PeTTSy: a computational tool for perturbation analysis of complex systems biology models

Abstract Background Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary. Results Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems. To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters. Conclusions PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities

PeTTSy : a computational tool for perturbation analysis of complex systems biology models

Background Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary. Results Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems. To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters. Conclusions PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities

Coordinated circadian timing through the integration of local inputs in Arabidopsis thaliana.

Individual plant cells have a genetic circuit, the circadian clock, that times key processes to the day-night cycle. These clocks are aligned to the day-night cycle by multiple environmental signals that vary across the plant. How does the plant integrate clock rhythms, both within and between organs, to ensure coordinated timing? To address this question, we examined the clock at the sub-tissue level across Arabidopsis thaliana seedlings under multiple environmental conditions and genetic backgrounds. Our results show that the clock runs at different speeds (periods) in each organ, which causes the clock to peak at different times across the plant in both constant environmental conditions and light-dark (LD) cycles. Closer examination reveals that spatial waves of clock gene expression propagate both within and between organs. Using a combination of modeling and experiment, we reveal that these spatial waves are the result of the period differences between organs and local coupling, rather than long-distance signaling. With further experiments we show that the endogenous period differences, and thus the spatial waves, can be generated by the organ specificity of inputs into the clock. We demonstrate this by modulating periods using light and metabolic signals, as well as with genetic perturbations. Our results reveal that plant clocks can be set locally by organ-specific inputs but coordinated globally via spatial waves of clock gene expression

ELF3 controls thermoresponsive growth in Arabidopsis

Plant development is highly responsive to ambient temperature, and this trait has been linked to the ability of plants to adapt to climate change [1]. The mechanisms by which natural populations modulate their thermoresponsiveness are not known [2]. To address this, we surveyed Arabidopsis accessions for variation in thermal responsiveness of elongation growth and mapped the corresponding loci. We find that the transcriptional regulator EARLY FLOWERING3 (ELF3) controls elongation growth in response to temperature. Through a combination of modeling and experiments, we show that high temperature relieves the gating of growth at night, highlighting the importance of temperature-dependent repressors of growth. ELF3 gating of transcriptional targets responds rapidly and reversibly to changes in temperature. We show that the binding of ELF3 to target promoters is temperature dependent, suggesting a mechanism where temperature directly controls ELF3 activity

Phytochromes function as thermosensors in Arabidopsis

Plants are responsive to temperature, and can distinguish differences of 1ºC. In Arabidopsis, warmer temperature accelerates flowering and increases elongation growth hermomorphogenesis). The mechanisms of temperature perception are however largely unknown. We describe a major thermosensory role for the phytochromes (red light receptors) during the night. Phytochrome null plants display a constitutive warm temperature response, and consistent with this, we show in this background that the warm temperature transcriptome becomes de-repressed at low temperatures. We have discovered phytochrome B (phyB) directly associates with the promoters of key target genes in a temperature dependent manner. The rate of phyB inactivation is proportional to temperature in the dark, enabling phytochromes to function as thermal timers, integrating temperature information over the course of the night

Balance equations can buffer noisy and sustained environmental perturbations of circadian clocks

We present a new approach to understanding how regulatory networks such as circadian clocks might evolve robustness to environmental fluctuations. The approach is in terms of new balance equations that we derive. We use it to describe how an entrained clock can buffer the effects of daily fluctuations in light and temperature levels. We also use it to study a different approach to temperature compensation where instead of considering a free-running clock, we study temperature buffering of the phases in a light-entrained clock, which we believe is a more physiological setting

Mathematical aspects of chemical reaction networks

Chemical and biological processes present a challenge when it comes to modelling and analysis. The models usually have to take into account many chemicals and complex interactions and in turn, they are often described by large ODE systems with complicated nonlinear terms. If there is a lack of quantitative information about the chemical interactions, there will also be parameter uncertainty in the systems. Such systems present a challenge to analyse. In response, an increasing consensus calls for emphasis on the underlying chemical reaction network structure and the use of network information to predict possible system dynamics.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Using constraints and their value for optimization of large ODE systems

We provide analytical tools to facilitate a rigorous assessment of the quality and value of the fit of a complex model to data. We use this to provide approaches to model fitting, parameter estimation, the design of optimization functions and experimental optimization. This is in the context where multiple constraints are used to select or optimize a large model defined by differential equations. We illustrate the approach using models of circadian clocks and the NF-κB signalling system