In this problem we are going to explore the symmetry properties of the continuou

Question

In this problem we are going to explore the symmetry properties of the continuous-time Fourier series. Consider the following real, periodic signals which are defined over a single period on an interval from -T/2 t T/2 as follows: Plot the signals f1(t) and f2(t) for a single period from [-T/2, T/2]. Are the signals even or odd? Compute the complex Fourier series for each signal, and plot the magnitude and phase of the Fourier coefficients cn for 5 n 5. Is there a pattern? Interpret your results. Prove that the Fourier series of a real and even signal has coefficients that are even and real. Prove that the Fourier series of a real and odd signal has coefficients that are odd and purely imaginary.

Explanation / Answer

The PEBP (phosphatidylethanolamine-binding protein) family is a large group of proteins whose human member, hPEBP1, has been shown to play multiple functions, influencing intracellular signaling cascades, cell cycle regulation, neurodegenerative processes, and reproduction. It also acts, by an unknown mechanism, as a metastasis suppressor in a number of cancers. A more complete understanding of its biological role is thus necessary. As the yeast Saccharomyces cerevisiae is a powerful and easy to handle model organism, we focused on Tfs1p, the yeast ortholog of hPEBP1. In a previous study based on a two-hybrid approach, we showed that Tfs1p interacts and inhibits Ira2p, a GTPase Activating Protein (GAP) of the small GTPase Ras. To further characterize the molecular functions of Tfs1p, we undertook the identification of protein complexes formed around Tfs1p using a targeted proteomics approach. Complexed proteins were purified by tandem-affinity, cleaved with trypsin, and identified by nanoflow liquid chromatography coupled with tandem mass spectrometry. Overall, 14 new interactors were identified, including several proteins involved in intermediate metabolism. We confirmed by co-immunoprecipitation that Tfs1p interacts with Glo3p, a GAP for Arf GTPases belonging to the Ras superfamily of small GTPases, indicating that Tfs1p may be involved in the regulation of another GAP. We similarly confirmed the binding of Tfs1p with the metabolic enzymes Idp1p and Pro1p. Integration of these results with known functional partners of Tfs1p shows that two subnetworks meet through the Tfs1p node, suggesting that it may act as a bridge between cell signaling and intermediate metabolism in yeast.

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