# Team:TU-Delft/Modeling

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## Revision as of 20:08, 26 September 2012

## Contents |

# Overview

We decided to use the modeling expertise of the team members to achieve three key objectives for our project.

- Develop scientific understanding of the yeast pheromone response pathway.
- Test the effects of the changes to the system.
- Aid decision making in the laboratory.

To achieve the stated objectives, we adopted a hierarchical modeling approach, in which we constructed heterogeneous models spanning

- population dynamics (diffusion model).
- extra-cellular interactions (structural model).
- intra-cellular dynamics (pathway model).

## Connected Multi-level Models

These three models interact with each other to represent the mechanism of our project in different perspectives. At the system level, **diffusion model** sheds light on how the oder in the petridish diffuses through gas into the disk of olfactory yeasts, which imitates the diffusion process in real life such as smelling banana by human. As a downstream of receiving odor ligands, the **pathway model** is built to functionally simulate the intra-cellular biochemical reactions in the signalling pathway. Parameters in pathway were fitted to the experimental data thus it can give a good estimation on how the important intra-cellular species evolve and predict the producing fluorescence in the experiment. Moreover, the **structural model** is designed to understand the ligand docking at the molecular level. It indicates how well the hydrogen bonds are and how stable of activated receptor, which give an insight into rates of receptor inactivation in the pathway model. Further research of structural model on receptor binding and niche shrink in volume may provide more knowledge about binging rate and G protein release.

Based on these models, a practical device, Snifferometer is designed to achieve the purpose of odor detection. The model of this device is developed to give an idea of the application of our project.

The models span a broad spectrum of techniques: PDE, MD (molecular dynamics), SDE and ODE, as well as alignment techniques. Various and diverse tools have been employed: COMSOL, YASARA, MATLAB, COPASI, BLAST, ClustalW2, Ensembl.

## Research Cycle

A cycle of research is an interactive boundary work between wetlab and "dry" modeling to gain a hierarchical in-depth understanding of our biological system. [1]

At the beginning, based on biological expertise and literature surveys, model hypotheses of system structures are proposed for signal transduction and ligand binding. However, due to the inadequate descriptions of dynamics and lack of information, analyses of hypothesized models are necessary to investigate the properties of models, including the analyses of parameter sensitivities and structural stability in pathway model. Then, experiments can be comprehended and even designed by the knowledge of model simulation. For example, based on the understanding of diffusion model, a practical device is designed, and the output of the device is provisional.

Next, the measured data from "wet" experiment, in turn, modifies the model to fit the reality by tuning the parameters and eliminating the inconsistent assumptions. For instance, ambiguous assumptions of the stability of pathway model is resolved by analysing the measured output GFP.

Later, the verified model gives a good comprehension for the biological system and useful predictions in different conditions can be simulated by "cheap" computations *in silco* instead of doing the time-consuming experiments.

## Future Work

1. fit and validate structural model

2. stochastic model for the whole pathway

3. diffusion model of blowing gas

4. estimation of minimum amount of ligand by structural model and pathway model

5. structural model give the way of receptor mutations

# Diffusion Model

# Structural Model

# Pathway Model

The bio-chemical pathway model was developed based on a scheme favouring the temporal order of the processes, which involved the four fundamental modules,

- Receptor Activation
- G - Protein Cycle
- MAPK Cascade
- Gene Expression

Three different models were used for the analysis of different aspects of the pathway. The dynamics of the system in these models were described using a set of differential equations governing the concentration changes of individual components and of complexes over time. On account of the gene expression module being noisy, a stochastic model of the gene expression module was implemented using stochastic differential equations.

Sensitivity and stability analysis were permformed to determine the sensitivity coefficients which were used to study the parametric dependence of the biological models. The results from the sensitivity analysis were then used in the parameter estimation to fit the model to the data provided by the experimentalists.

# References