Electrostatic interactions between the sample and the substrate can be described by the Debye-Hückel potential V e l e = ∑ i < j q i q j 4 π ϵ 0 ϵ k d i j e − d i j / λ D , λ D = ϵ 0 ϵ k k B T 2 N A e 2 I (1) which represents Coulomb interactions of point charges q _i and q _j separated by the spatial distance d _ij , effectively screened over the Debye length λ D . The Debye length can vary between 2.1 nm for ionic strength I = 20 mM and 0.8 nm for I = 150 mM (ionic strength under physiological conditions).

We considered three different AFM substrates, i.e., the mica surface, APTES-mica, and lipid bilayer surfaces and for the purpose of this study construct simplified 2D models of them. We employ an atomic model of the cleaved surface of the muscovite mica crystal structure (Fukuma et al., 2010). The oxygen atoms have charges q = − 2 e and although silicon atoms have charges + 4 e , we assign them effective charges q = + 2 e to roughly account for the charge compensation by the fourth oxygen atom which is covalently bound to each silicon atom but is not part of the cleaved surface. The charge density of this model reproduces the experimentally known value for mica − e / 0.48  nm² (Uchihashi et al., 2018a). Based on the known charge density we also considered a coarse-grained mica model which has point-like charges q = − e placed along a regular lattice with spacing 0.48  nm.

To construct a minimal 2D model of the APTES-mica surface, we first computed the average gyration radius of ten different 3D APTES conformers available from the PubChem website as R g = 3.4  Å. Viewing individual APTES molecules as spheres, it would be possible to construct a regular lattice with a spacing of 2 R g . However, since such an arrangement would result in an unrealistic charge distribution under commonly used APTES concentrations (i.e., it would practically represent the mica lattice geometry with positive charges), we instead imposed a regular grid of point-like positive charges with a spacing of R g , assuming contributions from internal conformational changes during the assembly process which are unknown. The charge density of this model is larger by factor of about 4 compared to the mica model.

To model lipid-bilayers self-assembled on the mica surface, we impose the 2D hexagonal packed geometry of lipid headgroups inferred from previous high-resolution AFM imaging (Higgins et al., 2006) with a measured intermolecular spacing of 0.51 nm, and view each group as a point-like particle with either neutral, positive, or negative charge, reflecting the most commonly used lipid types (DPPC, DPPE, DOPC lipids q = 0 ; DPTAP type q = + e ; DOPS type q = − e ). The fraction of charges can be specified and a random distribution along the lattice will be assumed. The Electrostatics Application within the BioAFMviewer allows to consider customized models of AFM substrates with specified lattice geometry parameters and adjusted ratio of charged particles too. Hence, a library of substrate surface models becomes available.

To construct the 3D surface of a macromolecular structure, the well-known marching cubes discretization algorithm (Lorensen and Cline, 1987) was employed, representing it by a set of triangles used for graphical rendering. For each triangle the electrostatic potential is evaluated at the center of mass (vertex) as the sum of Coulomb potentials arising from partial charges of all atoms. Hence, the potential for vertex i is V i = 4 π ϵ 0 − 1 ∑ j q j / d i j , where q j is the partial charge of atom j , d i j is the distance between vertex i and atom j , and ϵ 0 is the vacuum permittivity. This allows to compute the surface electrostatic potential for a given PDB structure. The Electrostatics Application within the BioAFMviewer implements a graphical representation of the generated 3D molecular surface where values of the electrostatic potential are visualized via a color scale. In the applications for Cas9, aptamer-CYP24, Monalysin, and ClpB, the partial charges of atoms were computed at pH value 7.0 condition.

