Structure-aware framework
for stochastic simulations
Carlo Masaia Supervisor:
Prof. Harold Fellermann
Pseudo-chemical systems
Pseudo-chemical systems
We are interested in building models for our chemical, biochemical and biological systems. And we want to simulate those models. Experiments in silico have few key advantages.
- They are cheaper and in many cases faster to execute, making them good candidates to solve optimization problems.
- They allow to precisely control parameters which may be harder to manipulate in the real world system, and to get precise measurements.
- They can be used to cross-validate results obtained with in vitro experiments to verify the soundness of our model.
Lotka-Volterra model
Pseudo-reactions
\[\begin{aligned} X& \rightarrow X &:A\\ Y& \rightarrow \varepsilon &:C\\ X+Y& \rightarrow \gamma Y &:B\\ \end{aligned} \]
ODE formulation
Most of the modern techniques are based on ODE and this is one of the flavour we can rewrite our system in, based on the law of mass action. \[\begin{aligned} \dot{x} & = (A-By)x\\ \dot{y} & = (B\gamma x-C)y \\ \end{aligned} \]
Lotka-Volterra - figures
ODE model
Stochastic model
Forgotten assumptions(a.k.a. petitio principii)
Forgotten assumptions
Our ODE model is based on a strict set of assumptions which are often overlooked. And results may not end up being pleasant.
In theory we should always verify them for each application, but often we just forget or ignore their existence.
Well stirred environment
Our physical space-dependent system is reduced to a condensed parameters one. It is virtually like a timescale separation between the diffusive process and all the other pseudo-reactions.
Continuous structure
The high number of objects for each class let us forget their granularity, and our difference operator gets replaced by a differential operator.
Deterministic behaviour
The evolution of a physical system with many components is often well captured by stochastic processes. Here instead, we assume some sort of convergence in distribution to a deterministic one.
Models comparison
Continuous models
Discrete models
Models comparison
Continuous models
Discrete models
Limit models
Representation artifacts
2D Plane shapes
Model representation
Transcription/Translation system
Toy model
\[\begin{aligned} \mathrm{DNA}_i &\rightarrow \mathrm{DNA}_i + \mathrm{RNA}_{\lbrace i,j\rbrace}\\ \mathrm{RNA}_{\lbrace i,j\rbrace} &\rightarrow \varepsilon\\ \mathrm{RNA}_{\lbrace i,j\rbrace} &\rightarrow \mathrm{RNA}_{\lbrace i,j\rbrace} + \mathrm{Protein}_{\lbrace i,j,k\rbrace} \end{aligned} \]
However...
Model complexity
There is not a unique way to represent a model. The complexity of our representation could be thought as the complexity of the evolution operator and the system state. Both in space and time. This affects the algorithmic feasibility of a certain approach.
Structureless objects
Most models are the result of a structureless approach. However chemistry is pretty much interpreted as structures, patterns and reactions among them. No free lunch, but for the class of problems we want to model is it smart to forget such a valuabe information?
Artifacts
- Combinatorial explosion in the base of “atomic” components and the reaction space
- Collective unphysical effective rates
- A model which is not easily explainable nor adaptable
Framework structure
Core feature
implemented by
is stochastic
Monte Carlo sampling scheme
is lazy
dependency system to partialize system updates
is structure-aware
hypergraph representation of objects and generalized hypergraphs for types
is modular
libraries of types and reactions. Layering system.
Current state
1st public release
The simulator as a component is scheduled to have its first public release on October. However most of the code has been already written and a first working prototype should be ready for the end of the month.
The framework on its whole is a three-year project. Its first public release is scheduled for the next year.
Applications
Collaboration with Nikolay Zetkin on trascription/translation with backtracking.
Potential collaboration with David Fulton on molecular molding.
And maybe your own system?
Bibliography
Walter Fontana and Leo W. Buss: “The Barrier of Objects: From Dynamical Systems to Bounded Organizations”
Jakob L. Andersen et al.: “A Software Package for Chemically Inspired Graph Transformation”
Daniel T. Gillespie: “A general method for numerically simulating the stochastic time evolution of coupled chemical reactions”.
The Kappa language: https://kappalanguage.org.
3rd PART MATERIAL
“When you assume” by XKCD @ https://xkcd.com/1339/
reveal.js @ https://revealjs.com
mathjax @ https://www.mathjax.org