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

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 feed-back oscillator with a hard hysteretic switch and rate constants with an Arrhenius-type temperature dependence. These oscillations can be considered as the result of a lowpass filtering operator acting on a train of rectangular pulses. Such a signal-processing 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

Kinetics and mechanisms of catalyzed dual-E (antithetic) controllers

Homeostasis plays a central role in our understanding how cells and organisms are able to oppose environmental disturbances and thereby maintain an internal stability. During the last two decades there has been an increased interest in using control engineering methods, especially integral control, in the analysis and design of homeostatic networks. Several reaction kinetic mechanisms have been discovered which lead to integral control. In two of them integral control is achieved, either by the removal of a single control species E by zero-order kinetics (“single-E controllers”), or by the removal of two control species by second-order kinetics (“antithetic or dual-E control”). In this paper we show results when the control species E1 and E2 in antithetic control are removed enzymatically by ping-pong or ternary-complex mechanisms. Our findings show that enzyme-catalyzed dual-E controllers can work in two control modes. In one mode, one of the two control species is active, but requires zero-order kinetics in its removal. In the other mode, both controller species are active and both are removed enzymatically. Conditions for the two control modes are put forward and biochemical examples with the structure of enzyme-catalyzed dual-E controllers are discussed.publishedVersio

Sparse Mixture Conditional Density Estimation by Superficial Regularization

In this paper, the estimation of conditional densities between continuous random variables from noisy samples is considered. The conditional densities are modeled as heteroscedastic Gaussian mixture densities allowing for closed-form solution of Bayesian inference with full-densities. The main contributions of this paper are an improved generalization quality of the estimates by the introduction of a superficial regularizer, the consideration of model uncertainty relative to local data densities by means of adaptive covariances, and the proposition of an efficient distance-based estimation algorithm. This algorithm corresponds to an iterative nested optimization scheme, optimizing hyper-parameters, component placement, and mixture weights. The obtained solutions are sparse, smooth, and generalize well as benchmark experiments, e.g., in nonlinear filtering show

Influence of Lithium ions on conidiophore size in Neurospora crassa

Lithium (Li) ions are known to affect Neurospora crassa’s growth speed and circadian clock period, while elevated temperatures abolish these influences. We wondered whether Li has also an effect on conidia size. We used cryo-SEM to investigate this question and report here the results of 1720 measurements showing that at 20°C the long and short conidial axes are significantly reduced at high Li concentrations (10-15 mM), while the ratio between the long and short axes remains approximately constant. An increased temperature (30°C) appears to abolish the Li effect on conidia size

Progressive Correction for Deterministic Dirac Mixture Approximations

Since the advent of Monte-Carlo particle filtering, particle representations of densities have become increasingly popular due to their flexibility and implicit adaptive resolution. In this paper, an algorithm for the multiplication of a systematic Dirac mixture (DM) approximation with a continuous likelihood function is presented, which applies a progressive correction scheme, in order to avoid the particle degeneration problem. The preservation of sample regularity and therefore, representation quality of the underlying smooth density, is ensured by including a new measure of smoothness for Dirac mixtures, the DM energy, into the distance measure. A comparison to common correction schemes in Monte-Carlo methods reveals large improvements especially in cases of small overlap between the likelihood and prior density, as well as for multi-modal likelihoods

Variable setpoint as a relaxing component in physiological control

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controller's ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.publishedVersio

An amplified derepression controller with multisite inhibition and positive feedback

