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DOI: https://doi.org/10.22184/1993-8578.2025.18.3-4.204.210
Force curves in atomic force microscopy (AFM) display the interaction between a cantilever and a sample. These curves are essential for understanding various material properties and interactions at the nanoscale, for studying elasticity, stiffness, and adhesive properties of biological samples. Force curves are used to study molecular interactions such as bond breaking and polymer stretching. Force mapping or volumetric maps of the distribution of force curves help reconstruct the spatial distribution of mechanical properties.
Force curves in atomic force microscopy (AFM) display the interaction between a cantilever and a sample. These curves are essential for understanding various material properties and interactions at the nanoscale, for studying elasticity, stiffness, and adhesive properties of biological samples. Force curves are used to study molecular interactions such as bond breaking and polymer stretching. Force mapping or volumetric maps of the distribution of force curves help reconstruct the spatial distribution of mechanical properties.
Теги: atomic force microscopy biomechanics force curves mechanical properties. scanning probe microscopy атомно-силовая микроскопия биомеханика механические свойства силовые кривые сканирующая зондовая микроскопия
INTRODUCTION
Force curves provide valuable information on local material properties such as elasticity, hardness, adhesion and surface charge density. For this reason, the force measurement curves has become essential in materials science and biology. Another application is to analyse surface forces per se to answer the question: what are the interactions between particles in a fluid? How can dispersion be stabilised? How do surfaces in general and particles in particular adhere to each other [1]?
Force curves are widely used in nanotechnology, biology, materials science and other fields for quantitative analysis of local properties of objects and materials.
Characterisation of biomechanical properties of tissues with high spatial resolution provides valuable information on a wide range of developmental, homeostasis and pathological processes in living organisms. The biomechanical properties of the basal membrane, a substructure of the extracellular matrix as small as ∼100–400 nm across, among others, are crucial for tumour progression and metastasis formation. Although the exact assignment of Young’s modulus E of such a delicate substructure of the extracellular matrix, especially between two cell layers, is still a challenge, biomechanical data of the basal membrane can provide information with outstanding diagnostic potential [2].
In a study [3], atomic force microscopy (AFM) was used to measure changes in the stiffness of human multipotent mesenchymal stromal stem cells cultured in a Petri dish and on polyacrylamide substrates during osteogenic differentiation. The results showed that the Young’s modulus of the cytoplasmic outer region of the cells increased with time during osteogenesis. There is a strong linear correlation between the time of osteogenic induction and Young’s modulus of cells cultured in rigid Petri dishes, Young’s modulus approaching a plateau after day 15.
RESEARCH METHODS
Force curves in AFM reflect the distance dependence of the interaction force between the probe and the sample. For their quantitative analysis, different theoretical models describing different types of interactions are used. In the area of mechanical contact between the probe and the sample, repulsive forces described by contact mechanics models prevail [4].
The power curve usually consists of two branches:
approach curve – the probe is approaching the surface, red line in Fig.1;
retract curve – the probe is moving away from the surface, green line in Fig.1.
In the graph, the distance (Z-position of the scanner) is plotted on the X-axis and the force (or cantilever deflection) is plotted on the Y-axis [5].
Characteristic sections of the power curve:
Non-interacting region – the probe is far from the surface, the forces are negligible;
When the probe approaches, attraction forces (van der Waals forces, capillary, electrostatic, steric forces, etc.) arise;
Contact region – repulsive forces (elastic and plastic deformations) predominate. When the magnitude of the attraction force becomes greater than the sum of the repulsive forces and the elastic resistance of the cantilever, the probe is pushed into the sample (C);
Adhesion Peak (on the green lead line) – "sticking" due to adhesion forces may be observed when the probe is removed.
A high adhesion peak characterises a strong "sticking" of the cantilever to the sample surface (e.g. due to capillary forces in humid air).
The slope in the contact region reflects stiffness of the specimen. When working with a soft specimen, the force curve in the same coordinates will look more hollow. Hysteresis between approach and departure – may indicate plastic deformation or viscoelastic properties.
The following algorithm is used to obtain information on mechanical properties. Force curves are measured at different points of the surface. A data array is obtained, for example, 128 × 128 inlet and outlet curves. Then, from the analysis of each force curve, images corresponding to adhesion, stiffness and deformation distribution maps of the surface are obtained. To display the entire data set, a 4-dimensional mapping has to be used: three XYZ coordinates and colour gradations are used to construct adhesion, stiffness and deformation maps (Fig.2).
MATERIALS AND METHODS
The method we developed was applied to analyse the effect of heating on tobacco mosaic virus. Tobacco mosaic virus after 5 min of heating at 90 °C was considered as a sample.
