De Novo Protein Structure Modeling from Cryoem Data Through a Dynamic Programming Algorithm in the Secondary Structure Topology Graph

Proteins are the molecules carry out the vital functions and make more than the half of dry weight in every cell. Protein in nature folds into a unique and energetically favorable 3-Dimensional (3-D) structure which is critical and unique to its biological function. In contrast to other methods for protein structure determination, Electron Cryorricroscopy (CryoEM) is able to produce volumetric maps of proteins that are poorly soluble, large and hard to crystallize. Furthermore, it studies the proteins in their native environment. Unfortunately, the volumetric maps generated by current advances in CryoEM technique produces protein maps at medium resolution about (~5 to 10Å) in which it is hard to determine the atomic-structure of the protein. However, the resolution of the volumetric maps is improving steadily, and recent works could obtain atomic models at higher resolutions (~3Å). De novo protein modeling is the process of building the structure of the protein using its CryoEM volumetric map. Thereupon, the volumetric maps at medium resolution generated by CryoEM technique proposed a new challenge. At the medium resolution, the location and orientation of secondary structure elements (SSE) can be visually and computationally identified. However, the order and direction (called protein topology) of the SSEs detected from the CryoEM volumetric map are not visible. In order to determine the protein structure, the topology of the SSEs has to be figured out and then the backbone can be built. Consequently, the topology problem has become a bottle neck for protein modeling using CryoEM In this dissertation, we focus to establish an effective computational framework to derive the atomic structure of a protein from the medium resolution CryoEM volumetric maps. This framework includes a topology graph component to rank effectively the topologies of the SSEs and a model building component. In order to generate the small subset of candidate topologies, the problem is translated into a layered graph representation. We developed a dynamic programming algorithm (TopoDP) for the new representation to overcome the problem of large search space. Our approach shows the improved accuracy, speed and memory use when compared with existing methods. However, the generating of such set was infeasible using a brute force method. Therefore, the topology graph component effectively reduces the topological space using the geometrical features of the secondary structures through a constrained K-shortest paths method in our layered graph. The model building component involves the bending of a helix and the loop construction using skeleton of the volumetric map. The forward-backward CCD is applied to bend the helices and model the loops

Structure prediction for the helical skeletons detected from the low resolution protein density map

<p>Abstract</p> <p>Background</p> <p>The current advances in electron cryo-microscopy technique have made it possible to obtain protein density maps at about 6-10 Å resolution. Although it is hard to derive the protein chain directly from such a low resolution map, the location of the secondary structures such as helices and strands can be computationally detected. It has been demonstrated that such low-resolution map can be used during the protein structure prediction process to enhance the structure prediction.</p> <p>Results</p> <p>We have developed an approach to predict the 3-dimensional structure for the helical skeletons that can be detected from the low resolution protein density map. This approach does not require the construction of the entire chain and distinguishes the structures based on the conformation of the helices. A test with 35 low resolution density maps shows that the highest ranked structure with the correct topology can be found within the top 1% of the list ranked by the effective energy formed by the helices.</p> <p>Conclusion</p> <p>The results in this paper suggest that it is possible to eliminate the great majority of the bad conformations of the helices even without the construction of the entire chain of the protein. For many proteins, the effective contact energy formed by the secondary structures alone can distinguish a small set of likely structures from the pool.</p

Forecasting the Number of Monthly Active Facebook and Twitter Worldwide Users Using ARMA Model

In this study, an Auto-Regressive Moving Average (ARMA) Model with optimal order has been developed to estimate and forecast the short term future numbers of the monthly active Facebook and Twitter worldwide users. In order to pickup the optimal estimation order, we analyzed the model order vs. the corresponding model error in terms of final prediction error. The simulation results showed that the optimal model order to estimate the given Facebook and Twitter time series are ARMA[5, 5] and ARMA[3, 3], respectively, since they correspond to the minimum acceptable prediction error values. Besides, the optimal models recorded a high-level of estimation accuracy with fit percents of 98.8% and 96.5% for Facebook and Twitter time series, respectively. Eventually, the developed framework can be used accurately to estimate the spectrum for any linear time series

Implementing a lightweight Schmidt-Samoa cryptosystem (SSC) for sensory communications

One of the remarkable issues that face wireless sensor networks (WSNs) nowadays is security. WSNs should provide a way to transfer data securely particularly when employed for mission-critical purposes. In this paper, we propose an enhanced architecture and implementation for 128-bit Schmidt-Samoa cryptosystem (SSC) to secure the data communication for wireless sensor networks (WSN) against external attacks. The proposed SSC cryptosystem has been efficiently implemented and verified using FPGA modules by exploiting the maximum allowable parallelism of the SSC internal operations. To verify the proposed SSC implementation, we have synthesized our VHDL coding using Quartus II CAD tool targeting the Altera Cyclone IV FPGA EP4CGX22CF19C7 device. Hence, the synthesizer results reveal that the proposed cryptographic FPGA processor recorded an attractive result in terms of critical path delay, hardware utilization, maximum operational frequency FPGA thermal power dissipation for low-power applications such as the wireless sensor networks

