## 1 Introduction  
Atomic force microscopy (AFM) allows us to visualize the surface of biomolecular structures, and high-speed AFM allows us to follow conformational dynamics in real time under near-physiological conditions [1; 2; 3; 4; 5; 6]. A major limitation of AFM is that only morphological changes within the probed molecular surface can be detected, missing information required to fully explore functional mechanisms from imaging alone. Furthermore, since the scanning tip is too large to resolve structural detail, the interpretation of measured AFM topographic images including information below the sub nano-meter range is generally difficult.  
The atomistic-resolution equilibrium molecular structures of most proteins are either known from a combination of experiments [7] or can be predicted by the artificial intelligence AlphaFold program [8]. On the other hand, functional conformational dynamics can be obtained from multi-scale molecular modelling [9; 10; 11; 12; 13]. The enormous amount of high-resolution protein data offers a great opportunity to better understand resolution-limited AFM scanning data. Simulation atomic force microscopy (S-AFM) is a computational method that mimics the experimental tip-scanning of a biomolecule to transform its available atomistic structure into a simulated topographic image, which can be compared with an experimental AFM image. A sufficiently high image similarity, quantified by correlation scores, indicates that the unknown atomistic arrangement behind a measured AFM topography may be best represented by the known template structure.  
Various computational methods of systematically fitting atomistic-level or coarse-grained structural templates into AFM images have been developed [14; 15; 16; 17; 18; 19] and evidenced to advance our understanding of molecular processes beyond resolution-limited experimental imaging (see the recent review [20]). For example, the method of rigid-body fitting relies on the exhaustive sampling of molecular orientations of an atomistic template structure, each time applying S-AFM, until eventually the molecular arrangement whose S-AFM image has the highest image similarity with an experimental target is identified. The speed-limiting process during fitting is the computation of the S-AFM image of each sampled molecular orientation required for comparison to the target AFM image. This is because, for a given molecular orientation, the computation generally involves evaluating the contacts of the scanning tip with all the atoms in order to generate a topographic image of a biomolecular structure. However, since the scanning tip can only contact the biomolecular surface without penetrating the structure, the computation can be significantly accelerated by filtering a set of relevant atoms. Here, we present a solution based on graphics processing unit (GPU) computations [21], utilizing the workflow for rendering molecular structures. The underlying idea is simple: for any arbitrary 3D molecular orientation of a biomolecular structure, the set of atoms which are directly exposed to the scanning tip and can potentially come into contact with it, contains exactly those which are displayed by rendering the corresponding graphical 2D view.  
The results are presented in the following way. We first explain our developed filtering method, consisting of primitive filtering in the horizontal/vertical scanning directions and an elegant GPU-based solution to atom filtering in the lateral scanning direction. Then, we explain the GPU-based computation of simulated AFM images, considering the filtered subset of atoms. To evaluate the efficiency gain of the developed methods, we apply simulated AFM computations to various proteins with different size and shape geometry and perform statistical analyses of the obtained data.