Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data.

In this paper, we address the problem of imaging membrane proteins for single-particle cryo-electron microscopy reconstruction of the isolated protein structure. More precisely, we propose a method for learning and removing the interfering vesicle signals from the micrograph, prior to reconstruction. In our approach, we estimate the subspace of the vesicle structures and project the micrographs onto the orthogonal complement of this subspace. We construct a 2D statistical model of the vesicle structure, based on higher order singular value decomposition (HOSVD), by considering the structural symmetries of the vesicles in the polar coordinate plane. We then propose to lift the HOSVD model to a novel hierarchical model by summarizing the multidimensional HOSVD coefficients by their principal components. Along with the model, a solid vesicle normalization scheme and model selection criterion are proposed to make a compact and general model. The results show that the vesicle structures are accurately separated from the background by the HOSVD model that is also able to adapt to the asymmetries of the vesicles. This is a promising result and suggests even wider applicability of the proposed approach in learning and removal of statistical structures.

We present the first, fully integrated, multi-channel implementation of a patch-clamp measurement system. The system was implemented in a 0.5 μm silicon-on-sapphire process. The system can record two simultaneous cell membrane currents up to ±20 μA with a rms noise of 8 pA in a 10 kHz bandwidth. The system can compensate for the capacitance and resistance of the pipette electrode, up to 10 pF and 100 MΩ respectively. The system die size is 3 × 3 mm and the power consumption is 5 mW per channel at 3.3 V.

We present a fully-integrated implementation of a patch-clamp measurement system. The system was implemented in a 0.5mum silicon-on-sapphire process and is capable of recording cell membrane currents up to plusmn20nA, with a rms noise of 5pA at 10kHz bandwidth. The system can compensate for the capacitance and resistance of the planar electrode, up to 20pF and 4MOmega respectively. The die size is 1150 by 700mum. The power consumption is 3.3mW at 3.3V. The integrated patch- clamp system will be used to fabricate high-throughput planar patch-clamp systems.

We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.

We fabricated an integrated patch-clamp amplifier capable of recording nano-amperes of current in whole-cell patch recording. Patch-clamp amplifiers presently consist of a head-stage and a large controller box that contains many hundreds of components. Our design compresses the function of the head-stage and the controller box into one chip that can be mounted near the patch-clamp electrode and can be controlled through a high-speed serial bus paving the way for higher densities in parallel patch-clamp systems. We report on the electrical measurements from the fabricated device.

We fabricated an integrated patch-clamp amplifier capable of recording from pico- to tens of micro-amperes of current. The high-dynamic range of seven decades and the pico-ampere sensitivity of the instrument was designed for whole-cell patch-clamp recordings. The prototype was fabricated on a 0.5/spl mu/m silicon-on-sapphire process. The device employs an integrating headstage with a frequency-modulated output pulse ranging from 3Hz to 10MHz. A digital interface produces a 16bit output conversion of the input currents. We report on electrical measurements from the fabricated device, and measurements conducted on cells in a typical patch-clamp experiment.