A strategy combining denoising and cryo-EM single particle analysis

In cryogenic electron microscopy (cryo-EM) single particle analysis (SPA), high-resolution three-dimensional structures of biological macromolecules are determined by iteratively aligning and averaging a large number of two-dimensional projections of molecules. Since the correlation measures are sensitive to the signal-to-noise ratio, various parameter estimation steps in SPA will be disturbed by the high-intensity noise in cryo-EM. However, denoising algorithms tend to damage high frequencies and suppress mid- and high-frequency contrast of micrographs, which exactly the precise parameter estimation relies on, therefore, limiting their application in SPA. In this study, we suggest combining a cryo-EM image processing pipeline with denoising and maximizing the signal's contribution in various parameter estimation steps. To solve the inherent flaws of denoising algorithms, we design an algorithm named MScale to correct the amplitude distortion caused by denoising and propose a new orientation determination strategy to compensate for the high-frequency loss. In the experiments on several real datasets, the denoised particles are successfully applied in the class assignment estimation and orientation determination tasks, ultimately enhancing the quality of biomacromolecule reconstruction. The case study on classification indicates that our strategy not only improves the resolution of difficult classes (up to 5 Å) but also resolves an additional class. In the case study on orientation determination, our strategy improves the resolution of the final reconstructed density map by 0.34 Å compared with conventional strategy. The code is available at https://github.com/zhanghui186/Mscale.

Disentangling the Orientations of Spectrally Overlapping Transition Dipoles in Dense Dye Layers

The transition dipole orientations of dye assemblies in heterostructures have a crucial impact on the efficiency of novel optoelectronic devices such as organic thin-film transistors and light-emitting diodes. These devices are frequently based on heterojunctions and tandem structures featuring multiple optical transitions. Precise knowledge of preferred orientations, spatial order, and spatial variations is highly relevant. We present a fast and universal large-area screening method to determine the transition dipole orientations in dye assemblies with diffraction-limited spatial resolution. Moreover, our hyperspectral imaging approach disentangles the orientations of different chromophores. As a demonstration, we apply our technique to dye monolayers with two optical transitions sandwiched between two ultrathin silicate nanosheets. A comprehensive model for dipole orientation distributions in monolayers reveals a long-range orientational order and a strong correlation between the two transitions.

Rapid Estimation of Membrane Protein Orientation in Liposomes

The topological organization of proteins embedded in biological membranes is crucial for the tight interplay between these enzymes and their accessibility to substrates in order to fulfil enzymatic activity. The orientation of a membrane protein reconstituted in artificial membranes depends on many parameters and is hardly predictable. Here, we present a convenient approach to assess this important property independent of the enzymatic activity of the reconstituted protein. Based on cysteine‐specific chemical modification of a target membrane protein with a cyanine fluorophore and a corresponding membrane‐impermeable fluorescence quencher, the novel strategy allows rapid evaluation of the distribution of the two orientations after reconstitution. The assay has been tested for the respiratory complexes bo₃ oxidase and ATP synthase of Escherichia coli and the results agree well with other orientation determination approaches. Given the simple procedure, the proposed method is a powerful tool for optimization of reconstitution conditions or quantitative orientation information prior to functional measurements.

Methods for Assessing and Optimizing Solar Orientation by Non-Planar Sensor Arrays

Non-planar sensor arrays are used to determine solar orientation based on the orientation matrix formed by orientation vectors of the sensor planes. Solar panels or existing photodiodes can be directly used without increasing the size or mass of the spacecraft. However, a limiting factor for the improvement of the accuracy of orientation lies with the lack of an assessment-based approach. A formulation was developed for the supremum (i.e., the least upper bound) of orientation error of an arbitrary orientation matrix in terms of its influencing factors. The new formulation offers a way to evaluate the supremum of orientation error considering interference with finite energy and interference with infinite energy but finite average energy. For a given non-planar sensor array, a sub-matrix of the full orientation matrix would reach the optimal accuracy of orientation if its supremum of orientation error is the least. Principles for designing an optimal sensor array relate to the configuration of the orientation matrix, which can be pre-determined for a given number of sensors. Simulations and field experiment tested and validated the methods, showing that our sensor array optimization method outperforms the existing methods, while providing a way of assessment and optimization.

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning (“PDR”). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model (“GMM”), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model (“GHM”). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation.

