Nondegenerate Parametric Resonance in Large Ensembles of Coupled Micromechanical Cantilevers with Varying Natural Frequencies.

We investigate the collective dynamics and nondegenerate parametric resonance (NPR) of coplanar, interdigitated arrays of microcantilevers distinguished by their cantilevers having linearly expanding lengths and thus varying natural frequencies. Within a certain excitation frequency range, the resonators begin oscillating via NPR across the entire array consisting of 200 single-crystal silicon cantilevers. Tunable coupling generated from fringing electrostatic fields provides a mechanism to vary the scope of the NPR. Our experimental results are supported by a reduced-order model that reproduces the leading features of our data including the NPR band. The potential for tailoring the coupled response of suspended mechanical structures using NPR presents new possibilities in mass, force, and energy sensing applications, energy harvesting devices, and optomechanical systems.

Actuation of higher harmonics in large arrays of micromechanical cantilevers for expanded resonant peak separation.

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced order model is used for numerical investigation of the array's dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the 3rd harmonic. Distinct resonant peak separation, coupled with the spatially-confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant based sensing applications.

Single-molecule analysis of combinatorial epigenomic states in normal and tumor cells.

Proper placement of epigenetic marks on DNA and histones is fundamental to normal development, and perturbations contribute to a variety of disease states. Combinations of marks act together to control gene expression; therefore, detecting their colocalization is important, but because of technical challenges, such measurements are rarely reported. Instead, measurements of epigenetic marks are typically performed one at a time in a population of cells, and their colocalization is inferred by association. Here, we describe a single-molecule analytical approach that can perform direct detection of multiple epigenetic marks simultaneously and use it to identify mechanisms coordinating placement of three gene silencing marks, trimethylated histone H3 lysine 9, lysine 27 (H3K9me3, H3K27me3), and cytosine methylation (mC), in the normal and cancer genome. We show that H3K9me3 and mC are present together on individual chromatin fragments in mouse embryonic stem cells and that half of the H3K9me3 marks require mC for their placement. In contrast, mC and H3K27me3 coincidence is rare, and in fact, mC antagonizes H3K27me3 in both embryonic stem cells and primary mouse fibroblasts, indicating this antagonism is shared among primary cells. However, upon immortalization or tumorigenic transformation of mouse fibroblasts, mC is required for complete H3K27me3 placement. Importantly, in human promyelocytic cells, H3K27me3 is also dependent on mC. Because aberrant placement of gene silencing marks at tumor suppressor genes contributes to tumor progression, the improper dependency of H3K27me3 by mC in immortalized cells is likely to be fundamental to cancer. Our platform can enable other studies involving coordination of epigenetic marks and leverage efforts to discover disease biomarkers and epigenome-modifying drugs.

The Nanolithography Toolbox.

This article introduces in archival form the Nanolithography Toolbox, a platform-independent software package for scripted lithography pattern layout generation. The Center for Nanoscale Science and Technology (CNST) at the National Institute of Standards and Technology (NIST) developed the Nanolithography Toolbox to help users of the CNST NanoFab design devices with complex curves and aggressive critical dimensions. Using parameterized shapes as building blocks, the Nanolithography Toolbox allows users to rapidly design and layout nanoscale devices of arbitrary complexity through scripting and programming. The Toolbox offers many parameterized shapes, including structure libraries for micro- and nanoelectromechanical systems (MEMS and NEMS) and nanophotonic devices. Furthermore, the Toolbox allows users to precisely define the number of vertices for each shape or create vectorized shapes using Bezier curves. Parameterized control allows users to design smooth curves with complex shapes. The Toolbox is applicable to a broad range of design tasks in the fabrication of microscale and nanoscale devices.

Absolute Deflection Measurements in a Micro- and Nano-Electromechanical Fabry-Perot Interferometry System.

Fabry-Perot laser interferometry is a common laboratory technique used to interrogate resonant micro- and nano-electromechanical systems (MEMS/NEMS). This method uses the substrate beneath a vibrating MEMS/NEMS device as a static reference mirror, encoding relative device motion in the reflected laser power. In this work, we present a general approach for calibrating these optical systems based on measurements of large-amplitude motion that exceeds one half of the laser wavelength. Utilizing the intrinsic nonlinearity of the optical transduction, our method enables the direct measurement of the system's transfer function (motion-to-detected-voltage). We experimentally demonstrate the use of this technique to measure vibration amplitudes and changes in the equilibrium position of a MEMS/NEMS device using monolithic silicon nitride and silicon cantilevers as sample systems. By scanning the laser along a cantilever surface, we spatially map static and dynamic deflection profiles simultaneously, and then compare the static profile against results from a commercial optical profilometer. We further demonstrate extension of our calibration technique to measurements taken at small amplitudes, where the optical transduction is linear, and to those taken in the frequency domain by a lock-in amplifier. Our aim is to present a robust calibration scheme that is independent of MEMS/NEMS materials and geometry, to completely negate the effects of nonlinear optical transduction, and to enable the assessment of excitation forces and MEMS/NEMS material properties through the accurate measurement of the MEMS/NEMS vibrational response.

Microfluidic extraction, stretching and analysis of human chromosomal DNA from single cells.

We describe a microfluidic device for the extraction, purification and stretching of human chromosomal DNA from single cells. A two-dimensional array of micropillars in a microfluidic polydimethylsiloxane channel was designed to capture a single human cell. Megabase-long DNA strands released from the cell upon lysis are trapped in the micropillar array and stretched under optimal hydrodynamic flow conditions. Intact chromosomal DNA is entangled in the array, while other cellular components are washed from the channel. To demonstrate the entrapment principle, a single chromosome was hybridized to whole chromosome paints, and imaged by fluorescence microscopy. DNA extracted from a single cell and small cell populations (less than 100) was released from the device by restriction endonuclease digestion under continuous flow and collected for off-chip analysis. Quantification of the extracted material reveals that the microdevice efficiently extracts essentially all chromosomal DNA. The device described represents a novel platform to perform a variety of analyses on chromosomal DNA at the single cell level.