For sampling 3D rigid-body orientations of a biomolecular structure, we discretized the search space evenly using the Fibonacci lattice algorithm (Swinbank and Purser, 2006; Gonzalez, 2010). In the applications for Cas9, aptamer-CYP24, Monalysin, and ClpB, sampling was performed for a set of 2000 conformations. The Electrostatics Application within the BioAFMviewer gives a choice for this number. For each single orientation, direct contact to the AFM substrate was always assumed, and the electrostatic interaction energy between all substrate point charges and the biomolecular surface was computed according to the Debye-Hückel form (Eq. 1). For a single substrate point charge q _i the electrostatic potential energy is E i = 1 ϵ k 1 A t o t a l ∑ j A j V j q i e − d i j / λ D , where V _j is the electrostatic potential value of triangle j (with area A _j ) on the sample surface, A _total is the total sample surface area, d _ij is the distance between the triangle center of mass and the charge q _i , and ϵ k is the dimensionless relative permittivity. Area weights were introduced because the marching cubes algorithm does not discretize the sample surface evenly, resulting in a heterogeneous density of vertices (triangle center of mass). To remove the density dependence in the electrostatic potential energy, individual contributions of triangles were therefore weighted considering their fraction to the total surface area. After completed sampling, a visualization of the energy landscape in the space of latitude and longitude angles ∅ , θ (characterizing the sample orientation relative to the substrate) was obtained.

The interpretation of pathways in this landscape is as follows. For any fixed value of the angle θ , changes in the angle ∅ always correspond to rotation of the biomolecular sample around the y-axis of the AFM substrate plane. Considering any fixed value of ∅ , changes in the angle θ correspond to the sample rotating around an axis which is given by the AFM substrate x-axis co-rotated by the ∅ value. We note that for the sake of better interpretation we always plot the energy landscape in the space of both latitude and longitude angles ∅ , θ covering the 360° range. For presentation purposes, we shift the energy scale such that the global minimum has zero energy. Furthermore, since the gross approximations applied in our modelling do not allow to infer a realistic magnitude of electrostatic interaction energies between the sample and the AFM substrate (see Discussion), we use rescaled dimensionless values such that the maximum value equals unity. For relative comparison in the case of the toy sphere models and in the ClpB case (high salt versus low salt buffer conditions) a common rescaling was used. The prediction of most favorable placements on the substrate was based on identifying the minima of the landscape. In the software the top five candidates, corresponding to the five lowest values, are displayed.

The developed methods are implemented via the Electrostatics Application tool within the BioAFMviewer interactive software interface. To use this application, the user has to upload a PQR file of the biomolecular structure which, as compared to a regular PDB file, contains information about partial charges of atoms. For a given biomolecular structure such data can be conveniently obtained using, for example, the PDB2PQR application (Jurrus et al., 2018) (server https://server.poissonboltzmann.org/pdb2pqr), which also considers calculations at variable pH value and for different force fields. After loading the PQR file, the biomolecular structure can be displayed in the surface representation with coloring according to the calculated electrostatic surface potential. In the Electrostatics Application tool, the user can either choose the AFM substrate from a list of commonly employed examples with preset charge distribution or provide alternative values. The prediction of electrostatically favorable biomolecular orientations can be started after fixing the size of the sampling set. After completed sampling, the landscape of electrostatic interaction energies is displayed in an interactive window, which allows to access by mouse-click any point and visualize the corresponding molecular placement on the AFM model substrate in the front view, bottom view, and scanning view perspectives, together with the simulated AFM image.

We have employed simulation AFM to compare the results from electrostatic predictions with measured HS-AFM topographies. Simulation AFM computationally emulates AFM scanning to convert available biomolecular structures into simulated AFM images that can be correlated with experimentally obtained images. It is based on the non-elastic collisions of a rigid cone-shaped tip with a rigid Van-der-Waals sphere atomistic model of the biomolecular structure. For details we refer to our previous work (Amyot and Flechsig, 2020). Simulation AFM calculations were performed within the BioAFMviewer software platform (Amyot and Flechsig, 2020; Amyot et al., 2023).