How organisms are able to maintain robust homeostasis has in recent years received increased attention by the use of combined control engineering and kinetic concepts, which led to the discovery of robust controller motifs. While these motifs employ kinetic conditions showing integral feedback and homeostasis for step-wise perturbations, the motifs’ performance differ significantly when exposing them to time dependent perturbations. One type of controller motifs which are able to handle exponentially and even hyperbolically growing perturbations are based on derepression. In these controllers the compensatory reaction, which neutralizes the perturbation, is derepressed, i.e. its reaction rate is increased by the decrease of an inhibitor acting on the compensatory flux. While controllers in this category can deal well with different time-dependent perturbations they have the disadvantage that they break down once the concentration of the regulatory inhibitor becomes too low and the compensatory flux has gained its maximum value. We wondered whether it would be possible to bypass this restriction, while still keeping the advantages of derepression kinetics. In this paper we show how the inclusion of multisite inhibition and the presence of positive feedback loops lead to an amplified controller which is still based on derepression kinetics but without showing the breakdown due to low inhibitor concentrations. By searching for the amplified feedback motif in natural systems, we found it as a part of the plant circadian clock where it is highly interlocked with other feedback loops.publishedVersio

Homeostatic controllers compensating for growth and perturbations

Cells and organisms have developed homeostatic mechanisms which protect them against a changing environment. How growth and homeostasis interact is still not well understood, but of increasing interest to the molecular and synthetic biology community to recognize and design control circuits which can oppose the diluting effects of cell growth. In this paper we describe the performance of selected negative feedback controllers in response to different applied growth laws and time dependent outflow perturbations of a controlled variable. The approach taken here is based on deterministic mass action kinetics assuming that cell content is instantaneously mixed. All controllers behave ideal in the sense that they for stepwise perturbations in volume and a controlled compound A are able to drive A precisely back to the controllers’ theoretical set-points. The applied growth kinetics reflect experimentally observed growth laws, which range from surface to volume ratio growth to linear and exponential growth. Our results show that the kinetic implementation of integral control and the structure of the negative feedback loop are two properties which affect controller performance. Best performance is observed for controllers based on derepression kinetics and controllers with an autocatalytic implementation of integral control. Both are able to defend exponential growth and perturbations, although the autocatalytic controller shows an offset from its theoretical set-point. Controllers with activating signaling using zero-order or bimolecular (antithetic) kinetics for integral control behave very similar but less well. Their performance can be improved by implementing negative feedback structures having repression/ derepression steps or by increasing controller aggressiveness. Our results provide a guide what type of feedback structures and integral control kinetics are suitable to oppose the dilution effects by different growth laws and time dependent perturbations on a deterministic level.publishedVersio

Life cycle assessment of tomato production for different production strategies in Norway

The availability of fresh vegetables grown in greenhouses under controlled conditions throughout the year has given rise to concerns about their impact on the environment. In high latitude countries such as Norway, greenhouse vegetable production requires large amounts of energy for heat and light, especially during the winter. The use of renewable energy such as hydroelectricity and its effect on the environment has not been well documented. Neither has the effect of different production strategies on the environment been studied to a large extent. We conducted a life cycle assessment (LCA) of greenhouse tomato production for mid-March to mid-October (seasonal production), 20th January to 20th November (extended seasonal) production, and year-round production including the processes from raw material extraction to farm gate. Three production seasons and six greenhouse designs were included, at one location in southwestern and one in northern Norway. The SimaPro software was used to calculate the environmental impact. Across the three production seasons, the lowest global warming (GW) potential (600 g CO2-eq per 1 kg tomatoes) was observed during year-round production in southwestern Norway for the design NDSFMLLED + LED, while the highest GW potential (3100 g CO2-eq per 1 kg tomatoes) was observed during seasonal production in northern Norway for the design NS. The choice of artificial lighting (HPS (High Pressure Sodium) or LED (Light Emitting Diodes)), heating system and the production season was found to have had a considerable effect on the environmental impact. Moreover, there was a significant reduction in most of the impact categories including GW potential, terrestrial acidification, and fossil resource scarcity from seasonal to year-round production. Overall, year-round production in southwestern Norway had the lowest environmental impact of the evaluated production types. Heating of the greenhouse using natural gas and electricity was the biggest contributor to most of the impact categories. The use of an electric heat pump and LED lights during extended seasonal and year-round production both decreased the environmental impact. However, while replacing natural gas with electricity resulted in decreased GW potential, it increased the ecotoxicity potential.publishedVersio