Atomic force microscopy (AFM) is a method that provides the nanometer-resolution three-dimensional imaging of living cells in their native state in their natural physiological environment. AFM is a versatile tool for the high-resolution three-dimensional imaging, nanomechanical characterization and measurement of inter- and intramolecular forces in living and non-living structures. The AFM probe, which has a nm-sized tip, measures the interatomic forces between the sample surface and the tip apex. Sample preparation for AFM measurements is simple, and there is no need for the freezing, metal coating or staining of the sample. As a result, there is little-to-no damage to the sample, and the functions of biological systems can be preserved. AFM works in both air and liquids; so, physiological buffers and growth media can be used to study living cells. The high resolution of AFM allows the imaging of atoms on hard surfaces and molecules on soft biological samples.
Atomic force microscopy is a type of scanning probe microscopy (SPM) and is one of the most commonly used ones. For the invention of the scanning tunneling microscope, the first type of SPM technique to be invented, Gerd Binnig and Heinrich Rohrer won the Nobel Prize in Physics and showed that it could be used to image single atoms 
. This was followed by the invention of a variety of other scanning probe techniques, including AFM. AFM’s basic principle is based on the scanning of a sharp tip over a sample’s surface 
. AFM not only provides three-dimensional topographic images of surfaces with nanometer to angstrom resolution, but it can also be used to study the forces between single molecules and the physical and mechanical properties of samples. The concept on which all scanning probe microscopes are based is to scan a probe above a sample surface, while monitoring the interaction between the probe and the surface. An AFM uses probe consisting of a nm-sized tip attached to the end of a flexible cantilever, and a laser light focused on the back of the cantilever is used to monitor the deflection of the cantilever through a four-quadrant photodiode detector (Figure 1
). An XYZ scanner, usually made of piezoelectric material, raster scans the sample versus the tip in a line-by-line manner, while trying to keep the same distance between the tip and the sample 
. The resulting three-dimensional topographic image is quantitative along all axes. Besides measuring topography, AFM can also be used to assess the sample’s properties, such as elasticity, viscoelasticity, adhesion and hydrophobicity. To perform these measurements, force–distance curves are acquired while the tip is pushed towards the sample, and then retracted back. The force–distance curves collected during this measurement can provide spatially resolved maps of the surface properties of the sample 
Figure 1. Schematic presentation of atomic force microscope.
There are three major imaging modes in AFM: contact, intermittent contact and non-contact. In contact mode, the AFM tip is in continuous contact with the sample surface, while the probe raster scans the surface, and the interaction forces between the tip and the sample is repulsive. There are two modes of imaging in contact mode: constant force and constant height mode. In constant force mode, the tip height is continually adjusted using a piezoelectric scanner to maintain a specified deflection (force), while in constant height mode, the height of the scanner is constant, and deflection is monitored. During contact-mode imaging, the applied force and the frictional force can damage soft biological samples, and thus, the force must be carefully controlled. In intermittent contact mode (also called AC mode or tapping mode), the cantilever is oscillated by a few nm, and the probe lightly touches the sample. The forces between the tip and the sample induce changes in the resonant behavior of the cantilever, and obtained images are based on frequency, phase shifts and amplitude changes. The intermittent contact mode reduces the contact and lateral forces between the tip and the sample, thus preserving soft biological samples 
. The third, least frequently used AFM mode of operation is non-contact (NC) mode, where the oscillating cantilever never touches the sample, and the forces between tip and the sample are attractive. In non-contact mode, a cantilever is oscillated near its resonant frequency (usually from 100 to 400 kHz), and the detection scheme, such as in the intermittent contact mode, is based on changes in the resonant frequency, phase or amplitude of the cantilever during scanning.
The high force sensitivity of AFM (down to 10−12
N) is one of its main benefits 
. This allows AFM to be used in so-called force spectroscopy mode, in which force–distance curves are generated based on the deflection of the cantilever as it moves towards and away from the sample. The force–distance curve can be further converted into a force–indentation curve, the analysis of which can provide information about the surface’s properties, such as elasticity, viscoelasticity, adhesion and hydrophobicity. This type of force mapping can be conducted at multiple locations on the (x, y) plane to obtain spatially resolved maps of properties and interactions 
AFM force spectroscopy is most often used to quantify and map the elastic properties of samples (Young’s modulus). Elasticity is measured by indenting a tip into the sample and recording a force–distance (FD) curve. Different contact mechanical models can be used to derive Young’s modulus, and the oldest model developed by Hertz utilizes a spherical indenter applied to a perfectly flat, isotropic and homogeneous sample and is widely used 
. To obtain the Young’s modulus of the sample, the FD curve must be transformed into a force–indentation curve, which depicts the force required to indent a sample at a certain depth 
. The Young’s modulus of the sample can then be calculated as follows:
is Young’s modulus of the sample; ν is the Poisson’s ratio of the sample; F
is the force applied by the cantilever; r
is the radius of the cantilever tip; δ is the indentation depth. Several alternative models for measuring elasticity have been further developed, such as the Sneddon, Derjaguin–Muller–Toporov (DMT) and Johnson–Kendall–Roberts models (JKR) 
. The selection of the right model for analysis is not trivial, since most biological samples do not fully satisfy all assumptions for existing contact mechanics models.
