Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting

Beguerisse-Díaz, Mariano; Desikan, Radhika; Barahona, Mauricio

doi:10.1098/rsif.2011.0767

Cited by 9 publications

(18 citation statements)

References 24 publications

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“…We fit the model to experimental data using the Squeeze-and-Breathe algorithm [84], a recent optimisation method that can efficiently fit temporal data using an accelerated Monte Carlo search and fit process (see Methods section). The parameters of the model found using the Squeeze-and-Breathe algorithm are shown in Table S1 of the Additional file 1.…”

Section: Resultsmentioning

confidence: 99%

Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells

et al. 2012

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BackgroundStomata are tiny pores in plant leaves that regulate gas and water exchange between the plant and its environment. Abscisic acid and ethylene are two well-known elicitors of stomatal closure when acting independently. However, when stomata are presented with a combination of both signals, they fail to close.ResultsToshed light on this unexplained behaviour, we have collected time course measurements of stomatal aperture and hydrogen peroxide production in Arabidopsis thaliana guard cells treated with abscisic acid, ethylene, and a combination of both. Our experiments show that stomatal closure is linked to sustained high levels of hydrogen peroxide in guard cells. When treated with a combined dose of abscisic acid and ethylene, guard cells exhibit increased antioxidant activity that reduces hydrogen peroxide levels and precludes closure. We construct a simplified model of stomatal closure derived from known biochemical pathways that captures the experimentally observed behaviour.ConclusionsOur experiments and modelling results suggest a distinct role for two antioxidant mechanisms during stomatal closure: a slower, delayed response activated by a single stimulus (abscisic acid ‘or’ ethylene) and another more rapid ‘and’ mechanism that is only activated when both stimuli are present. Our model indicates that the presence of this rapid ‘and’ mechanism in the antioxidant response is key to explain the lack of closure under a combined stimulus.

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Section: Resultsmentioning

confidence: 99%

Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells

et al. 2012

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“…Each model corresponds to a different mechanistic hypothesis of the dynamics in the pathways (see electronic supplementary material, appendix III.C). To find the models that best describe the response of each of the five clusters, we estimate parameters using the squeeze-and-breathe algorithm [59], and rank them using the Akaike information criterion score (AICc) (see electronic supplementary material, appendix IV.D). The best models for each cluster are shown in figure 4.…”

Section: Resultsmentioning

confidence: 99%

Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer

Seigal

Beguerisse-Díaz

Schoeberl

et al. 2019

J. R. Soc. Interface.

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We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detection of clusters of data in the presence of structural requirements which we encode as algebraic constraints in a linear program. Our clustering method is general and can be tailored to a variety of applications in science and industry. We illustrate our method on a collection of experiments measuring the response of genetically diverse breast cancer cell lines to an array of ligands. Each experiment consists of a cell line–ligand combination, and contains time-course measurements of the early signalling kinases MAPK and AKT at two different ligand dose levels. By imposing appropriate structural constraints and respecting the multi-indexed structure of the data, the analysis of clusters can be optimized for biological interpretation and therapeutic understanding. We then perform a systematic, large-scale exploration of mechanistic models of MAPK–AKT crosstalk for each cluster. This analysis allows us to quantify the heterogeneity of breast cancer cell subtypes, and leads to hypotheses about the signalling mechanisms that mediate the response of the cell lines to ligands.

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“…We consider these samples as our 'noisy data' (squares in Fig. 2B,C) and we fit the gamma function expressions (11) 1 and (15), respectively, using a Matlab implementation of the Squeeze and Breathe evolutionary Monte-Carlo method which is especially appropriate for time-course series [5] 2 . The dashed lines in Fig.…”

Section: Model Simplification and Parameter Fittingmentioning

confidence: 99%

“…The dashed lines are fits of the noisy data using the corresponding incomplete gamma function expressions, equations (3.2) and (3.6). The fits were carried out using the squeeze-and-breathe algorithm [ 20 ]. (Online version in colour.)…”

Section: Applications Of the Analytical Solutions To The Coarse-grainmentioning

confidence: 99%

Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

Beguerisse-Díaz

Desikan

Barahona

2016

J. R. Soc. Interface.

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Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here, we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal gain cascades (i.e. when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

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Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting

Cited by 9 publications

References 24 publications

Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells

Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells

Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer

Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

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