1. alia joko 21st Nordic Process Control Workshop 19.01.18
Neural network-based pruning and sensitivity analysis of an apoptosis model
alia joko
21st Nordic Process Control Workshop

2. Apoptosis – what and why?
Programmed and morphologically distinct form of cell death
Relevance
Development
Sculpting of fingers
Homeostasis
Millions of blood cells eliminated daily to balance production
Immune Surveillance
Killing cancer and virus infected cells

3. Apoptosis – information processing and response
Large number of signalling proteins
Complex interactions
Emergent Systems behaviour
What is the ‘point of no return’ ? How robust is this decision point?
Which signalling motifs are responsible – positive feedback loops, competitive inhibition
Why are some cells in a population more sensitivity to cell death stimuli than others?
What principles underlie this variability?

4. Mechanistic Apoptosis Model Formalisms
Cell  , DOI: ( /j.cell )

5. Data-driven models of signal transduction
New technologies are permitting large-scale quantitative studies of signal transduction networks
Data-driven modelling approaches becoming the standard tools
Which are the essential features,
Nature Cell Biology 8, 1195–1203 (2006) doi: /ncb1497

6. Modelling by Feedforward Networks
No or little a priori knowledge of the process required
Captures nonlinear relations between process variables
Works in arbitrary dimensions
Resulting models are fast
Requires many data points
Default network architecture not a good choice
Risk of Trash in Trash out
May overfit the data
Remedies
Judicious choice of inputs based on “process” knowledge
Limit the architecture (“don’t use too many hidden nodes”)
Pruning large networks or let small network grow
Simultaneous optimization of weights and connections
Judicious choice of inputs based on “process” knowledge
Limit the architecture (“don’t use too many hidden nodes”)
Pruning large networks or let small network grow
Simultaneous optimization of weights and connections

7. Saxén - Petterson neural network pruning algorithm
Multiple networks evolved by a pruning algorithm
Rank the resulting models, retaining the best ones
Appearance of the inputs in these reflects their importance
Pruning Algorithm
Randomly generate lower-layer weights, W0. Set i = 1.
Reset in turn each weight, j, in Wi and determine the upper layer weights, wj , by linear least squares, giving the objective function value Fij
Set Wi = Wi-1 and reset permanently the weight with minimum Fij. Call this index
Set and save this variable in a book-keeping matrix
Set i = i + 1. If i < n N, go to 2, else end.
Fij w W

8. Bentele-Toivonen Apoptosis Model
Single cell model with 41 molecules, 32 reactions, 50 parameters to be estimated
Reactions modelled by mass action and Michaelis- Menten kinetics
Stochastic log-normal distributions of protein concentrations and reaction rates to mimic cell population
Populations with 1000 cells simulated
Time to apoptosis :

9. Results from the network pruning
Networks with 10 hidden nodes and 59 inputs were pruned 500 times from different starting weight matrices
For each lower layer complexity the run with the minimum error is retained
Minimum approximation error

10. Relevant model parameters
The occurrences of 56 inputs on the Pareto fronts of the 20 best models show 11 relevant parameters

11. Model – data fit

12. Local sensitivity analysis

13. Reduced model : new insights?
Experimentally verified

14. Summary
Fast and easy generation of promising reduced model subsets (as collected on Pareto fronts)
Successfully finds relevant parameters in a complex model of cell death (apoptosis)
Provides a means of analysing the sensitivity of the output to the identified relevant parameters
Introduces possibilities for experiment design

15. Henrik Saxén, Prof Frank Petterson, Ph.D
Acknowledgements
Henrik Saxén, Prof Frank Petterson, Ph.D
Thank you for your attention