The most widely used way to analyze cell mechanics is to obtain an apparent elastic modulus, considering that the cell is purely elastic. However, in mechanical characterization experiments on cells, it has been noticed that the mechanical properties of cells cannot be fully described as purely elastic, as confirmed by hysteresis between the approach and retract parts of the AFM force–indentation curve 
. Because cells display both elastic and viscous behaviors, they are best defined as viscoelastic 
. As a result, evaluating this viscoelastic behavior is important for understanding the complexity of cells 
. For viscoelastic characterization in the frequency domain, in the AFM setup (also known as AFM microrheology), the cantilever is oscillated with a small fixed amplitude at several frequencies, either during the indentation period or during the scanning process. The complex elastic modulus (E
)) is calculated as follows:
) is the elastic (storage) modulus; E
) is the viscous (loss) modulus; ω
is the frequency of cantilever oscillation; δ
is the indentation; ν
is the Poisson’s ratio of the sample; θ
is half-open angle of the AFM probe;
. The storage and loss moduli together form the complex elastic modulus of the material, E
). For materials that are purely elastic, the force is in phase with the input deformation, and the loss modulus (E″(ω
)) is 0, while for a purely viscous material, the induced stress is out of phase with the input deformation, and the storage modulus E
) is 0. As a result, the value of the loss tangent (loss tangent = E
)) can be utilized as an indicator of a solid-like or liquid-like behavior 
2. Methods of Sample Preparation for Microalgae
AFM sample preparation is rather simple, and there is no need for freezing or coating samples with metals or staining. The samples must, however, be strongly attached to a substrate to be able to withstand lateral forces during scanning. Biomolecules in a solution are deposited on extremely flat surfaces (typically mica or graphite) and are held to the surface using weak forces (electrostatic and/or van der Waals forces). However, the immobilization of whole cells is not so easy to achieve due to the large size of cells and their weak binding to surfaces. Various immobilization strategies have been established for studies on living microalgal cells. Glass coverslips coated with poly-L-lysine 
or with polyethylenimine (PEI) 
have been used for the imaging of live microalgal cells. Growing cells directly on a mica or glass substrate is another way to immobilize them 
. Pletikapić and co-workers 
used a direct drop deposition method, which was optimized for marine samples 
for imaging diatoms in both air and seawater. An interesting approach was presented by Gebeshuber and co-workers 
using freshwater snails that feed on algae. In this approach, different diatom species were grown on glass slides in the presence of snails, and only diatoms that produced strongest adhesive remained on the glass slide. Recently, Evans and co-workers 
used a 3D printed array to mechanically immobilize microalgal cells. Alternatively, chemical fixation can be used to facilitate the attachment of cells to the substrate; however, it can result in substantial sample denaturation. For the AFM analysis of cleaned diatom frustules, prior to AFM measurements, the organic material is removed with sulfuric acid 
or hydrogen peroxide to prevent silicified frustules from dissolving in strong acids 
. Cleaned diatoms are then transferred to a substrate (glass slide or mica), which is usually modified with poly-L-lysine.
3. Advantages and Limitations of AFM
The main advantage of AFM over traditionally used SEM to study microalgae is that AFM allows the study of living microalgal cells in their natural physiological environment. This is because sample preparation for AFM does not involve the drying, metal coating or staining of the sample, which potentially alters the properties of the sample. In addition, AFM can be conducted in both air and liquids, allowing the imaging of microalgal cells in their growth medium. The resulting topographic AFM images of the sample are three-dimensional, while SEM provides two-dimensional images. Further, AFM can resolve very small differences in height on the cell surface due to its high vertical resolution. Besides imaging, AFM can also provide information about various surface properties, including mechanical properties, such as elasticity and viscoelasticity, and also, hydrophobicity and adhesion, which cannot be assessed via electron microscopy. Despite the great potential of AFM in the study of microalgae, there are also some limitations. The maximum scanning area of an AFM image can be a disadvantage of AFM, since AFM can only be used to scan a maximum area (XY) of about 100 µm × 100 µm and a maximum height in the order of 10–20 µm. SEM, however, can image an area in the order of mm2, with a depth of field in the order of millimeters. Therefore, it is not possible to image the entire cell if the microalgal cells are larger than the maximum scan area and higher than the maximum vertical range of the AFM instrument used. However, different parts of those larger cells can be imaged via AFM. Another limitation of standard AFM is the low speed of AFM measurement, which leads to a low temporal resolution, as standard AFM instruments require several minutes for a typical scan. Therefore, it is difficult to follow fast dynamic processes, while SEM is able to scan in near real time. However, this can be bridged by using a high-speed AFM that can even image surfaces at video rates. Overall, SEM and AFM can complement each other very well and can provide a wealth of information about a sample.