A multiscale approximation in a heat shock response model of E. coli

Kang, Hye-Won

doi:10.1186/1752-0509-6-143

Cited by 15 publications

(29 citation statements)

References 18 publications

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“…Finally, this regulatory network is well defined, well separated from other regulatory functions in the cell, and composed of a relatively small number of protein families, making it amenable for modeling. Correspondingly, the heat shock response has been modeled in bacteria (Kang, 2012), yeast (Castells-Roca et al, 2011), and HeLA cells .…”

Section: Discussionmentioning

confidence: 99%

Dynamics of Heat Shock Detection and Response in the Intestine ofCaenorhabditis elegans

Levine

2019

Preprint

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The heat shock response is the organized molecular response to stressors which disrupt proteostasis, potentially leading to protein misfolding and aggregation. While the regulation of the heat shock response is well-studied in single cells, its coordination at the cell, tissue, and systemic levels of a multicellular organism is poorly understood. To probe the interplay between systemic and cell-autonomous responses, we studied the upregulation of HSP-16.2, a molecular chaperone induced throughout the intestine of Caenorhabditis elegans following a heat shock, by taking longitudinal measurements in a microfluidic environment. Based on the dynamics of HSP-16.2 accumulation, we showed that a combination of heat shock temperature and duration define the intensity of stress inflicted on the worm and identified two regimes of low and high intensity stress. Modeling the underlying regulatory dynamics implicated the saturation of heat shock protein mRNA production in defining these two regimes and emphasized the importance of time separation between transcription and translation in establishing these dynamics. By applying a heat shock and measuring the response in separate parts of the animals, we implicated thermosensory neurons in accelerating the response and transducing information within the animal. We discuss possible implications of the systemic and cell level aspects and how they coordinate to facilitate the organismal response.

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Section: Discussionmentioning

confidence: 99%

Dynamics of Heat Shock Detection and Response in the Intestine ofCaenorhabditis elegans

Levine

2019

Preprint

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“…Complex balanced networks are also embedded in many signalling networks such as receptor-ligand signal pathways in response to various stimuli such as heat [26, 72], inflammation [73], and blood glucose [74]. Furthermore, a feedforward network is one of fundamental motifs of gene and protein regulatory networks [64, 65].…”

Section: Discussionmentioning

confidence: 99%

Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation

Kim

Sontag

2017

PLoS Comput Biol

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Biochemical reaction networks (BRNs) in a cell frequently consist of reactions with disparate timescales. The stochastic simulations of such multiscale BRNs are prohibitively slow due to high computational cost for the simulations of fast reactions. One way to resolve this problem uses the fact that fast species regulated by fast reactions quickly equilibrate to their stationary distribution while slow species are unlikely to be changed. Thus, on a slow timescale, fast species can be replaced by their quasi-steady state (QSS): their stationary conditional expectation values for given slow species. As the QSS are determined solely by the state of slow species, such replacement leads to a reduced model, where fast species are eliminated. However, it is challenging to derive the QSS in the presence of nonlinear reactions. While various approximation schemes for the QSS have been developed, they often lead to considerable errors. Here, we propose two classes of multiscale BRNs which can be reduced by deriving an exact QSS rather than approximations. Specifically, if fast species constitute either a feedforward network or a complex balanced network, the reduced model based on the exact QSS can be derived. Such BRNs are frequently observed in a cell as the feedforward network is one of fundamental motifs of gene or protein regulatory networks. Furthermore, complex balanced networks also include various types of fast reversible bindings such as bindings between transcriptional factors and gene regulatory sites. The reduced models based on exact QSS, which can be calculated by the computational packages provided in this work, accurately approximate the slow scale dynamics of the original full model with much lower computational cost.

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“…In the following subsections, we briefly describe how to derive the reduced system approximating the slow-scale dynamics of (2) with the multiscale approximation method [5,33,34].…”

Section: Stochastic Multiscale Approximation Methodsmentioning

confidence: 99%

“…α S = 0) for simplicity even when its order of magnitude of species abundance changes in time. In such case, α S is supposed to be adjusted throughout time as suggested in the original multiscale approximation method [33,34]. Specifically, when X S (0) = O(N 0 ) as in the case of Fig.…”

Section: Deriving the Average Of Fast Variables And Limiting Modelmentioning

confidence: 99%

Reduction for Stochastic Biochemical Reaction Networks with Multiscale Conservations

Kim¹,

Rempała²,

Kang³

2017

Multiscale Model. Simul.

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Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic approximations on the timescale of interest. One of the rigorous and popular approaches is the multiscale approximation method for continuous time Markov processes. In this approach, by scaling species abundances and reaction rates, a family of processes parameterized by a scaling parameter is defined. The limiting process of this family is then used to approximate the original process. However, we find that such approximations become inaccurate when combinations of species with disparate abundances either constitute conservation laws or form virtual slow auxiliary species. To obtain more accurate approximation in such cases, we propose here an appropriate modification of the original method.

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A multiscale approximation in a heat shock response model of E. coli

Cited by 15 publications

References 18 publications

Dynamics of Heat Shock Detection and Response in the Intestine ofCaenorhabditis elegans

Dynamics of Heat Shock Detection and Response in the Intestine ofCaenorhabditis elegans

Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation

Reduction for Stochastic Biochemical Reaction Networks with Multiscale Conservations

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