(t):
return np.array([0.5, 0.0, -0.2]) # Drive for each reaction
dynamics.external_drive = atp_drive
solution = solver.solve(
initial_conditions=network.get_initial_concentrations(),
t_span=(0, 20)
)
# Plot results
fig = visualizer.plot_dynamics(solution)
```
## API Reference
### Core Classes
- **`SBMLParser`**: Parse SBML models and extract network information
- **`ReactionNetwork`**: Represent reaction networks with stoichiometry and species
- **`LLRQDynamics`**: Implement log-linear dynamics system
- **`LLRQSolver`**: Solve dynamics with analytical and numerical methods
- **`LLRQVisualizer`**: Create publication-quality plots
### Control Systems
- **`LLRQController`**: Base controller class with LQR optimal control
- **`CVXController`**: Advanced optimization-based control using CVXPY
- **`FrequencySpaceController`**: Frequency-domain control for sinusoidal inputs
- **`ThermodynamicAccountant`**: Entropy production calculations and energy balance
### Convenience Functions
- **`llrq.from_sbml()`**: Load SBML model and create complete LLRQ system
- **`llrq.simple_reaction()`**: Create simple A ⇌ B reaction system
- **`llrq.simulate_to_target()`**: One-line controlled simulation to target state
- **`llrq.compare_control_methods()`**: Compare LLRQ vs mass action control performance
- **`llrq.create_entropy_aware_cvx_controller()`**: Create entropy-aware optimization controller
## Examples
See the `examples/` directory for complete working examples:
### Basic Usage
- **`simple_example.py`**: Basic A ⇌ B reaction with visualization
- **`linear_vs_mass_action_simple.py`**: Compare LLRQ approximation with mass action
- **`mass_action_example.py`**: Mass action kinetics integration
### Control Systems
- **`lqr_complete_example.py`**: Linear Quadratic Regulator control design
- **`cvx_sparse_control.py`**: Sparse control using L1 regularization
- **`cvx_constrained_control.py`**: Control with constraints and bounds
- **`cvx_custom_objective.py`**: Custom optimization objectives
- **`frequency_space_control.py`**: Frequency-domain control design
- **`frequency_space_simulation.py`**: Sinusoidal control simulation
### Advanced Features
- **`entropy_production_demo.py`**: Thermodynamic entropy calculations
- **`entropy_aware_control.py`**: Control design with entropy constraints
- **`frequency_entropy_control.py`**: Frequency-domain entropy optimization
- **`integrated_control_demo.py`**: Complete control workflow demonstration
## Mathematical Framework
### Single Reaction Dynamics
For a single reaction with external drive:
```
d/dt ln Q = -k ln(Q/Keq) + u(t)
```
**Analytical solution** (constant u):
```
Q(t) = Keq * exp[(ln(Q₀/Keq) - u/k) * exp(-kt) + u/k]
```
### Multiple Reactions
Vector form for reaction networks:
```
d/dt ln Q = -K ln(Q/Keq) + u(t)
```
**Matrix exponential solution** (constant u):
```
ln Q(t) = exp(-Kt) * [ln(Q₀/Keq) - K⁻¹u] + K⁻¹u + ln Keq
```
### Connection to Mass Action
For single reaction A ⇌ B with mass action rates kf, kr:
- Equilibrium constant: `Keq = kf/kr`
- Relaxation rate: `k = kr(1 + Keq)` (ensures agreement near equilibrium)
### Control Theory Integration
The linear dynamics enable direct application of control theory:
**LQR Control**: For quadratic cost J = ∫[x^T Q x + u^T R u]dt:
```
u*(t) = -R⁻¹B^T P x(t)
```
where P solves the Riccati equation: PA + A^T P - PBR⁻¹B^T P + Q = 0
**Frequency Response**: Transfer function H(s) = (K + sI)⁻¹B enables:
- Bode plot analysis for stability margins
- Optimal sinusoidal control design
- Frequency-domain entropy optimization
**Thermodynamic Constraints**: Entropy production rate:
```
dS/dt = x^T K x + x^T u
```
enables entropy-aware control design balancing performance and thermodynamic cost.
## Applications
This framework enables:
### Traditional Applications
- **Metabolic Engineering**: Optimize pathway design using K as design variable
- **Drug Discovery**: Predict drug effects throughout metabolic networks
- **Systems Medicine**: Classify metabolic disorders via eigenvalue analysis
### Advanced Control Applications
- **Optimal Control**: LQR and model predictive control for metabolic regulation
- **Sparse Control**: L1-regularized control for minimal intervention strategies
- **Constrained Optimization**: Control with resource limits and safety constraints
- **Frequency-Domain Design**: Sinusoidal control for periodic metabolic cycles
- **Thermodynamic Control**: Entropy-aware control balancing performance and energy cost
- **Robust Control**: Uncertainty-aware control for model variations
- **Real-Time Control**: Adaptive control with online parameter estimation
## Citation
If you use this package in research, please cite:
```bibtex
@article{diamond2025loglinear,
title={Log-Linear Reaction Quotient Dynamics},
author={Diamond, Steven},
journal={arXiv preprint arXiv:2508.18523},
year={2025}
}
```
## License
Licensed under the Apache License 2.0. See `LICENSE` file for details.
