Generic temperature compensation of biological clocks by autonomous regulation of catalyst concentration

Circadian clocks ubiquitous in life forms ranging bacteria to multi-cellular organisms, often exhibit intrinsic temperature compensation; the period of circadian oscillators is maintained constant over a range of physiological temperatures, despite the expected Arrhenius form for the reaction coefficient. Observations have shown that the amplitude of the oscillation depends on the temperature but the period does not---this suggests that although not every reaction step is temperature independent, the total system comprising several reactions still exhibits compensation. We present a general mechanism for such temperature compensation. Consider a system with multiple activation energy barriers for reactions, with a common enzyme shared across several reaction steps with a higher activation energy. These reaction steps rate-limit the cycle if the temperature is not high. If the total abundance of the enzyme is limited, the amount of free enzyme available to catalyze a specific reaction decreases as more substrates bind to common enzyme. We show that this change in free enzyme abundance compensate for the Arrhenius-type temperature dependence of the reaction coefficient. Taking the example of circadian clocks with cyanobacterial proteins KaiABC consisting of several phosphorylation sites, we show that this temperature compensation mechanisms is indeed valid. Specifically, if the activation energy for phosphorylation is larger than that for dephosphorylation, competition for KaiA shared among the phosphorylation reactions leads to temperature compensation. Moreover, taking a simpler model, we demonstrate the generality of the proposed compensation mechanism, suggesting relevance not only to circadian clocks but to other (bio)chemical oscillators as well.Comment: 21 pages, 12 figure

Regulation of Clock-Controlled Genes in Mammals

The complexity of tissue- and day time-specific regulation of thousands of clock-controlled genes (CCGs) suggests that many regulatory mechanisms contribute to the transcriptional output of the circadian clock. We aim to predict these mechanisms using a large scale promoter analysis of CCGs

Effects of Ploidy and Recombination on Evolution of Robustness in a Model of the Segment Polarity Network

Many genetic networks are astonishingly robust to quantitative variation, allowing these networks to continue functioning in the face of mutation and environmental perturbation. However, the evolution of such robustness remains poorly understood for real genetic networks. Here we explore whether and how ploidy and recombination affect the evolution of robustness in a detailed computational model of the segment polarity network. We introduce a novel computational method that predicts the quantitative values of biochemical parameters from bit sequences representing genotype, allowing our model to bridge genotype to phenotype. Using this, we simulate 2,000 generations of evolution in a population of individuals under stabilizing and truncation selection, selecting for individuals that could sharpen the initial pattern of engrailed and wingless expression. Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation. We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction. In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone. Diploidy conferred increased robustness by allowing most deleterious mutations to be rescued by a working allele. Sex (recombination) conferred a robustness advantage through “survival of the compatible”: those alleles that can work with a wide variety of genetically diverse partners persist, and this selects for robust alleles

‘Glocal’ Robustness Analysis and Model Discrimination for Circadian Oscillators

To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a high-dimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This ‘global’ analysis is then supplemented by a ‘local’ analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the two-sites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our ‘glocal’ combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and different parameter sets

A model of the cell-autonomous mammalian circadian clock

Circadian timekeeping by intracellular molecular clocks is evident widely in prokaryotes and eukaryotes. The clockworks are driven by autoregulatory feedback loops that lead to oscillating levels of components whose maxima are in fixed phase relationships with one another. These phase relationships are the key metric characterizing the operation of the clocks. In this study, we built a mathematical model from the regulatory structure of the intracellular circadian clock in mice and identified its parameters using an iterative evolutionary strategy, with minimum cost achieved through conformance to phase separations seen in cell-autonomous oscillators. The model was evaluated against the experimentally observed cell-autonomous circadian phenotypes of gene knockouts, particularly retention of rhythmicity and changes in expression level of molecular clock components. These tests reveal excellent de novo predictive ability of the model. Furthermore, sensitivity analysis shows that these knockout phenotypes are robust to parameter perturbation