MCTT_Autodiff_CRN

Learning Chemical Reaction Networks (CRNs)

Affiliation

UM-DAE Centre for Excellence in Basic Sciences, Mumbai
Max Planck Institute of Molecular Cell Biology and Genetics, Dresden
Center for Systems Biology Dresden

Author

• Vishvas RANJAN
  UM-DAE Centre for Excellence in Basic Sciences, Mumbai

Supervisors

• Dr. Abhishek BEHERA
  Max Planck Institute of Molecular Cell Biology and Genetics, Dresden
• Prof. Dr. Ivo F. SBALZARINI
  Max Planck Institute of Molecular Cell Biology and Genetics, Dresden

Thesis Overview

This research explores how living systems learn and adapt through molecular interactions, using Chemical Reaction Networks (CRNs) as a mathematical framework to bridge microscopic chemical processes and macroscopic biological behaviors. The work focuses on stochastic CRNs as computational models for biological learning, particularly in single-celled organisms.

Research Questions

This thesis explores fundamental questions about biological learning mechanisms:

• How do living systems learn and adapt?
• How can abstract mathematical models unravel molecular complexity?
• Can chemical systems be mathematically "learnable"?
• How can CRNs capture spatial dynamics (e.g., molecular diffusion)?
• What are CRNs' limitations in representing complex systems?

Research Focus

• Framework: Stochastic Chemical Reaction Networks (CRNs)
• Approach: Direct application of Markov Chain Tree Theorem (MCTI) to:
  • Compute parameter likelihoods
  • Derive stationary distributions
  • Avoid PDE approximations of chemical master equations
• Key Insight: Stochastic CRNs induce finite Markov chains on discrete integer lattices when excluding species birth/death reactions

Methodology

1. Inverse Problem Framework:
   Recover reaction rate parameters from observed stationary distributions or target distributions
2. Computational Techniques:
   • Markov Chain Tree Theorem (MCTI) for distribution calculation
   • Gradient descent with automatic differentiation for optimization
   • Gillespie Algorithm verification ((1/\sqrt{n}) convergence achieved)
   • Developed learning rule to recover reaction rate from a target data or a target distribution
3. Learning Approaches:
   • Brute-force combinatorial search
   • Automatic differentiation + gradient descent
   • Gradient computation using Clamping

Key Findings

1. Demonstrated mathematical "learnability" of small chemical systems
2. Established MCTI's validity for stationary distributions
3. Developed parameter learning framework for reaction rate constants
4. Executed Clamping method as Sampling in CRN
5. Identified scalability limitations for complex systems

Challenges and Future Directions

• Challenge: Complex distribution forms resist closed-form solutions
• Challenge: Computational scalability beyond small systems
• Path Forward: Imposing additional structures on CRNs for tractability
• Biological Relevance: Focus on cellular-scale learning in single-celled organisms ("chemical soup" abstraction)

Research Significance

Opens new avenues for modeling biological learning through CRNs, bridging microscopic molecular interactions and macroscopic behaviors in:

• Cellular process modeling
• Nature-inspired AI systems
• Adaptive chemical computing

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