Strengths and Weaknesses of Hybrid TPR Technology for Obtaining Structural and Mechanistic Insights into TPR Proteins

Tetratricopeptide (TPR) repeats are a 34-residue helix-turn-helix motif that when repeated pack into a superhelical structure. TPR domains are frequently found mediating protein-protein interactions, often through a central groove. One protein complex bearing numerous TPR repeats is the Anaphase Promoting Complex (APC). The anaphase-promoting complex (APC) is a multi-subunit complex, which orchestrates mitotic cell cycles. APC is an E3 ligase in the ubiquitin cascade, and directs the 26S proteosome degradation of cell-cycle regulators. Throughout mitotic progression, proteins that are key regulators of the cell cycle are assembled with polyubiquitin chains by APC. One domain of the human APC is comprised of four related TPR proteins, APC8, APC6, APC3, and APC7, with each found in pairs. Crystal structures of some of these indicate that each has an N-terminal dimerization domain and a C-terminal domain that APC3 extends away from the dimer interface. The TPR C-terminal domains are thought to play major roles in mediating protein interactions within the APC. The subunit APC3 plays major roles in regulating APC function. Within an APC3 dimer, each C-terminal domain recruits the Ile-Arg motifs of substrate coreceptors Cdh1 (or Cdc20) and APC10. Cdh1 and APC10 together recruit substrates for ubiquitination. Therefore, it is important to understand the structure of APC3, and how APC3 mediates interactions. To address this problem, I used a novel “hybrid TPR” technology, in which some TPRs from a distant relative of APC3 are fused upstream of the C-terminal domain from human APC3. This approach enabled determination of a 3Å resolution structure encompassing the sequence of the APC3 C-terminal domain. Interestingly, only a fraction of the structure resembles canonical TPR repeats. Interpretation of the crystal structure based on published structures of complexes between TPR proteins and their partners, and on published electron microscopy structures of APC-Cdh1-APC10, reveal that the region containing the Cdh1/APC10 binding site adopts 3 canonical TPR repeats. The remainder of the portion of the structure corresponding to human APC3 is folded into an alternative conformation, in which a helix from the atypical portion of APC3 buries the Cdh1/APC10-interacting groove within the crystal. Accordingly, unlike wildtype APC3, the hybrid TPR APC3 fails to bind Cdh1 and APC10. Nonetheless, the crystal structure of “hybrid TPR APC3 C-terminal domain” allows the prediction of potentially important residues for binding to Cdh1 and APC10. Taken together, the data reveal strengths and weaknesses of hybrid TPR technology for obtaining structural insights into TPR subunits of multiprotein assemblies such as APC

ChebNet: Efficient and Stable Constructions of Deep Neural Networks with Rectified Power Units using Chebyshev Approximations

In a recent paper [B. Li, S. Tang and H. Yu, arXiv:1903.05858], it was shown that deep neural networks built with rectified power units (RePU) can give better approximation for sufficient smooth functions than those with rectified linear units, by converting polynomial approximation given in power series into deep neural networks with optimal complexity and no approximation error. However, in practice, power series are not easy to compute. In this paper, we propose a new and more stable way to construct deep RePU neural networks based on Chebyshev polynomial approximations. By using a hierarchical structure of Chebyshev polynomial approximation in frequency domain, we build efficient and stable deep neural network constructions. In theory, ChebNets and the deep RePU nets based on Power series have the same upper error bounds for general function approximations. But numerically, ChebNets are much more stable. Numerical results show that the constructed ChebNets can be further trained and obtain much better results than those obtained by training deep RePU nets constructed basing on power series.Comment: 18 pages, 6 figures, 2 table

Protocol for dissecting cascade computational components in neural networks of a visual system

Finding the complete functional circuits of neurons is a challenging problem in brain research. Here, we present a protocol, based on visual stimuli and spikes, for obtaining the complete circuit of recorded neurons using spike-triggered nonnegative matrix factorization. We describe steps for data preprocessing, inferring the spatial receptive field of the subunits, and analyzing the module matrix. This approach identifies computational components of the feedforward network of retinal ganglion cells and dissects the network structure based on natural image stimuli.For complete details on the use and execution of this protocol, please refer to Jia et al. (2021).