A mica substrate (∼0.1 mm in height and 1.5 mm in diameter) was glued with epoxy on the top of a cylindrical glass stage (2 mm in height and 2 mm in diameter). The mica surface was prepared by cleaving the top layers of mica disk, which was then immediately imaged with HS-AFM in the observation buffer (10 mM Tris-HCl, pH 7.5). The 3-aminopropyltriethoxysilane modified mica (APTES-mica) surface was prepared as previously reported (Yoshimi et al., 2022), using an APTES solution diluted to 0.1% with MilliQ-water, after which the surface was imaged with HS-AFM in the observation buffer.

HS-AFM imaging was performed in the tapping mode using small cantilevers (BLAC10DS-A2, Olympus) (resonant frequency, ∼0.5 MHz in water; quality factor, ∼1.5 in water; spring constant, ∼0.1 N·m⁻¹). The cantilever’s free oscillation amplitude A ₀ and set-point amplitude were set at ∼2 nm and ∼0.9 × A ₀, respectively. The scan size and pixel size for each AFM image are 80 × 80 nm² and 160 × 160 pixel, respectively. The frame rate for the mica and APTES-mica surfaces were 0.5 and 0.25 s/frame, respectively.

For image analysis, a low-pass filter to remove spike noise and a flattening filter to make the xy-plane flat were applied to each image. The height distributions of the mica and APTES-mica surfaces were fitted with single and double Gaussian functions, respectively. For the mica, the center of the Gaussian peak was set to 0 nm. For the APTES-mica, the center of the first Gaussian peak, which corresponds to the mean height of the mica surface, was set to 0 nm.

Relevant for our study is the modelling of three different AFM substrates. Because of its surface flatness at the atomic level over a large area, the negatively charged mica substrate is most frequently used. The mica surface modified with APTES molecules is preferred when imaging, e.g., proteins complexed with nucleic acids, because in water the NH₂ group of an APTES molecule is protonated to the positively charged NH₃ ⁺ under typical pH conditions. The processes by which APTES molecules interact with mica and the formation of the coated surface are largely unexplored. We have performed HS-AFM imaging of the APTES-mica and compared it with an image of bare mica (see Figures 3A, B). Under typically used molecular concentration of APTES, the surface appears much more rugged showing irregular accumulations of larger blobs and indentations (Figures 3A, C). While the distribution of measured topography heights for bare mica is Gaussian, that obtained from the APTES-mica image is clearly asymmetric towards larger height values (Figure 3D). These observations indicate the complexity underlying the formation of the ATPES-mica substrate, possibly involving aggregation of individual APTES molecules and inhomogeneous binding to the Mica surface.

For the mica surface, we consider an atomic resolution model as well as a simplified lattice model. In the framework of our study, we can only formulate a simplified minimal model of the ATPES-mica surface viewing it as a regular lattice of point-like positive charges. The substrate models are illustrated in Figure 3E. For details we refer to the Methods section.

The third model substrate is that of a lipid bilayer self-assembled on the mica surface. We employ a model of the lipid headgroups in the hexagonally packed geometry inferred from previous high-resolution AFM imaging (Fukuma et al., 2010) (see Figure 3F). Since commonly a mixture of various lipid types is used in experiments, we consider a combination of neutral charges (e.g., DPPC, DPPE lipids) and positive charged headgroups (e.g., DPTAP lipid type), see Methods.

We first considered the Cas 9 endonuclease protein which binds guide RNA and cleaves duplex target DNA with a sequence complementary to the RNA guide, playing a key role in genetic engineering applications (CRISPR-Cas9 genome editing). Several PDB structures of Cas9 complexes are available. Figure 2A shows the atomistic structure of Cas9-RNA with a bound single-strand target DNA together with the computed molecular surface representation colored according to the calculated electrostatic potential. The presence of nucleic acid strands with the phosphate groups in nucleotides generates a negatively charged molecular surface. HS-AFM experiments to visualize structural dynamics of the Cas9-RNA-DNA complex (Shibata et al., 2017) were therefore performed on a modified surface known as APTES-mica which has a positive charge distribution (see Methods). Figure 4A shows the predicted molecular placement on the supporting surface predicted from our electrostatic interaction model. As can be seen from the bottom view perspective, the Cas9 complex binds to APTES-mica with the flat molecular surface that has the negatively charged guide RNA strand attached, which acts like a glue between Cas9 and APTES-mica (Figure 4C). The scanning view showing the molecular surface probed by the AFM tip is also provided (Figure 4A).

