Resolving Structure and Mechanical Properties at the Nanoscale of Viruses with Frequency Modulation Atomic Force Microscopy

Structural Biology (SB) techniques are particularly successful in solving virus structures. Taking advantage of the symmetries, a heavy averaging on the data of a large number of specimens, results in an accurate determination of the structure of the sample. However, these techniques do not provide true single molecule information of viruses in physiological conditions. To answer many fundamental questions about the quickly expanding physical virology it is important to develop techniques with the capability to reach nanometer scale resolution on both structure and physical properties of individual molecules in physiological conditions. Atomic force microscopy (AFM) fulfills these requirements providing images of individual virus particles under physiological conditions, along with the characterization of a variety of properties including local adhesion and elasticity. Using conventional AFM modes is easy to obtain molecular resolved images on flat samples, such as the purple membrane, or large viruses as the Giant Mimivirus. On the contrary, small virus particles (25–50 nm) cannot be easily imaged. In this work we present Frequency Modulation atomic force microscopy (FM-AFM) working in physiological conditions as an accurate and powerful technique to study virus particles. Our interpretation of the so called “dissipation channel” in terms of mechanical properties allows us to provide maps where the local stiffness of the virus particles are resolved with nanometer resolution. FM-AFM can be considered as a non invasive technique since, as we demonstrate in our experiments, we are able to sense forces down to 20 pN. The methodology reported here is of general interest since it can be applied to a large number of biological samples. In particular, the importance of mechanical interactions is a hot topic in different aspects of biotechnology ranging from protein folding to stem cells differentiation where conventional AFM modes are already being used

Nonlinear dynamics of the atomic force microscope at the liquid-solid interface

The measurement of intermolecular forces at the liquid-solid interface is key to many studies of electrochemistry, wetting, catalysis, biochemistry, and mechanobiology. The atomic force microscope (AFM) is unique in its ability to measure and map these forces with nanometer resolution using the oscillating sharp tip of an AFM cantilever. These surface forces are only measured by observing the changes they induce in the dynamics of the resonant AFM probe. However, AFM cantilever dynamics at this interface can be significantly different when compared to air/vacuum environments due to the nature of nanoscale forces at the interface and the low-quality factors in liquids. In this work, we study the nonlinear dynamics of magnetically excited AFM microcantilevers on graphite and mica immersed in deionized water, high-concentration buffers, and methanol. By combining theory and experiments, a wealth of nonlinear dynamical phenomena such as superharmonic resonance, hysteretic jumps, and multimodal interactions are demonstrated and their dependence on hydration/solvation forces is clarified. These results are expected to aid ongoing efforts to link liquid-solid interface properties to cantilever dynamics and lead to accurate interpretation of data from experiments

Microcantilever dynamics in liquid environment dynamic atomic force microscopy when using higher-order cantilever eigenmodes

Dynamic atomic force microscopy is currently evolving from a single to a multifrequency instrument for nanoscale imaging often employing higher-order microcantilever eigenmodes for improved resolution and force spectroscopy. In this work the authors study the fundamentals of cantilever dynamics and energy dissipation when soft cantilevers are driven at their second flexural eigenmode and interact with samples in liquid environments. Contrary to the conventional first eigenmode operation, second eigenmode operation in liquids is often dominated by a subharmonic response (e.g., one tap every four drive cycles) and there is an energy transfer to the first eigenmode creating a new channel of energy dissipation and compositional contrast

On eigenmodes, stiffness, and sensitivity of atomic force microscope cantilevers in air versus liquids

The effect of hydrodynamic loading on the eigenmode shapes, modal stiffnesses, and optical lever sensitivities of atomic force microscope (AFM) microcantilevers is investigated by measuring the vibrations of such microcantilevers in air and water using a scanning laser Doppler vibrometer. It is found that for rectangular tipless microcantilevers, the measured fundamental and higher eigenmodes and their equivalent stiffnesses are nearly identical in air and in water. However, for microcantilevers with a tip mass or for picket shaped cantilevers, there is a marked difference in the second (and higher) eigenmode shapes between air and water that leads to a large decrease in their modal stiffness in water as compared to air as well as a decrease in their optical lever sensitivity. These results are explained in terms of hydrodynamic interactions of microcantilevers with nonuniform mass distribution. The results clearly demonstrate that tip mass and hydrodynamic loading must be taken into account in stiffness calibration and optical lever sensitivity calibration while using higher-order eigenmodes in dynamic AFM

Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator

Dynamic atomic force microscopy (dAFM) continues to grow in popularity among scientists in many different fields, and research on new methods and operating modes continues to expand the resolution, capabilities, and types of samples that can be studied. But many promising increases in capability are accompanied by increases in complexity. Indeed, interpreting modern dAFM data can be challenging, especially on complicated material systems, or in liquid environments where the behavior is often contrary to what is known in air or vacuum environments. Mathematical simulations have proven to be an effective tool in providing physical insight into these non-intuitive systems. In this article we describe recent developments in the VEDA (virtual environment for dynamic AFM) simulator, which is a suite of freely available, open-source simulation tools that are delivered through the cloud computing cyber-infrastructure of nanoHUB (www.nanohub.org). Here we describe three major developments. First, simulations in liquid environments are improved by enhancements in the modeling of cantilever dynamics, excitation methods, and solvation shell forces. Second, VEDA is now able to simulate many new advanced modes of operation (bimodal, phase-modulation, frequency-modulation, etc.). Finally, nineteen different tip-sample models are available to simulate the surface physics of a wide variety different material systems including capillary, specific adhesion, van der Waals, electrostatic, viscoelasticity, and hydration forces. These features are demonstrated through example simulations and validated against experimental data, in order to provide insight into practical problems in dynamic AFM. (C) 2012 American Institute of Physics. [doi:10.1063/1.3669638

