AI-based atomic force microscopy image analysis allows to predict electrochemical impedance spectra of defects in tethered bilayer membranes

Atomic Force Microscopy (AFM) is increasingly used for studying interaction of lipid bilayers with proteins including pore-forming toxins (PFTs) and membrane disrupting peptides^1,2,3. AFM is capable of detecting insertion of proteins, heterogeneous distribution of proteins in membranes² in phase separated membranes³, formation of rings of PFTs¹ and other structural details important to understand how membrane protein interact with cell membranes.

While providing nanoscale-level structural details of reconstituted PFT’s and peptides in membranes, AFM does not directly access function of these proteins, neither it can predict the extent of dielectric damage by PFTs and peptide. Such information is important in establishing fundamental relation between structure and function of biological systems.

Because of evident reasons the AFM studies of membrane proteins are performed using solid supported phospholipid bilayers⁴. In case the electrical conductance data reflecting functional effects of PFTs or peptides on membranes is sought the tethered bilayer systems are used^5,6. Also, both techniques, AFM and EIS, are used simultaneously or in parallel to characterize structure and function of PFTs in membranes^7,8,9,10.

The electrochemical impedance spectroscopy (EIS) is a method of choice for detailed studies of electrical effects of PFTs in membranes. The EIS allows accessing the dielectric properties and conductance data of tBLMs (tethered bilayer membranes), and in some cases though not being structural method per se, provides insights into lateral distribution of defects in membranes^8,9,10. So far, however, there were no attempts to quantitatively relate structural data obtained by AFM and the membrane conductance data measured by EIS, even though experimental capabilities to apply both techniques on the same membrane samples are straightforward. Such comparative measurements would be of great value in studying function of both single and multiple ensembles of membrane damaging protein entities as well as in developing precision biosensors based on tBLMs^11,12.

Recently, significant progress has been made in the development of EIS data analysis of solid supported (tethered) phospholipid membranes^8,9,10,13. In particular, the theoretical analysis demonstrated that the amount of reconstituted protein pores per surface area can be retrieved from the EIS spectral data. Nevertheless, such theoretical approaches, strictly speaking, should be verified by using data from the independent structural techniques such as AFM.

The objective of current study is to explore the possibility to predict the electrochemical impedance spectra from the AFM images of membranes with reconstituted PFTs. The AFM technique allows to detect PFT entities which appear on tBLM surface upon exposure of bilayer to the protein solution. The coordinates of these entities may be measured, and the finite element analysis (FEA) can be applied to model EIS response of such supported membranes. The comparison of predicted and experimental EIS curves obtained from the same sample would allow (1) to independently verify the applicability of FEA approach to theoretically predict EIS spectra developed earlier^9,10 on real, AFM imaged surfaces, (2) to precisely evaluate the physical parameters of supported bilayer membranes, among which the specific resistance of submembrane reservoir separating bilayer from the solid support is of upmost importance. This parameter is strongly correlated with the density of PFT defects in tBLMs^13,14, therefore, independent verification by AFM can resolve the ambiguities related to such correlation.

Typically, only a tiny patch compared to a whole surface area is interrogated by the AFM technique. To establish representative defect densities and their distribution patterns, the sufficiently large areas, in our case, containing hundreds and thousands of defects must by tested. The determination of coordinates of large defect ensembles is a highly time consuming process. To overcome such and similar problems automated algorithms can be applied for AFM image analysis.

Typically, the features of different shapes in AFM images are detected via particle or grain analysis based on edge detection. In the majority of cases, a pre-processing takes place to make it easier to measure and observe the features that have been measured¹⁵. AFM images are always affected by the geometry of a tip and external noise that disturb image features. Although basic image segmentation approaches work well for good-quality image data containing clear and easily distinguishable objects, analysis of noisy, low-resolution or otherwise degraded images requires more sophisticated methods. An important factor is the scarcity of such image data which limits the possibilities of applying machine learning or deep learning methods in a practical way. In some cases researchers still resort to manual work of annotating and quantifying objects of interest in microscopy images^7,16.

