TUNING OF SYNTHETIC GENE
NETWORKS
1
Grégory Batt, Boyan Yordanov,
Ron Weiss, and Calin Belta
VC Lab, Dept. of Computer Science, NTHU,
Taiwan
ROBUSTNESS ANALYSIS AND
OVERVIEW
Introduction
VC Lab, Dept. of Computer Science, NTHU, Taiwan

Problems of biological system design
 Previous solution


Problem
Piecewise-Multiaffine Models
 Linear Temporal Logic(LTL)
 Two problems

Conclusion
 Reference

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INTRODUCTION
Problems of biological system design

VC Lab, Dept. of Computer Science, NTHU, Taiwan

Lack of precise knowledge
Molecular concentrations
 Parameter values


Previous solution



Coarse-grained models
Nonlinear differential equation models
Stochastic models
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PIECEWISE-MULTIAFFINE MODELS
VC Lab, Dept. of Computer Science, NTHU, Taiwan

Non-linear model

Smooth sigmoidal function

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PIECEWISE-MULTIAFFINE MODELS
VC Lab, Dept. of Computer Science, NTHU, Taiwan

Non-linear model

Smooth sigmoidal function

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LTL
Linear Temporal Logic(LTL)

VC Lab, Dept. of Computer Science, NTHU, Taiwan

logical operators
negation (¬)
 logical and (^), logical or ( ˇ )
 implication (→)


temporal operators
future ( F ), globally (G), and until (U)
 EX:

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PROBLEM
Let Σ be a PMA system, P an hyperrectangular
parameter space, and φ an LTL formula.

Robustness: Check whether P is valid for φ.


VC Lab, Dept. of Computer Science, NTHU, Taiwan

Can’t be solve by numerical integration
Tuning: Find a set P  P such that P is valid for φ.
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PROBLEM 1: ROBUSTNESS
Discrete abstractions
VC Lab, Dept. of Computer Science, NTHU, Taiwan

Partition of state space
 Discrete transition
system

Finite
 Test
→ Σ satisfies φ

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PROBLEM 2: TUNING
VC Lab, Dept. of Computer Science, NTHU, Taiwan

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PROBLEM 2: TUNING

15 valid parameters (1.8%)
(total 2.27% from 20,000 parameter)
No more than ±20% parameter variations
VC Lab, Dept. of Computer Science, NTHU, Taiwan

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CONCLUSION
VC Lab, Dept. of Computer Science, NTHU, Taiwan
RoVerGeNe
 A PMA model, an LTL specification
 Generate the temporal space and test the
property range
 Parameter tuning
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REFERENCE
VC Lab, Dept. of Computer Science, NTHU, Taiwan
Batt,G. et al. (2007a) Model checking genetic
regulatory networks with parameter uncertainty.
In Bemporad,A. et al. (eds). Hybrid Systems:
Computation and Control, HSCC’07
 Belta,C. and Habets,L.C.G.J.M. (2006)
Controlling a class of nonlinear systems on
rectangles. Trans. Aut. Control, 51, 1749–1759.
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