Final results on modeling the spectrum of ammonia 2V2 and V4 states

At this symposium in 2013, we reported our preliminary results on modeling the spectrum of ammonia 2$\nu_2$ and $\nu_4$ states (see Paper TB09 in 2013). This presentation reports the final results on our extensive experimental measurements and data analysis for the 2$\nu_2$ and $\nu_4$ inversion-rotation and vibrational transitions. We measured 159 new transition frequencies with microwave precision and assigned 1680 new ones from existing Fourier Transform spectra recorded in Synchrotron SOLEIL. The newly assigned data significantly expand the range of assigned quantum numbers. Combined with all the previously published high-resolution data, the 2$\nu_2$ and $\nu_4$ states are reproduced to 1.3$\sigma$ using a global model. We will discuss the types of transitions included in our global analysis, and fit statistics for date sets from individual experimental work

Coupling of large amplitude inversion with other states

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward

High-resolution laboratory spectroscopy of transient metal-containing molecules

Ten gaseous transient metal-containing molecules have been synthesized and studied by high resolution spectroscopy. Transient molecules are molecules with a short lifetime, and they play an important role in chemistry because they are reaction intermediates. One of the difficulties faced in studying transient molecules is their typically low concentrations under laboratory conditions. Three types of sources were used to generate these molecules: 1) an emission source that combines a high temperature furnace with an electrical discharge was used to generate SbH, SbD, TeH, TeD, CdH2, CdD2, HZnCl and BeF2; 2) a King furnace (carbon tube furnace) was used to synthesize CoS; 3) a Broida-type oven (metal flow reactor) was used to generate SrOD. Two spectroscopic techniques were employed to study these molecules: 1) Fourier transform infrared emission spectroscopy was used to study SbH, SbD, TeH, TeD, CdH2, CdD2, HZnCl, BeF2, and CoS. 2) Laser-induced fluorescence spectroscopy was employed to study SrOD. One or two lasers were used to excite the SrOD molecules from the ground state to excited electronic states and then these SrOD molecules relaxed back to the ground state by emitting fluorescence, which was detected by a photomultiplier tube. Significantly-improved spectroscopic constants have been obtained for SbH, SbD, TeH and TeD. For SbH and SbD, the infrared X 3– vibration-rotation bands and the near infrared b 1+ – X 3– transition were observed and rotationally analyzed, and a Hund’s case (a) fit was performed for each of the four observed SbH isotopologues. For TeH and TeD, the X 23/2 vibration-rotation bands and the near infrared X 21/2– X 23/2 transition have been observed and rotationally analyzed, and Hund’s case (a) and case (c) fits were performed for each of the ten observed TeH isotopologues. New spectroscopic constants were obtained for HZnCl, CdH2 and CdD2. These three molecules have been successfully generated in the gas phase for the first time. The fundamental band and one hot band were obtained for the H–Zn stretching mode (1) and for the antisymmetric stretching mode (3) of CdH2 and CdD2. A least-squares fit was performed for each of the four observed HZnCl isotopologues and the twelve observed CdH2 isotopologues For the first time, a complete set of molecular constants for all three vibrational frequencies was experimentally determined for BeF2. Thirteen new hot bands were rotationally analyzed and the 1, 2, and3 vibrational frequencies were directly determined by fitting nineteen bands together. The traditional equilibrium vibrational and rotational constants were obtained for BeF2 by simultaneously fitting the observed vibrational term values and B rotational constants. New spectroscopic constants were obtained for two electronic states of CoS and SrOD, respectively. The A 4i – X 4i and B 4i – X 4i transitions of CoS and the and transitions of SrOD were observed for the first time. Hund’s case (c) fits were performed for the CoS transitions and Hund’s case (a) fits were performed for the SrOD transitions