Looking closer at the predicted orientation of the Cas9 complex relative to the APTES-mica surface, an interesting observation can be made. The bound target DNA strand is located in a tunnel within the Cas9 structure and both the entry and exit paths are not blocked by contacts with APTES-mica. In fact, the orientation of both DNA gates is roughly parallel to the surface (Figure 4C). We then generated a simulated AFM image of the predicted orientation of the molecular structure in the scanning view perspective and compared it with a snapshot obtained from HS-AFM imaging the dynamics of Cas9 interactions with DNA (Shibata et al., 2017). As we find, in the experimental image the orientation of the DNA strand in the Cas9 complex correlates remarkably well with the position of the two DNA gates in the predicted molecular orientation. It should also be noted that the predicted molecular orientation of Cas9 relative to the AFM surface based on electrostatic modelling agrees remarkably well with our previous result (Amyot and Flechsig, 2020), where automatized rigid-body fitting of the Cas9 structure without the nucleic acids was employed to validate the domain arrangement seen in HS-AFM imaging.

Figure 4B shows the landscape of electrostatic interaction energies in the space of latitude and longitude angles ∅ , θ which characterize the protein orientation in 3D space. The landscape shows a clear valley localized around the minima which corresponds to the predicted favorable placements of the Cas9-RNA-DNA structural template. This valley is confined by steep walls characterized by the gradient ∂ V / ∂ ϕ which corresponds to the force magnitude of a perturbation that would be required to destabilize the placement on the protein on the APTES-mica surface. Hence, the presence of such a barrier would resist possible perturbations applied by the AFM tip in the horizontal scanning direction. However, the model simplifications underlying our predictions (see Discussion) do not allow to provide quantitative estimates that could be compared with those obtained from HS-AFM experiments.

Nonetheless, our findings based on electrostatics offer an explanation why under HS-AFM observations functional relative motions of target DNA and Cas9 can be reliably observed, and DNA cleavage could be captured at the single molecule level (Shibata et al., 2017).

Next, we considered a complex of a 70-nucleotide DNA aptamer and the CYP24 protein, which has been demonstrated to be relevant for antiproliferative activity in cancer cells and was previously observed under HS-AFM (Biyani et al., 2022). The 3D atomistic structure of the complex as predicted from molecular docking simulations and the computed molecular surface representation with charge coloring according to the electrostatic potential are shown in Figure 2B. Similar to the previous case of the Cas9-RNA-DNA complex, the presence of the DNA aptamer which due to the phosphate groups in nucleotides is negatively charged, does generally not allow stable AFM observations on the standard negatively charged bare mica surface. Therefore, the experiment was conducted with a mica surface modified by a positively charged lipid bilayer which self-assembled on its top [for details see Biyani et al. (2022)].

Taking into the account the used lipid mixture (i.e., ∼ 90% DPPC and 10% DPTAP type) in our model of the lipid-bilayer substrate (see Methods) and electrostatic interactions with the aptamer-protein complex, we predict the favorable molecular placement. Figure 5A shows the top candidate found from scanning the space of possible rigid-body orientations relative to the surface and evaluating electrostatic interaction energies. As can be seen in the front view perspective, and particularly well from the bottom view, the predicted orientations are those in which the two longer DNA strands are placed on the surface in a flat arrangement with the CYP24 protein sitting on top. The scanning view showing the molecular surface probed by the AFM tip is also provided.

