Oscillations are an important feature of cell signaling that often result from complicated combinations of positive and negative feedback loops. The encoding and decoding mechanism of oscillations based on amplitude and frequency have been extensively discussed in literature in the context of inter-cellular and intra-cellular signaling . To name a few, the oscillation patterns of cytosolic calcium , p53 tumor suppressor protein , NF-κB transcription factor  and many more have been studied in their respective networks. Although most signaling mechanisms in real physiological systems likely have an extremely complicated mode of modulation, in some cases it is possible to identify the key molecules in a given pathway to determine how one influences another. Among these cases, amplitude-to-amplitude modulation is relatively straight forward, and consequently this idea was applied early in the study of receptor-mediated signaling under sub-saturation regions [1, 3, 5]. In contrast, frequency-modulated mode of cellular signaling, especially decoding, is more convoluted. This mode of signaling has been most extensively studied in the context of calcium signaling, and while it is generally agreed that frequency is the main drive that leads to differentiated downstream events, there is also an argument that cumulative peak duration, not frequency, defines signaling specificity . All of the aforementioned efforts attempt to understand in depth the oscillatory behavior in cellular and intercellular signaling. However, the fundamental question of why cellular signals appear in periodic manner as opposed to a non-oscillatory manner has not been fully answered.
In an attempt to answer this question, we designed a study to analyze oscillatory characteristics of both signaling molecule and system output. To do this, we modified two classic feedback models, the Goodwin oscillator and PER oscillator, and compared periodic signals to steady signals of identical time-averaged values. The two oscillators were selected as experimental systems because: 1) they are both self-sustained oscillators driven by negative feedback; 2) the signaling molecules of these two models exhibit opposite skewness, Goodwin oscillator having fast ascension and slow descension, and PER oscillator having slow ascension and fast descension. Furthermore, it is easy to generate a range of different intensities of skewness in both models by modifying the degree of inhibition, represented by the Hill coefficient or the cooperativity coefficient.
Currently our research into these periodic systems lends the following observations. As the inhibition of both models is increased, the resource generation develops more drastic skewness, which is correlated with an increased efficiency of the oscillatory system as compared to the output of no-feedback counterpart systems. As the cooperativity coefficient is increased in the PER model, the resource tends to skew negatively (toward the right side of the center), indicating slower ascension and faster descension of the signal. This correlates with an increased frequency and output of the system. As the Hill coefficient increases for the Goodwin model, the resource exhibits the opposite effect – it skews positively and is correlated with increased frequency and system output. Combining these results, we hypothesize the existence of regions of degree of inhibition and signaling asymmetry that will improve system output and efficiency. Furthermore, we observe a strong positive correlation between output amplitude and system output (and efficiency), and hypothesize that strong sustained oscillations give rise to a more efficient system. Our hypotheses address the fundamental question of why cellular signals and responses are periodic. From the results, we also search for the underlying mechanism that drives system efficiency.
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