William F. Heinz

Relative Microelastic Mapping of Living Cells by Atomic Force Microscopy

The spatial and temporal changes of the mechanical properties of living cells reflect complex underlying physiological processes. Following these changes should provide valuable insight into the biological importance of cellular mechanics and their regulation. The tip of an atomic force microscope (AFM) can be used to indent soft samples, and the force versus indentation measurement provides information about the local viscoelasticity. By collecting force-distance curves on a time scale where viscous contributions are small, the forces measured are dominated by the elastic properties of the sample. We have developed an experimental approach, using atomic force microscopy, called force integration to equal limits (FIEL) mapping, to produce robust, internally quantitative maps of relative elasticity. FIEL mapping has the advantage of essentially being independent of the tip-sample contact point and the cantilever spring constant. FIEL maps of living Madine-Darby canine kidney (MDCK) cells show that elasticity is uncoupled from topography and reveal a number of unexpected features. These results present a mode of high-resolution visualization in which the contrast is based on the mechanical properties of the sample.

Spatially resolved force spectroscopy of biological surfaces using the atomic force microscope

The spatial distribution of intermolecular forces governs macromolecular interactions. The atomic force microscope, a relatively new tool for investigating interaction forces between nanometer-scale objects, can be used to produce spatially resolved maps of the surface or material properties of a sample; these include charge density, adhesion and stiffness, as well as the force required to break specific ligand-receptor bonds. Maps such as these will provide fundamental insights into biological structure and will become an important tool for characterizing technologically important biological systems.

Relative Surface Charge Density Mapping with the Atomic Force Microscope

An experimental approach for producing relative charge density maps of biological surfaces using the atomic force microscope is presented. This approach, called D minus D (D-D) mapping, uses isoforce surfaces collected at different salt concentrations to remove topography and isolate electrostatic contributions to the tip-sample interaction force. This approach is quantitative for surface potentials below 25 mV, and does not require prior knowledge of the cantilever spring constant, tip radius, or tip charge. In addition, D-D mapping does not require tip-sample contact. The performance of D-D mapping is demonstrated on surfaces of constant charge and varying topography (mechanically roughened mica and stacked bilayers of dipalmitolphosphatidylserine), a surface of varying charge and varying topography (patches of dipalmitolphosphatidylcholine on mica), and bacteriorhopsin membranes adsorbed to mica.

Microelastic properties of lung cell-derived extracellular matrix

The mechanical properties of the extracellular microenvironment regulate cell behavior, including migration, proliferation and morphogenesis. Although the elastic moduli of synthetic materials have been studied, little is known about the properties of naturally produced extracellular matrix. Here we have utilized atomic force microscopy to characterize the microelastic properties of decellularized cell-derived matrix from human pulmonary fibroblasts. This heterogeneous three-dimensional matrix had an average thickness of 5 ± 0.4 μm and a Youngs modulus of 105 ± 14 Pa. Ascorbate treatment of the lung fibroblasts prior to extraction produced a twofold increase in collagen I content, but did not affect the stiffness of the matrices compared with matrices produced in standard medium. However, fibroblast-derived matrices that were crosslinked with glutaraldehyde demonstrated a 67% increase in stiffness. This work provides a microscale characterization of fibroblast-derived matrix mechanical properties. An accurate understanding of native three-dimensional extracellular microenvironments will be essential for controlling cell responses in tissue engineering applications.

Probing deep interaction potentials with white-noise-driven atomic force microscope cantilevers

Perturbations to the thermally driven motion of an atomic force microscope (AFM) cantilever can be used to probe tip-sample interactions. One limitation of such thermal-noise-based measurements is that they fail for large attractive interactions with force gradients that exceed the stiffness of the cantilever. In such cases, the AFM tip jumps to the surface and is trapped there for long periods of time. Here, we describe an approach to overcome this limitation by driving the AFM cantilever with white noise, essentially simulating high temperatures. Effective temperatures of several thousand Kelvin are easily obtained. We show that this approach allows the AFM tip to “thermally” sample interactions that would otherwise capture the tip.

Spatial information analysis of chemotactic trajectories.