The virus was applied on a mica substrate, and force curves were measured with an NP-S10 cantilever in Force Mapping mode on a Nanoscope-3A atomic force microscope (Digital Instruments, USA).
The force curves were taken at a resolution of 32 × 32 points. Fig.3 shows two types of data display – topography on the top left and force curves display on the right. Characteristic size of the formed particles: 0.5–1.2 μm. When selecting force curves for Young’s modulus estimation on the substrate it is important to pay attention to the adhesion peak, on a clean substrate the cantilever will not stick because the adhesion peak is significantly smaller than for a viral particle.
Using "FemtoScan Online" software it is possible to open several curves and process the obtained data (Fig.4). This option may be more convenient when averaging several curves. It is important to set "Yes" in the "Match documents" item when opening files.
Two combined force curves recorded on the mica surface and the viral particle during cantilever approach are shown in Fig.4b. The viral particle shows an increase in the slope of the force curve after contact, indicating deformation of the sample by the cantilever. The difference of changes in vertical coordinates (cantilever deflection) of the two force curves at a fixed difference of horizontal coordinate (movement of the sample to the cantilever) allows us to calculate deformation of the sample, which in the given example was 2.3 nm.
Considering the envelope proteins denaturation, the viral particles interact more strongly and are distributed on the substrate, the height of the particles is significantly reduced compared to the control VTM samples. In this case, the Young’s modulus values are strongly influenced by the sample substrate.
Thanks to the four-dimensional visualisation option of the Force Volume mode implemented in the early versions of "FemtoScan Online" software, it is possible to clearly trace the sample elasticity and adhesion by moving in different planes of the force curve (Fig.5).
CONCLUSIONS
In this work, the effect of heat treatment on tobacco mosaic virus was evaluated. The possibilities of processing the data obtained in Force volume mode in "FemtoScan Online" software are shown, and the possibilities of four-dimensional data presentation are also presented.
Force curves help to analyse fundamental interactions such as van der Waals forces, Coulomb forces and capillary forces between surfaces or particles. Force curves have become a versatile tool in AFM research, allowing detailed characterisation of materials and biological systems at the nanoscale.
Atomic force microscopy force curve acquisition and analysis is a well-established procedure for obtaining high-resolution non-topographic information from any sample, including biological samples. In particular, these analyses are commonly used to study elasticity, stiffness or adhesion properties of samples. In addition, the collection of multiple force curves over a wide area of samples allows the reconstruction of maps of spatial distribution of mechanical properties. Accurate analyses often require combination of several models and numerical simulations (e.g. finite element method).
Combining these maps with the sample surface topography provides a deeper understanding of physical properties of the sample in terms of structure and nanomechanics [6].
ACKNOWLEDGEMENTS
This work was performed under the state
order of the Lomonosov Moscow State University. FemtoScan Online software is provided by "Advanced Technologies Center", www.femtoscan.ru
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Force curves provide valuable information on local material properties such as elasticity, hardness, adhesion and surface charge density. For this reason, the force measurement curves has become essential in materials science and biology. Another application is to analyse surface forces per se to answer the question: what are the interactions between particles in a fluid? How can dispersion be stabilised? How do surfaces in general and particles in particular adhere to each other [1]?
Force curves are widely used in nanotechnology, biology, materials science and other fields for quantitative analysis of local properties of objects and materials.
Characterisation of biomechanical properties of tissues with high spatial resolution provides valuable information on a wide range of developmental, homeostasis and pathological processes in living organisms. The biomechanical properties of the basal membrane, a substructure of the extracellular matrix as small as ∼100–400 nm across, among others, are crucial for tumour progression and metastasis formation. Although the exact assignment of Young’s modulus E of such a delicate substructure of the extracellular matrix, especially between two cell layers, is still a challenge, biomechanical data of the basal membrane can provide information with outstanding diagnostic potential [2].
In a study [3], atomic force microscopy (AFM) was used to measure changes in the stiffness of human multipotent mesenchymal stromal stem cells cultured in a Petri dish and on polyacrylamide substrates during osteogenic differentiation. The results showed that the Young’s modulus of the cytoplasmic outer region of the cells increased with time during osteogenesis. There is a strong linear correlation between the time of osteogenic induction and Young’s modulus of cells cultured in rigid Petri dishes, Young’s modulus approaching a plateau after day 15.
RESEARCH METHODS
Force curves in AFM reflect the distance dependence of the interaction force between the probe and the sample. For their quantitative analysis, different theoretical models describing different types of interactions are used. In the area of mechanical contact between the probe and the sample, repulsive forces described by contact mechanics models prevail [4].
