Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. But existing approaches can not efficiently recover N -dimensional exponential signals with N ≥ 3. In this paper, we study the problem of recovering N -dimensional (particularly N ≥ 3) exponential signals from partial observations, and formulate this problem as a low-rank tensor completion problem with exponential factor vectors. The full signal is reconstructed by simultaneously exploiting the CANDECOMP/PARAFAC structure and the exponential structure of the associated factor vectors. The latter is promoted by minimizing an objective function involving the nuclear norm of Hankel matrices. Experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank.

Recognition of specific chromatin modifications by distinct structural domains within “reader” proteins plays a critical role in the maintenance of genomic stability. However, the specific mechanisms involved in this process remain unclear. Here we report that the PHD-Bromo tandem domain of tripartite motif-containing 66 (TRIM66) recognizes the unmodified H3R2-H3K4 and acetylated H3K56. The aberrant deletion of Trim66 results in severe DNA damage and genomic instability in embryonic stem cells (ESCs). Moreover, we find that the recognition of histone modification by TRIM66 is critical for DNA damage repair (DDR) in ESCs. TRIM66 recruits Sirt6 to deacetylate H3K56ac, negatively regulating the level of H3K56ac and facilitating the initiation of DDR. Importantly, Trim66-deficient blastocysts also exhibit higher levels of H3K56ac and DNA damage. Collectively, the present findings indicate the vital role of TRIM66 in DDR in ESCs, establishing the relationship between histone readers and maintenance of genomic stability.

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Nuclear magnetic resonance (NMR) is a powerful tool to interrogate protein structure and dynamics residue by residue. However, the prerequisite chemical-shift assignment remains a bottleneck for large proteins due to the fast relaxation and the frequency degeneracy of the (13) Cα nuclei. Herein, we present a covariance NMR strategy to assign the backbone chemical shifts by using only HN(CO)CA and HNCA spectra that has a high sensitivity even for large proteins. By using the peak linear correlation coefficient (LCC), which is a sensitive probe even for tiny chemical-shift displacements, we correctly identify the fidelity of approximately 92 % cross-peaks in the covariance spectrum, which is thus a significant improvement on the approach developed by Snyder and Brüschweiler (66 %) and the use of spectral derivatives (50 %). Thus, we calculate the 4D covariance spectrum from HN(CO)CA and HNCA experiments, in which cross-peaks with LCCs above a universal threshold are considered as true correlations. This 4D covariance spectrum enables the sequential assignment of a 42 kDa maltose binding protein (MBP), in which about 95 % residues are successfully assigned with a high accuracy of 98 %. Our LCC approach, therefore, paves the way for a residue-by-residue study of the backbone structure and dynamics of large proteins.