During bacterial chemotaxis, a cell acquires information about its environment by sampling changes in the local concentration of a chemoattractant, and then uses that information to bias its motion relative to the source of the chemoattractant. The trajectory of a chemotaxing bacteria is thus a spatial manifestation of the information gathered by the cell. Here we show that a recently developed approach for computing spatial information using Fourier coefficient probabilities, the k-space information (kSI), can be used to quantify the information in such trajectories. The kSI is shown to capture expected responses to gradients of a chemoattractant. We then extend the k-space approach by developing an experimental probability distribution (EPD) that is computed from chemotactic trajectories collected under a reference condition. The EPD accounts for connectivity and other constraints that the nature of the trajectories imposes on the k-space computation. The EPD is used to compute the spatial information from any trajectory of interest, relative to the reference condition. The EPD-based spatial information also captures the expected responses to gradients of a chemoattractant, although the results differ in significant ways from the original kSI computation. In addition, the entropy calculated from the EPD provides a useful measure of trajectory space. The methods developed are highly general, and can be applied to a wide range of other trajectory types as well as non-trajectory data.

Spatial information dynamics during early zebrafish development.

During development inherited information directs growth and specifies the complex spatial organization of cells and molecules. Here we show that a new information metric, the k-space information (kSI), captures the growth and emergence of spatial organization in a developing embryo. Using zebrafish as a model, we quantify the rate of development over the first 24h and demonstrate that important developmental landmarks are associated with well-defined transitions in information dynamics. The rate of development during this time is highest immediately before and after gastrulation, as well early in the segmentation period. We also find that the majority of the information arises from spatial correlations on the length scale of 20-80 μm, but there are contributions from many length scales that change over time. A comparison of the information dynamics in the maternal-zygotic one-eyed pinhead mutant, which is defective in mesoderm induction, with the wild-type embryo shows that the information dynamics diverge near the onset of gastrulation. Subsequently the mutant lacks a peak in the information dynamics that appears to be associated with the formation of trunk somites in the wild-type embryo. These findings provide a common and objective basis by which to quantify spatial organization, compare mutants and quantify developmental dynamics. The kSI can also be applied to any form of developmental data of arbitrary dimensions, and it offers a broad conceptual framework with which to organize the large amounts of data emerging from various sources.

Computing Spatial Information from Fourier Coefficient Distributions

The spatial relationships between molecules can be quantified in terms of information. In the case of membranes, the spatial organization of molecules in a bilayer is closely related to biophysically and biologically important properties. Here, we present an approach to computing spatial information based on Fourier coefficient distributions. The Fourier transform (FT) of an image contains a complete description of the image, and the values of the FT coefficients are uniquely associated with that image. For an image where the distribution of pixels is uncorrelated, the FT coefficients are normally distributed and uncorrelated. Further, the probability distribution for the FT coefficients of such an image can readily be obtained by Parseval’s theorem. We take advantage of these properties to compute the spatial information in an image by determining the probability of each coefficient (both real and imaginary parts) in the FT, then using the Shannon formalism to calculate information. By using the probability distribution obtained from Parseval’s theorem, an effective distance from the uncorrelated or most uncertain case is obtained. The resulting quantity is an information computed in k-space (kSI). This approach provides a robust, facile and highly flexible framework for quantifying spatial information in images and other types of data (of arbitrary dimensions). The kSI metric is tested on a 2D Ising model, frequently used as a model for lipid bilayer; and the temperature-dependent phase transition is accurately determined from the spatial information in configurations of the system.

Nanometer-Scale Embossing of Polydimethylsiloxane

Microstructured polydimethylsiloxane (PDMS) is an important and widely used material in biology and chemistry. Here we report that micrometer- and nanometer-scale features can be introduced into the surface of PDMS in a process that is functionally equivalent to embossing. We show that surface features <50 nm can be replicated onto the surface of previously cured PDMS at room temperature and at low pressure. This type of embossing can be performed on samples in solution. It also allows one template to be used for many different types of microstructures by changing the embossing time or serial embossing at different alignments. The balance between elastic and plastic properties of the PDMS has the effect of high-pass filtering the features that are captured and produces a sample that is suitable for sensitive surface characterization technologies such as atomic force microscopy. These findings extend the applications of PDMS as well as open the possibility for new uses.