Non-linear dynamics, fluid-structure interactions, and vibrations of microcantilevers in air and liquids

Micro- and nano-scale technologies are enabling scientists to visualize, sense, and measure the world at scales not possible just a few decades ago. In particular, the atomic force microscope (AFM) uses microscale cantilevers for imaging and force sensing down to molecular or even atomic resolution. A distinguishing feature of AFM is its ability to operate in liquid environments. This makes it a key instrument in microbiology and biophysics because of its ability to measure biological samples in their native environment - aqueous solutions. Further, it can be used to study solid-liquid interfaces at nanometer resolution and make electrochemical measurements in situ. Yet, operation of AFM in liquid environments is significantly more complicated than operation in air or vacuum. The dynamics of the microcantilever probe are strongly affected by non-linear surface forces and hydrodynamic loading. Herein, we examine several topics related to fluid-structure interactions and non-linear dynamics of AFM cantilevers in liquids. These results will allow researchers to better interpret experimental data, and design hardware that is suited to exploit the unique dynamics in liquid environments

Structured Vibration Modes of General Compound Planetary Gear Systems”,

ABSTRACT This paper extends previous analytical models of simple, singlestage planetary gears to compound, multi-stage planetary gears. This model is then used to investigate the structured vibration mode and natural frequency properties of compound planetary gears of general description, including those with equally-spaced planets and diametrically opposed planet pairs. The well-defined cyclic structure of simple, single-stage planetary gears is shown to be preserved in compound, multi-stage planetary gears. The vibration modes are classified into rotational, translational, and planet modes and the unique properties of each type are examined and proved for general compound planetary gears. All vibration modes fall into one of these three categories. For most cases, both the properties of the modes and the modes themselves are shown to be insensitive to relative planet positions between stages of a multi-stage system

Quantitative force and dissipation measurements in liquids using piezo-excited atomic force microscopy: a unifying theory

The use of a piezoelectric element (acoustic excitation) to vibrate the base of microcantilevers is a popular method for dynamic atomic force microscopy. In air or vacuum, the base motion is so small (relative to tip motion) that it can be neglected. However, in liquid environments the base motion can be large and cannot be neglected. Yet it cannot be directly observed in most AFMs. Therefore, in liquids, quantitative force and energy dissipation spectroscopy with acoustic AFM relies on theoretical formulae and models to estimate the magnitude of the base motion. However, such formulae can be inaccurate due to several effects. For example, a significant component of the piezo excitation does not mechanically excite the cantilever but rather transmits acoustic waves through the surrounding liquid, which in turn indirectly excites the cantilever. Moreover, resonances of the piezo, chip and holder can obscure the true cantilever dynamics even in well-designed liquid cells. Although some groups have tried to overcome these limitations (either by theory modification or better design of piezos and liquid cells), it is generally accepted that acoustic excitation is unsuitable for quantitative force and dissipation spectroscopy in liquids. In this paper the authors present a careful study of the base motion and excitation forces and propose a method by which quantitative analysis is in fact possible, thus opening this popular method for quantitative force and dissipation spectroscopy using dynamic AFM in liquids. This method is validated by experiments in water on mica using a scanning laser Doppler vibrometer, which can measure the actual base motion. Finally, the method is demonstrated by using small-amplitude dynamic AFM to extract the force gradients and dissipation on solvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica

High efficiency laser photothermal excitation of microcantilever vibrations in air and liquids

Photothermal excitation is a promising means of actuating microscale structures. It is gaining increased interest for its capability to excite atomic force microscopy (AFM) microcantilevers with wide frequency bandwidth in liquid environments yielding clean resonance peaks without spurious resonances. These capabilities are particularly relevant for high speed and high resolution, quantitative AFM. However, photothermal efficiency is low, which means a large amount of laser power is required for a given mechanical response. The high laser power may cause local heating effects, or spill over the cantilever and damage sensitive samples. In this work, it is shown that by simply changing from a probe with a rectangular cross-section to one with a trapezoidal cross-section, the photothermal efficiency of an uncoated silicon cantilever can be increased by more than a order of magnitude, and the efficiency of a coated cantilever can be increased by a factor of 2. This effect is demonstrated experimentally and explained theoretically using thermomechanical analysis. Results are shown for both air and water, and for normal bending and torsional oscillations

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

One of the key goals in atomic force microscopy (AFM) imaging is to enhance material property contrast with high resolution. Bimodal AFM, where two eigenmodes are simultaneously excited, confers significant advantages over conventional single-frequency tapping mode AFM due to its ability to provide contrast between regions with different material properties under gentle imaging conditions. Bimodal AFM traditionally uses the first two eigenmodes of the AFM cantilever. In this work, the authors explore the use of higher eigenmodes in bimodal AFM (e.g., exciting the first and fourth eigenmodes). It is found that such operation leads to interesting contrast reversals compared to traditional bimodal AFM. A series of experiments and numerical simulations shows that the primary cause of the contrast reversals is not the choice of eigenmode itself (e.g., second versus fourth), but rather the relative kinetic energy between the higher eigenmode and the first eigenmode. This leads to the identification of three distinct imaging regimes in bimodal AFM. This result, which is applicable even to traditional bimodal AFM, should allow researchers to choose cantilever and operating parameters in a more rational manner in order to optimize resolution and contrast during nanoscale imaging of materials