# Fast and Interactive Positioning of Proteins within Membranes
## 1 Introduction  
Proteins are an essential component of all cells and perform a variety of functions. An important role of proteins is that they act as functional and structural elements of cell membranes, the fluid barrier that separates the cell from its environment [1]. The position of the protein within the membrane is a critical element in understanding many processes and can be predicted computationally, since direct experimental measurement is not routinely possible [2]. The incorporation into the membrane can affect the stability, folding, and activity of the protein, as well as its interactions with other molecules such as ligands, substrates, or surrounding macromolecules. To take a single biological example, for membrane fusion, the incorporation of transmembrane domains into the membranes to be fused is crucial [3; 4; 5]. Several databases have been developed to collect information on membrane incorporation and alignment, such as [2; 6; 7]. In certain cases, direct linkage of computational predictions with experiments is possible, for example, with data from electronic paramagnetic resonance experiments [8]. Computational algorithms range from simple implicit membrane representations [9] to computationally intensive molecular dynamics simulations in fully hydrated lipid bilayers [10; 11] and are not interactive. Interactive molecular simulations (IMS), as recently revisited in [12], offer a different approach: the scientist performs the manipulations interactively, providing intuitive insight into the process. Biologically and functionally relevant structural information can be obtained through IMS. The purpose of this work is to develop an interactive approach for protein positioning in membranes. By extending a robust bioinformatics method into an interactive method, non-experts can effortlessly perform and analyze such calculations, offering a valuable and novel tool tocomplement experimentally oriented studies. This use of interactive simulations is particularly interesting in the context of integrative structural biology [13], where inaccuracies in computational predictions are corrected by the experimental data guiding the refinement until a match between the computational model and the experimental characterization is achieved. The positioning of a protein in the membrane can be defined by several geometric measures, the most important of which are the insertion depth and angle. The insertion depth is the distance of the center of mass of the protein from the plane of the center of the membrane, measured in the direction perpendicular to this plane. It is common to refer to this direction as the \(z\)-axis of the coordinate system. To calculate the insertion angle, we define a local axis passing through two residues of the protein and calculate its angle with respect to the membrane normal, e.g., the \(z\)-axis. The research field of computational assessment of membrane protein positioning and incorporation into lipid bilayers has reached an advanced level of maturity, but interactive approaches have been largely neglected. Here, we build on the method of Integral Membrane Protein and Lipid Association (IMPALA) developed by [PERSON]'s team, which studied the interactions of different proteins with the implicit membrane representation. We chose this method because it is simple and computationally efficient, making it well suited for real-time interactive experiments and subsequent incorporation into an integrative modeling workflow. Molecular modeling studies using IMPALA, for example, aimed to calculate the conformations of a nisin compound in the membrane, confirming experimental results [14], and helped characterize new synthetic cell-penetrating peptides [15] or known peptides [16]. The orientation and insertion depth of integral membrane proteins were also studied in [17]. The main parameter of interest is the insertion angle, which provides information about the configuration that a protein adopts in the membrane according to its structural hydrophobicity.