Figure 5B shows the landscape of electrostatic interaction energies between the aptamer-protein complex and the modified mica surface in the space of latitude and longitude angles ∅ , θ . It shows a highly localized valley which is confined by steep and high walls and at its bottom has energy minima that correspond to the well-defined placement of the protein-DNA complex predicted from them. The existence of such a highly confined deep energy valley is clearly due to the presence of the DNA aptamer, dominating the electrostatic interactions by attraction forces with the positively charged lipid bilayer on mica. Any structural orientations deviating from the predicted highly stable conformation would be practically impossible, which is confirmed by single molecule HS-AFM observations of the CYP24-aptamer [see SI movie in Biyani et al. (2022)].

When comparing a simulated AFM image obtained in the scanning perspective of the predicted protein complex relative to the AFM substrate (Figure 5C) to our previous result from automatized fitting (Amyot and Flechsig, 2020) and a measured HS-AFM image (Figure 5D), excellent agreement is found.

The third application is for the bacterial Monalysin protein which has been identified to form pores in cell membranes, thus contributing to the death of fruit flies (Opota et al., 2011). HS-AFM has previously revealed the structure of Monalysin in solution on a mica surface and on an effectively negative charged lipid membrane (Nonaka et al., 2020). For the application of our model, we have used the crystal structure of the pro-form Monalysin (PDB 4MJT), representing however the functionally inactive state (Monalysin active structures are missing). As a structural template of the active state we have used a nonameric structure with removed N-terminal segments, roughly taking into account their cleavage upon activation [see Leone et al. (2015) and Nonaka et al. (2020) for details].

Figure 2C shows the ring-shaped atomistic structure and the corresponding electrostatic surface representation. In this orientation the molecular surface exhibits a ring-shaped region with positive electrostatic potential. However, a significant area of the surface at the opposite protein side is also positively charged. Hence, which orientation can be expected to be preferential under the formation of the sample-substrate complex is unclear.

Our electrostatic interaction model indeed predicts those two placements of Monalysin on mica to be the only stable states, as can be seen from the landscape of electrostatic interaction energies (Figure 6C). The favorable placement corresponds to that of the oligomer in the dome-shape shown in Figure 6A. The corresponding molecular structure in the bottom view perspective showing the interface towards the substrate is displayed in Figure 6B together with the surface representation colored according to the electrostatic potential. It can be concluded that the positively charged regions at the tip of monomers, whose arrangement resembles the jags of a crown, play a dominant role in the interactions with the AFM substrate and the sample placement. Images for the scanning view perspective are also shown in Figure 6B. Simulations considering the membrane model as a substrate with the lipid mixture according to the experimental conditions (i.e., ∼80% DOPC and 20% DOPS type) used in Nonaka et al. (2020) resulted in very similar predictions.

An important observation is that our predictions are consistent with the currently available models of membrane pore formation by the Monalysin protein (Leone et al., 2015; Nonaka et al., 2020), stating that binding to the membrane in the dome-shaped orientation is required to generate further conformational changes leading to the formation of nanopores. Furthermore, a simulated AFM image generated for the scanning view perspective of the predicted Monalysin orientation relative to the AFM substrate shows good agreement with the HS-AFM image obtained from previous experiments (Figure 6D). The differences in the size of simulated and measured topographies are attributed to the fact that the experiments visualize the active Monalysin as an octamer, whereas the used model structure is a nonamer and the conformational changes underlying a transition to the active form cannot be resolved.