Merging single-shot XFEL diffraction data from inorganic nanoparticles: a new approach to size and orientation determination

X-ray free-electron lasers (XFELs) provide new opportunities for structure determination of biomolecules, viruses and nanomaterials. With unprecedented peak brilliance and ultra-short pulse duration, XFELs can tolerate higher X-ray doses by exploiting the femtosecond-scale exposure time, and can thus go beyond the resolution limits achieved with conventional X-ray diffraction imaging techniques. Using XFELs, it is possible to collect scattering information from single particles at high resolution, however particle heterogeneity and unknown orientations complicate data merging in three-dimensional space. Using the Linac Coherent Light Source (LCLS), synthetic inorganic nanocrystals with a core-shell architecture were used as a model system for proof-of-principle coherent diffractive single-particle imaging experiments. To deal with the heterogeneity of the core-shell particles, new computational methods have been developed to extract the particle size and orientation from the scattering data to assist data merging. The size distribution agrees with that obtained by electron microscopy and the merged data support a model with a core-shell architecture.

A Dual-Linear Kalman Filter for Real-Time Orientation Determination System Using Low-Cost MEMS Sensors

To provide a long-time reliable orientation, sensor fusion technologies are widely used to integrate available inertial sensors for the low-cost orientation estimation. In this paper, a novel dual-linear Kalman filter was designed for a multi-sensor system integrating MEMS gyros, an accelerometer, and a magnetometer. The proposed filter precludes the impacts of magnetic disturbances on the pitch and roll which the heading is subjected to. The filter can achieve robust orientation estimation for different statistical models of the sensors. The root mean square errors (RMSE) of the estimated attitude angles are reduced by 30.6% under magnetic disturbances. Owing to the reduction of system complexity achieved by smaller matrix operations, the mean total time consumption is reduced by 23.8%. Meanwhile, the separated filter offers greater flexibility for the system configuration, as it is possible to switch on or off the second stage filter to include or exclude the magnetometer compensation for the heading. Online experiments were performed on the homemade miniature orientation determination system (MODS) with the turntable. The average RMSE of estimated orientation are less than 0.4° and 1° during the static and low-dynamic tests, respectively. More realistic tests on two-wheel self-balancing vehicle driving and indoor pedestrian walking were carried out to evaluate the performance of the designed MODS when high accelerations and angular rates were introduced. Test results demonstrate that the MODS is applicable for the orientation estimation under various dynamic conditions. This paper provides a feasible alternative for low-cost orientation determination.

Real-time Imaging Orientation Determination System to Verify Imaging Polarization Navigation Algorithm

Bio-inspired imaging polarization navigation which can provide navigation information and is capable of sensing polarization information has advantages of high-precision and anti-interference over polarization navigation sensors that use photodiodes. Although all types of imaging polarimeters exist, they may not qualify for the research on the imaging polarization navigation algorithm. To verify the algorithm, a real-time imaging orientation determination system was designed and implemented. Essential calibration procedures for the type of system that contained camera parameter calibration and the inconsistency of complementary metal oxide semiconductor calibration were discussed, designed, and implemented. Calibration results were used to undistort and rectify the multi-camera system. An orientation determination experiment was conducted. The results indicated that the system could acquire and compute the polarized skylight images throughout the calibrations and resolve orientation by the algorithm to verify in real-time. An orientation determination algorithm based on image processing was tested on the system. The performance and properties of the algorithm were evaluated. The rate of the algorithm was over 1 Hz, the error was over 0.313°, and the population standard deviation was 0.148° without any data filter.

Variable-State-Dimension Kalman-based Filter for orientation determination using inertial and magnetic sensors

In this paper a quaternion-based Variable-State-Dimension Extended Kalman Filter (VSD-EKF) is developed for estimating the three-dimensional orientation of a rigid body using the measurements from an Inertial Measurement Unit (IMU) integrated with a triaxial magnetic sensor. Gyro bias and magnetic disturbances are modeled and compensated by including them in the filter state vector. The VSD-EKF switches between a quiescent EKF, where the magnetic disturbance is modeled as a first-order Gauss-Markov stochastic process (GM-1), and a higher-order EKF where extra state components are introduced to model the time-rate of change of the magnetic field as a GM-1 stochastic process, namely the magnetic disturbance is modeled as a second-order Gauss-Markov stochastic process (GM-2). Experimental validation tests show the effectiveness of the VSD-EKF, as compared to either the quiescent EKF or the higher-order EKF when they run separately.

Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation

In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system that describes the process of motion tracking by the IMU is observable, namely it may provide sufficient information for performing the estimation task with bounded estimation errors. The observability conditions are that the magnetic field, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear and that the IMU is subject to some angular motions. Computer simulations and experimental testing are presented to evaluate the algorithm performance, including when the observability conditions are critical.