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.2005 Feb 22;102(8):2736-41.
doi: 10.1073/pnas.0403510102. Epub 2005 Jan 24.

Surviving heat shock: control strategies for robustness and performance

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Surviving heat shock: control strategies for robustness and performance

H El-Samad et al. Proc Natl Acad Sci U S A..

Abstract

Molecular biology studies the cause-and-effect relationships among microscopic processes initiated by individual molecules within a cell and observes their macroscopic phenotypic effects on cells and organisms. These studies provide a wealth of information about the underlying networks and pathways responsible for the basic functionality and robustness of biological systems. At the same time, these studies create exciting opportunities for the development of quantitative and predictive models that connect the mechanism to its phenotype then examine various modular structures and the range of their dynamical behavior. The use of such models enables a deeper understanding of the design principles underlying biological organization and makes their reverse engineering and manipulation both possible and tractable The heat shock response presents an interesting mechanism where such an endeavor is possible. Using a model of heat shock, we extract the design motifs in the system and justify their existence in terms of various performance objectives. We also offer a modular decomposition that parallels that of traditional engineering control architectures.

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Figures

Fig. 1.
Fig. 1.
Modular decomposition of the hsr. The functional modules, such as the plant, sensors, computational unit, and actuator, consist of various molecular species and their interactions
Fig. 2.
Fig. 2.
Hypothetical design models for the hsr. (a) Simple open-loop design. The feedforward element achieves temperature sensing (b). Closed-loop design with feedforward and sequestration loop to regulate the activity of σ32. (c) Closed loop with feedforward, sequestration, and degradation of σ32 loop, which corresponds to the wild-type heat shock system.
Fig. 3.
Fig. 3.
Levels of σ32, DnaK, and unfolded proteins for the open-loop design in Fig. 2a, closed-loop design with sequestration loop in Fig. 2b, and closed loop with both sequestration and degradation loops in Fig. 2c. Heat shock occurs at time 0. The rate of production of σ32 is tuned to produce the same levels at low temperature as the wild-type design, and performance is assessed at a high temperature.
Fig. 4.
Fig. 4.
Robustness as an outcome of feedback in hsr. (a) Plot of the percentage change in the level of chaperones vs. the percentage change in the transcription rate for the open-loop model in Fig. 2a and the closed-loop model with sequestration loop in Fig. 2b. (b) Small signal sensitivity of the level of chaperones to their synthesis rate (dotted lines) and to the binding between σ32 and the core RNAP (solid lines). The plots are shown for the open-loop design in Fig. 2a and the closed-loop design with sequestrion in Fig. 2b. Sensitivity is computed as the derivative of the chaperone level to the corresponding parameters along the trajectories of the system. The plots are in log space. Heat shock occurs at time 0.
Fig. 5.
Fig. 5.
A stochastic realization using the Gillespie stochastic simulation algorithm (10). The heat shock model with constitutive degradation of σ32 (red) shows larger excursions around the mean than the model with regulated degradation of σ32 (green). The mean value for the number of chaperones per cell is comparable for both cases, <DnaK> ≃8,950. The standard deviation for the regulated degradation case was computed to be σr ≃ 1,500, whereas that for the constitutive degradation case was σu ≃ 2,700. [Reproduced with permission from ref. (Copyright 2004, IEEE)].
Fig. 6.
Fig. 6.
Levels of σ32, DnaK, and unfolded proteins for the open-loop design in Fig. 2a; closed loop with sequestration and degradations loops in Fig. 2c; closed loop with sequestration and degradation but lacking the feedforward component; and closed loop with feedforward, sequestration, and degradation and a lower σ32 turnover rate. The rate of production of σ32 is tuned to produce the same levels at low temperature as the wild-type design, and performance is assessed at high temperature. Heat shock occurs at time 0.
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