As a last application, we chose the ClpB chaperone which is an ATP-powered molecular machine involved, e.g., in disaggregation of proteins under heat stress conditions. Functional conformational dynamics of ClpB was previously investigated in HS-AFM experiments (Uchihashi et al., 2018b). The atomistic structure of the hexameric Hsp104 disaggregase (yeast homologue of bacterial ClpB) in the conformation with bound ATP analog is shown in Figure 2D. In the chosen orientation, the molecular surface representation reveals a ring-shaped region with predominantly positive electrostatic potential. It can therefore be expected that this protein side forms contacts with the mica surface. Our electrostatic interaction model employing a bare mica surface as used in ClpB HS-AFM observations indeed predicted orientations with similar contact surfaces. A single chosen predicted placement is shown in Figure 7A in the front view. The corresponding bottom view perspective displaying the protein side facing the mica surface together with its molecular surface representation colored according to the electrostatic potential is shown in Figure 7B. Also shown is the molecular structure in the opposite view corresponding to the scanning view perspective together with its surface representation (Figure 7B). As can clearly be seen, the ring-shaped region with predominantly positive electrostatic potential is guiding the placement of the hexameric chaperone on the negatively charged mica surface.

An interesting aspect is that for successful imaging of ClpB under HS-AFM the buffer composition was critical as stated in Uchihashi et al. (2018b): “The salt concentration was a key to successful imaging of TClpB because high salt concentrations such as 150 mM KCl weakened the affinity of molecules to mica substrate, resulting in fast diffusion of molecules and thus hampering imaging. Therefore, we used a lower concentration of KCl (20 mM) which enabled moderate binding of ClpB onto mica substrate.” While in the employed electrostatic model the buffer conditions can only be phenomenologically accounted for by the parameter for the ionic strength, our predictions can still provide an explanation of this situation. In Figure 7C we show the landscape of electrostatic interaction energies between the Hsp104 structural template and the mica surface for two cases, corresponding to high- and low-salt concentrations, respectively. Common to both landscapes is the presence of a valley isolating favorable protein placements on mica. However, the stark difference between them is that under low-salt conditions, electrostatic interaction energies, and therefore the barriers around the valley, are larger by one order of magnitude as compared to the high-salt case. This is because in the latter case, electrostatic interactions are screened over a much shorter Debye length (see Eq. 1). Hence, the interpretation is that a buffer condition with low-salt concentration significantly stabilizes the formation of electrostatically favorable orientations of ClpB on mica and therefore allows reliable imaging under HS-AFM scanning. Notably, the landscape of electrostatic interaction energies resembles that obtained for the toy Janus sphere (Figure 1D), reflecting the stability of the sample-substrate complex in the obtained orientation, whereas the placement in the opposite upside-down protein arrangement represents the most unstable arrangement.

The simulated AFM image of the predicted orientation resembles the spiral shape topography seen in HS-AFM imaging (Figure 7D), which arises from the domain protrusions in the hexameric arrangement. Interestingly, our previous result of automatized fitting the PDB structural template into the same HS-AFM image predicted the hexamer structure to be in the opposite upside-down orientation. There, fitting was based on exhaustive sampling of possible molecular orientations without an underlying physical model, aiming to identify the orientation whose simulated AFM image best matched to the target HS-AFM image. In fact, the thus obtained simulated AFM image matches much better to the HS-AFM image compared to the one obtained from our electrostatic model predictions (Figure 7D). A well-known drawback in the interpretation of results is that simulated topographies (like the measured AFM topographies) have a limited spatial resolution. Especially for symmetrically shaped proteins this may lead to ambiguities. While the atomistic structure on opposite sides of the ClpB ring is clearly distinct, the corresponding simulated AFM images resulting from a convolution of the tip shape with the molecular structure can show similar looking spiral shapes.

Predictions based on our electrostatic model should in principle be prioritized over the sampling method without any physical interactions. However, a drawback of the modeling is that in the absence of structural ClpB data used in HS-AFM experiments (T. thermophilus ClpB) the yeast homologue Hsp104 structure was used. Therefore, the expected differences in the sequence may also result in a different surface electrostatic potential compared to ClpB and predictions of the sample-substrate complex will change.

A so far overlooked issue is that HS-AFM observations were performed under a high protein concentration imaging assembly of ClpB rather than single molecules. Therefore, additional inter-molecular interactions may influence the placement on the mica substrate and imaging stability.