Semi-algebraic optimization of temperature compensation in a general switch-type negative feedback model of circadian clocks

Abstract

Temperature compensation is an essential property of circadian oscillators which enables them to act as physiological clocks. We have analyzed the temperature compensating behavior of a generalized transcriptional-translational negative feedback oscillator with a hard hysteretic switch and rate constants with an Arrheniustype temperature dependence. These oscillations can be considered as the result of a lowpass filtering operator acting on a train of rectangular pulses. Such a signalprocessing viewpoint makes it possible to express, in a semi-algebraic manner, the period length, the oscillator's control (sensitivity) coefficients, and the first and second-order derivatives of the period-temperature relationship. We have used the semi-algebraic approach to investigate a 3-dimensional Goodwin-type representation of the oscillator, where local optimization for temperature compensation has been considered. In the local optimization, activation energies are found, which lead to a zero first order derivative and to a closest-to-zero second order derivative at a given reference temperature. We find that the major contribution to temperature compensation over an extended temperature range is given by the (local) zero first order derivative, while only minor contributions to temperature compensation are given by an optimized second order derivative. In biological terms this could be interpreted to relate to a circadian clock mechanism which during evolution is being optimized for a certain but relative narrow (habitat) temperature range.

Reconstruction of transcriptional dynamics from gene reporter data using differential equations

“…We believe that the functional specifications for τ( t ) suggested in our case studies are useful in conjunction with gene transcription. A theoretical application of the switch function in clock modeling can be found in Aase and Ruoff (2008). Although the estimation of the switch model seems too high dimensional for datasets with many switches, this could be overcome by assigning probability distributions to the on- and off-times in the framework of a Bayesian hierarchical model.…”

The Control of the Controller: Molecular Mechanisms for Robust Perfect Adaptation and Temperature Compensation

“…4) requires a fine-tuning between the control coefficients and activation energies. In general, the resulting temperature compensation in A is not robust, i.e., temperature compensation is only observed within a local region around T ref (see, for example, (24)). Considering the network in Fig.…”

“…5, where the balancing is reduced to a few parameters (39). Characteristic to all physiological and chemical temperature compensated systems (20,24,38,(40)(41)(42)(43)(44)(45)(46)(47)(48) is that the compensation mechanism operates at a local (for the organism) important temperature range and not globally over the whole temperature range such as shown in Fig. 5.…”

Information Surfaces in Systems Biology and Applications to Engineering Sustainable Agriculture

“…After constructing the Eigensurface, InfoSurf calculates the first and second derivatives of the surface. These derivatives are useful for identifying circadian clock information of dynamical systems [49,50]. The derivatives are calculated by a second order approximation method [51].…”