Despite the difficulties associated with the automated analysis of AFM images, substantial progress has been recently made in developing practical solutions for certain types of such problems. Meng et al.¹⁷ presented an algorithm based on local adaptive Canny edge detection and circular Hough transform which is suitable for recognizing particles in scanning electron microscope (SEM) or transmission electron microscope (TEM) images. Another study conducted by Venkataraman et al.¹⁸ showed that rotavirus particles in AFM images can be detected by applying a series of image pre-processing, segmentation and morphological operations. Marsh et al.¹⁹ proposed the Hessian blob algorithm for detecting biomolecules in AFM images and showed its superiority against the threshold and watershed image segmentation algorithms. Other recent studies also showed that deep learning techniques can be successfully applied to detect complex-shaped objects in microscopy images. Sotres et al.²⁰ used the YOLOv3 object detection model and a Siamese neural network to determine the locations of DNA molecules in AFM images and identify the same molecule in different images. Okunev et al.²¹ applied a Cascade Mask-RCNN neural network to detect metal nanoparticles in scanning tunneling microscopy (STM) images. In both of these cases the researchers used precision and recall metrics to measure the performance of the proposed models. One more study by Sundstrom et al.²² involved a supervised learning approach of estimating lengths of DNA molecules in AFM images. A software tool for the automated biomolecule tracing in AFM data (TopoStats) was also recently developed and presented by Beton et al.²³

In this study we investigate the problem of automated detection of membrane bound PFTs in AFM images. Performing this task with adequate accuracy is of practical importance, as the determined coordinates would allow to theoretically calculate EIS spectral features and to compare those features with the experimental EIS data. In addition to applying and testing one of the popular computer vision techniques—convolutional neural network, we present a method for generating synthetic defect sets which resemble detection results of varying accuracy, similar to those obtained by using an actual object detection model. Such datasets are used to perform FEA modeling of EIS spectra and examine the relationship between defect detection accuracy and corresponding variations of EIS spectral features. By doing so we address the question—whether there is some minimal requirement for the precision of the AI based image processing algorithm so that the EIS spectra prediction would fall into acceptable range of uncertainty?

AFM imaging

AFM image data was obtained by measuring three separate tBLM membrane cells. Assembled tethered lipid bilayers were incubated for 30 min with vaginolysin (VLY). Aliquot of a toxin was added to the cell, so that final concentration of VLY was 1nM1nM. After incubation, cell was washed with 10 mL of phosphate buffer pH7.1pH7.1 to remove any unbound protein debris, and disassembled under water. AFM imaging was carried out in aqueous environment. More detailed description of experimental settings can be found elsewhere¹⁰.

For each cell a surface patch of 6μm×6μm6μm×6μm was scanned by capturing one 2μm×2μm2μm×2μm fragment at a time. Each fragment was imaged with 512×512512×512 resolution, thus the overall stitched image consisting of 3×33×3 fragments had 1536×15361536×1536 resolution. Each image fragment was manually annotated by marking center coordinates (X and Y) of each defect visible in the image. Image fragment sets of each cell were partitioned into training and test subsets by assigning 5 fragments for training and 4 for testing. Test fragments were selected to represent a cohesive 4μm×4μm4μm×4μm surface patch at the lower right corner of the fully stitched image. Table 1 shows the total number of annotated defects (N) and average defect density (Ndef����) for each AFM image cell and training/test subset. Defect density is expressed as the number of defects per square micrometer.

In addition to aforementioned parameters each surface image is also characterized by metric σσ which is obtained by computing the Voronoi diagram for a given defect set and calculating the standard deviation of the normalized Voronoi sector areas (multiplied by defect density Ndef����). This quantity summarizes the degree of defect clustering where higher values correspond to stronger clustering effect (example of defect cluster is highlighted in Fig. 1). Defect clustering has been shown to have significant influence on EIS spectra of tBLM membranes, as presented in earlier research¹⁰.

Example of an AFM image fragment with an instance of defect cluster zoomed in.