Module-Based Analysis of Robustness Tradeoffs in the Heat Shock Response System Using module-based analysis coupled with rigorous mathematical comparisons, we propose that in analogy to control engineering architectures, the complexity of cellular systems and the presence of hierarchical modular structures can be attributed to the necessity of achieving robustness.

What is a modular architecture?

What is protocol? Existing Module New module New Module How is a new module added to the existing system? TCP/IP USB

What is robustness? Biological systems maintain their homeostasis against environmental stress, genetic changes and noises. Time Parameter Perturbation

What is a tradeoff? A tradeoff usually refers to losing one quality or aspect of something in return for gaining another quality or aspect. It implies a decision to be made with full comprehension of both the upside and downside of a particular choice. (from WIKIPEDIA)

Heat shock response A universal principle? Robustness tradeoffs generate complexity.

1 Molecular module 2 Functional module 3.Flux module Hierarchical modular structure

Modular Decomposition in the Heat Shock Response 1. Molecular module RNAP,  32, DnaK FtsH, gene, mRNA,…. 2. Functional module PLANT FF SENSOR FB SENSOR COMPUTER ACTUATOR FF=feedfoward, FB=feedback PLANT FB SENSOR FF SENSOR COMPUTER ACTUATOR

3. FLUX Module FF Feedforward flux module SEQ-FB SEQ-Feedback flux module DEG-FB DEG-Feedback flux module  32 amplification flux module 1. FF: Temperature-induced translation of the rpoH mRNA 2. SEQ-FB: DnaK-mediated sequestering  DEG-FB: FtsH-mediated  32 degradation

 32 amplification SEQ-FB DEG-FB FF Four flux module

Mathematical module decomposition A simple model for the heat shock response

Mathematical functional decomposition of the reduced order heat shock system

SEQ-FB FF DEG-FB Mathematical flux decomposition of the reduced order heat shock system

Mathematical system analysis The main objective of the heat shock response system is to refold denatured proteins upon exposure of higher temperatures by the heat shock proteins (hsps: e.g. chaperone, DnaK, FtsH,…).

1. Response speed 2. Yield for refolded proteins How much proteins are refolded? 3. Efficiency for chaperones How less chaperones are employed for refolding process? 4. Robustness (e.g. sensitivity analysis) Sensitivity of chaperone (DnaK) to parameter uncertainty Resistance of chaperone (DnaK) to noise Characterization criteria

Virtual knockout mutant A flux module is removed while conserving the other modules in computers. A flux module is disabled to explore the function of it.

Mathematical comparison for robustness Some performances are compared while the others are set to the same. Wild: SEQ+DEG+FF Yield Efficiency Response speed Mutant: SEQ+FF Yield Efficiency Response speed ==== > For example, a response speed is compared between wild type and a virtual knockout mutant while the yield and efficiency are set to the same.

SEQ-FB ( DnaK-mediated sequestering  32 ) It seems sufficient for refolding proteins. Why other flux modules are added? 1. (FF) Temperature-induced translation of the rpoH mRNA 2. (DEG-FB) FtsH-mediated  32 degradation At least two flux modules are added to the heat shock response.

Time course of  32 and yield A response time is compared ： FF slow SEQslow SEQ+DEGmiddle SEQ+DEG+FFfast

FF SEQ+FF SEQ+DEG+FF FF slow SEQ+DEG+FF very fast SEQ +FF very fast at a high concentration of  32 Response time

Robustness of chaperone against parameter uncertainty Sensitivity analysis SEQ enhances the robustness (low sensitivity), while neither DEG addition nor FF addition does it. SEQ +DEG SEQ +DEG +FF SEQ

Addition of DEG-FB provides the robustness to noise Robustness to noise SEQ SEQ+DEG Stochastic simulation

YieldParameter Uncertainty Stochastic fluctuation Response speed FF ○ ＸＸ△ SEQ-FB △ ○○ △ DEG-FB Ｘ△ ○○ FF +SEQ-FB +DEG-FB ○○○○ Robustness and Tradeoff Robustness tradeoffs generate complex regulations.

SEQ SEQ+DEG SEQ+DEG+FF +Fast response +Resistance to noise SEQ+FF Two cinarios for the heat shock response evolution +High yield Resistance to parameter uncertainty Resistance to noise +Fast response +High yield Low  32 concentration in cytoplasm High  32 concnetration in periplasm

 32 is very weak. Interconnected feedback loops Fragility is generated.

Evolvable architecture of the interconnected feedback Protocol for new flux module addition

Hierarchical module architecture Robustness tradeoffs evolve complex systems Similarity between biology and engineering

Biological systems Virtual biological systems Engineering systems Kurata, 2000 Comparison In silico modeling Design principle underlying molecular networks (bioalgorithm) In analogy to engineering systems Strategy for exploring design principles