The power curve usually consists of two branches:
approach curve – the probe is approaching the surface, red line in Fig.1;
retract curve – the probe is moving away from the surface, green line in Fig.1.
In the graph, the distance (Z-position of the scanner) is plotted on the X-axis and the force (or cantilever deflection) is plotted on the Y-axis [5].
Characteristic sections of the power curve:
Non-interacting region – the probe is far from the surface, the forces are negligible;
When the probe approaches, attraction forces (van der Waals forces, capillary, electrostatic, steric forces, etc.) arise;
Contact region – repulsive forces (elastic and plastic deformations) predominate. When the magnitude of the attraction force becomes greater than the sum of the repulsive forces and the elastic resistance of the cantilever, the probe is pushed into the sample (C);
Adhesion Peak (on the green lead line) – "sticking" due to adhesion forces may be observed when the probe is removed.
A high adhesion peak characterises a strong "sticking" of the cantilever to the sample surface (e.g. due to capillary forces in humid air).
The slope in the contact region reflects stiffness of the specimen. When working with a soft specimen, the force curve in the same coordinates will look more hollow. Hysteresis between approach and departure – may indicate plastic deformation or viscoelastic properties.
The following algorithm is used to obtain information on mechanical properties. Force curves are measured at different points of the surface. A data array is obtained, for example, 128 × 128 inlet and outlet curves. Then, from the analysis of each force curve, images corresponding to adhesion, stiffness and deformation distribution maps of the surface are obtained. To display the entire data set, a 4-dimensional mapping has to be used: three XYZ coordinates and colour gradations are used to construct adhesion, stiffness and deformation maps (Fig.2).
MATERIALS AND METHODS
The method we developed was applied to analyse the effect of heating on tobacco mosaic virus. Tobacco mosaic virus after 5 min of heating at 90 °C was considered as a sample.
The virus was applied on a mica substrate, and force curves were measured with an NP-S10 cantilever in Force Mapping mode on a Nanoscope-3A atomic force microscope (Digital Instruments, USA).
The force curves were taken at a resolution of 32 × 32 points. Fig.3 shows two types of data display – topography on the top left and force curves display on the right. Characteristic size of the formed particles: 0.5–1.2 μm. When selecting force curves for Young’s modulus estimation on the substrate it is important to pay attention to the adhesion peak, on a clean substrate the cantilever will not stick because the adhesion peak is significantly smaller than for a viral particle.
Using "FemtoScan Online" software it is possible to open several curves and process the obtained data (Fig.4). This option may be more convenient when averaging several curves. It is important to set "Yes" in the "Match documents" item when opening files.
Two combined force curves recorded on the mica surface and the viral particle during cantilever approach are shown in Fig.4b. The viral particle shows an increase in the slope of the force curve after contact, indicating deformation of the sample by the cantilever. The difference of changes in vertical coordinates (cantilever deflection) of the two force curves at a fixed difference of horizontal coordinate (movement of the sample to the cantilever) allows us to calculate deformation of the sample, which in the given example was 2.3 nm.
Considering the envelope proteins denaturation, the viral particles interact more strongly and are distributed on the substrate, the height of the particles is significantly reduced compared to the control VTM samples. In this case, the Young’s modulus values are strongly influenced by the sample substrate.
Thanks to the four-dimensional visualisation option of the Force Volume mode implemented in the early versions of "FemtoScan Online" software, it is possible to clearly trace the sample elasticity and adhesion by moving in different planes of the force curve (Fig.5).
CONCLUSIONS
In this work, the effect of heat treatment on tobacco mosaic virus was evaluated. The possibilities of processing the data obtained in Force volume mode in "FemtoScan Online" software are shown, and the possibilities of four-dimensional data presentation are also presented.
Force curves help to analyse fundamental interactions such as van der Waals forces, Coulomb forces and capillary forces between surfaces or particles. Force curves have become a versatile tool in AFM research, allowing detailed characterisation of materials and biological systems at the nanoscale.
Atomic force microscopy force curve acquisition and analysis is a well-established procedure for obtaining high-resolution non-topographic information from any sample, including biological samples. In particular, these analyses are commonly used to study elasticity, stiffness or adhesion properties of samples. In addition, the collection of multiple force curves over a wide area of samples allows the reconstruction of maps of spatial distribution of mechanical properties. Accurate analyses often require combination of several models and numerical simulations (e.g. finite element method).
Combining these maps with the sample surface topography provides a deeper understanding of physical properties of the sample in terms of structure and nanomechanics [6].
ACKNOWLEDGEMENTS
This work was performed under the state
order of the Lomonosov Moscow State University. FemtoScan Online software is provided by "Advanced Technologies Center", www.femtoscan.ru
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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