## Contact
- **Author**: Steven Diamond
- **Email**: steven@gridmatic.com
- **Paper**: [arXiv:2508.18523](https://arxiv.org/pdf/2508.18523)
Raw data
{
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"maintainer": null,
"docs_url": null,
"requires_python": ">=3.8",
"maintainer_email": null,
"keywords": "reaction networks, systems biology, SBML, chemical kinetics, reaction quotient",
"author": null,
"author_email": "Steven Diamond <steven@gridmatic.com>",
"download_url": "https://files.pythonhosted.org/packages/f3/12/f26c4731c4324584af0105b909a9c3ae07f3a5503b49235f14f620aa4caf/llrq-0.0.3.tar.gz",
"platform": null,
"description": "# LLRQ - Log-Linear Reaction Quotient Dynamics\n\nA Python package for analyzing chemical reaction networks using the log-linear reaction quotient dynamics framework described in Diamond (2025) \"Log-Linear Reaction Quotient Dynamics\" ([arXiv:2508.18523](https://arxiv.org/pdf/2508.18523)).\n\n## Overview\n\nThis framework introduces a novel approach to modeling chemical reaction networks where reaction quotients (Q) evolve exponentially toward equilibrium when viewed on a logarithmic scale. Unlike traditional mass action kinetics, this yields analytically tractable linear dynamics in log-space.\n\n### Key Equation\n\nFor reaction networks, the dynamics follow:\n```\nd/dt ln Q = -K ln(Q/Keq) + u(t)\n```\n\nWhere:\n- **Q**: Vector of reaction quotients measuring distance from equilibrium\n- **Keq**: Vector of equilibrium constants\n- **K**: Relaxation rate matrix\n- **u(t)**: External drive vector (e.g., ATP/ADP ratios)\n\n## Framework Advantages\n\n1. **Analytical Solutions**: Exact solutions exist for arbitrary network topologies\n2. **Thermodynamic Integration**: Automatic incorporation of constraints via \u0394G = RT ln(Q/Keq)\n3. **Decoupled Dynamics**: Conservation laws separate from reaction quotient evolution\n4. **Linear Control**: External energy sources couple linearly to dynamics\n5. **Tractable Analysis**: Decades of linear systems theory become applicable\n\n## Installation\n\n### From PyPI (when available)\n```bash\npip install llrq\n```\n\n### From source\n```bash\ngit clone <repository-url>\ncd llrq\npip install -e .\n```\n\n### Requirements\n- Python \u22653.8\n- numpy \u22651.20.0\n- scipy \u22651.7.0\n- matplotlib \u22653.3.0\n- python-libsbml \u22655.19.0\n- tellurium \u22652.2.0\n- cvxpy \u22651.7.2\n\n## Quick Start\n\n### Simple Reaction Example\n\n```python\nimport llrq\nimport numpy as np\n\n# Create a simple A \u21cc B reaction\nnetwork, dynamics, solver, visualizer = llrq.simple_reaction(\n reactant_species=\"A\",\n product_species=\"B\",\n equilibrium_constant=2.0,\n relaxation_rate=1.0,\n initial_concentrations={\"A\": 1.0, \"B\": 0.1}\n)\n\n# Solve the dynamics\nsolution = solver.solve(\n initial_conditions={\"A\": 1.0, \"B\": 0.1},\n t_span=(0, 10),\n method='analytical'\n)\n\n# Visualize results\nfig = visualizer.plot_dynamics(solution)\n```\n\n### SBML Model Example\n\n```python\nimport llrq\n\n# Load SBML model\nnetwork, dynamics, solver, visualizer = llrq.from_sbml(\n 'model.xml',\n equilibrium_constants=np.array([2.0, 1.5, 0.8]), # Keq for each reaction\n relaxation_matrix=np.diag([1.0, 0.5, 1.2]) # K matrix (diagonal)\n)\n\n# Solve with external drive\ndef atp_drive(t):\n return np.array([0.5, 0.0, -0.2]) # Drive for each reaction\n\ndynamics.external_drive = atp_drive\nsolution = solver.solve(\n initial_conditions=network.get_initial_concentrations(),\n t_span=(0, 20)\n)\n\n# Plot results\nfig = visualizer.plot_dynamics(solution)\n```\n\n## API Reference\n\n### Core Classes\n\n- **`SBMLParser`**: Parse SBML models and extract network information\n- **`ReactionNetwork`**: Represent reaction networks with stoichiometry and species\n- **`LLRQDynamics`**: Implement log-linear dynamics system\n- **`LLRQSolver`**: Solve dynamics with analytical and numerical methods\n- **`LLRQVisualizer`**: Create publication-quality plots\n\n### Control Systems\n\n- **`LLRQController`**: Base controller class with LQR optimal control\n- **`CVXController`**: Advanced optimization-based control using CVXPY\n- **`FrequencySpaceController`**: Frequency-domain control for sinusoidal inputs\n- **`ThermodynamicAccountant`**: Entropy production calculations and energy balance\n\n### Convenience Functions\n\n- **`llrq.from_sbml()`**: Load SBML