Intensity-Based Skeletonization of CryoEM Gray-Scale Images Using a True Segmentation-Free Algorithm

Cryo-electron microscopy is an experimental technique that is able to produce 3D gray-scale images of protein molecules. In contrast to other experimental techniques, cryo-electron microscopy is capable of visualizing large molecular complexes such as viruses and ribosomes. At medium resolution, the positions of the atoms are not visible and the process cannot proceed. The medium-resolution images produced by cryo-electron microscopy are used to derive the atomic structure of the proteins in de novo modeling. The skeletons of the 3D gray-scale images are used to interpret important information that is helpful in de novo modeling. Unfortunately, not all features of the image can be captured using a single segmentation. In this paper, we present a segmentation-free approach to extract the gray-scale curve-like skeletons. The approach relies on a novel representation of the 3D image, where the image is modeled as a graph and a set of volume trees. A test containing 36 synthesized maps and one authentic map shows that our approach can improve the performance of the two tested tools used in de novo modeling. The improvements were 62 and 13 percent for Gorgon and DP-TOSS, respectively

Mathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Cα Coordinates

Determining Secondary Structure Elements (SSEs) for any protein is crucial as an intermediate step for experimental tertiary structure determination. SSEs are identified using popular tools such as DSSP and STRIDE. These tools use atomic information to locate hydrogen bonds to identify SSEs. When some spatial atomic details are missing, locating SSEs becomes a hinder. To address the problem, when some atomic information is missing, three approaches for classifying SSE types using Ca atoms in protein chains were developed: (1) a mathematical approach, (2) a deep learning approach, and (3) an ensemble of five machine learning models. The proposed methods were compared against each other and with a state-of-the-art approach, PCASSO

An Effective Computational Method Incorporating Multiple Secondary Structure Predictions in Topology Determination for Cryo-EM Images

A key idea in de novo modeling of a medium-resolution density image obtained from cryo-electron microscopy is to compute the optimal mapping between the secondary structure traces observed in the density image and those predicted on the protein sequence. When secondary structures are not determined precisely, either from the image or from the amino acid sequence of the protein, the computational problem becomes more complex. We present an efficient method that addresses the secondary structure placement problem in presence of multiple secondary structure predictions and computes the optimal mapping. We tested the method using 12 simulated images from alpha-proteins and two Cryo-EM images of α-β proteins. We observed that the rank of the true topologies is consistently improved by using multiple secondary structure predictions instead of a single prediction. The results show that the algorithm is robust and works well even when errors/ misses in the predicted secondary structures are present in the image or the sequence. The results also show that the algorithm is efficient and is able to handle proteins with as many as 33 helices

Estimating loop length from CryoEM images at medium resolutions

Background: De novo protein modeling approaches utilize 3-dimensional (3D) images derived from electron cryomicroscopy (CryoEM) experiments. The skeleton connecting two secondary structures such as α-helices represent the loop in the 3D image. The accuracy of the skeleton and of the detected secondary structures are critical in De novo modeling. It is important to measure the length along the skeleton accurately since the length can be used as a constraint in modeling the protein. Results: We have developed a novel computational geometric approach to derive a simplified curve in order to estimate the loop length along the skeleton. The method was tested using fifty simulated density images of helix-loop-helix segments of atomic structures and eighteen experimentally derived density data from Electron Microscopy Data Bank (EMDB). The test using simulated density maps shows that it is possible to estimate within 0.5 angstrom of the expected length for 48 of the 50 cases. The experiments, involving eighteen experimentally derived CryoEM images, show that twelve cases have error within 2 angstrom. Conclusions:The tests using both simulated and experimentally derived images show that it is possible for our proposed method to estimate the loop length along the skeleton if the secondary structure elements, such as α-helices, can be detected accurately, and there is a continuous skeleton linking the α-helices

Estimating Loop Length from CryoEM Images at Medium Resolutions

Background: De novo protein modeling approaches utilize 3-dimensional (3D) images derived from electron cryomicroscopy (CryoEM) experiments. The skeleton connecting two secondary structures such as α-helices represent the loop in the 3D image. The accuracy of the skeleton and of the detected secondary structures are critical in De novo modeling. It is important to measure the length along the skeleton accurately since the length can be used as a constraint in modeling the protein. Results: We have developed a novel computational geometric approach to derive a simplified curve in order to estimate the loop length along the skeleton. The method was tested using fifty simulated density images of helix-loop-helix segments of atomic structures and eighteen experimentally derived density data from Electron Microscopy Data Bank (EMDB). The test using simulated density maps shows that it is possible to estimate within 0.5 angstrom of the expected length for 48 of the 50 cases. The experiments, involving eighteen experimentally derived CryoEM images, show that twelve cases have error within 2 angstrom. Conclusions:The tests using both simulated and experimentally derived images show that it is possible for our proposed method to estimate the loop length along the skeleton if the secondary structure elements, such as α-helices, can be detected accurately, and there is a continuous skeleton linking the α-helices