model and create complete LLRQ system\n- **`llrq.simple_reaction()`**: Create simple A \u21cc B reaction system\n- **`llrq.simulate_to_target()`**: One-line controlled simulation to target state\n- **`llrq.compare_control_methods()`**: Compare LLRQ vs mass action control performance\n- **`llrq.create_entropy_aware_cvx_controller()`**: Create entropy-aware optimization controller\n\n## Examples\n\nSee the `examples/` directory for complete working examples:\n\n### Basic Usage\n- **`simple_example.py`**: Basic A \u21cc B reaction with visualization\n- **`linear_vs_mass_action_simple.py`**: Compare LLRQ approximation with mass action\n- **`mass_action_example.py`**: Mass action kinetics integration\n\n### Control Systems\n- **`lqr_complete_example.py`**: Linear Quadratic Regulator control design\n- **`cvx_sparse_control.py`**: Sparse control using L1 regularization\n- **`cvx_constrained_control.py`**: Control with constraints and bounds\n- **`cvx_custom_objective.py`**: Custom optimization objectives\n- **`frequency_space_control.py`**: Frequency-domain control design\n- **`frequency_space_simulation.py`**: Sinusoidal control simulation\n\n### Advanced Features\n- **`entropy_production_demo.py`**: Thermodynamic entropy calculations\n- **`entropy_aware_control.py`**: Control design with entropy constraints\n- **`frequency_entropy_control.py`**: Frequency-domain entropy optimization\n- **`integrated_control_demo.py`**: Complete control workflow demonstration\n\n## Mathematical Framework\n\n### Single Reaction Dynamics\nFor a single reaction with external drive:\n```\nd/dt ln Q = -k ln(Q/Keq) + u(t)\n```\n\n**Analytical solution** (constant u):\n```\nQ(t) = Keq * exp[(ln(Q\u2080/Keq) - u/k) * exp(-kt) + u/k]\n```\n\n### Multiple Reactions\nVector form for reaction networks:\n```\nd/dt ln Q = -K ln(Q/Keq) + u(t)\n```\n\n**Matrix exponential solution** (constant u):\n```\nln Q(t) = exp(-Kt) * [ln(Q\u2080/Keq) - K\u207b\u00b9u] + K\u207b\u00b9u + ln Keq\n```\n\n### Connection to Mass Action\nFor single reaction A \u21cc B with mass action rates kf, kr:\n- Equilibrium constant: `Keq = kf/kr`\n- Relaxation rate: `k = kr(1 + Keq)` (ensures agreement near equilibrium)\n\n### Control Theory Integration\nThe linear dynamics enable direct application of control theory:\n\n**LQR Control**: For quadratic cost J = \u222b[x^T Q x + u^T R u]dt:\n```\nu*(t) = -R\u207b\u00b9B^T P x(t)\n```\nwhere P solves the Riccati equation: PA + A^T P - PBR\u207b\u00b9B^T P + Q = 0\n\n**Frequency Response**: Transfer function H(s) = (K + sI)\u207b\u00b9B enables:\n- Bode plot analysis for stability margins\n- Optimal sinusoidal control design\n- Frequency-domain entropy optimization\n\n**Thermodynamic Constraints**: Entropy production rate:\n```\ndS/dt = x^T K x + x^T u\n```\nenables entropy-aware control design balancing performance and thermodynamic cost.\n\n## Applications\n\nThis framework enables:\n\n### Traditional Applications\n- **Metabolic Engineering**: Optimize pathway design using K as design variable\n- **Drug Discovery**: Predict drug effects throughout metabolic networks\n- **Systems Medicine**: Classify metabolic disorders via eigenvalue analysis\n\n### Advanced Control Applications\n- **Optimal Control**: LQR and model predictive control for metabolic regulation\n- **Sparse Control**: L1-regularized control for minimal intervention strategies\n- **Constrained Optimization**: Control with resource limits and safety constraints\n- **Frequency-Domain Design**: Sinusoidal control for periodic metabolic cycles\n- **Thermodynamic Control**: Entropy-aware control balancing performance and energy cost\n- **Robust Control**: Uncertainty-aware control for model variations\n- **Real-Time Control**: Adaptive control with online parameter estimation\n\n## Citation\n\nIf you use this package in research, please cite:\n\n```bibtex\n@article{diamond2025loglinear,\n title={Log-Linear Reaction Quotient Dynamics},\n author={Diamond, Steven},\n journal={arXiv preprint arXiv:2508.18523},\n year={2025}\n}\n```\n\n## License\n\nLicensed under the Apache License 2.0. See `LICENSE` file for details.\n\n## Contact\n\n- **Author**: Steven Diamond\n- **Email**: steven@gridmatic.com\n- **Paper**: [arXiv:2508.18523](https://arxiv.org/pdf/2508.18523)\n",
"bugtrack_url": null,
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