## 1 Introduction
### Computing Influx  
The creation of specific inhibitors for emerging Gram-negative bacterial targets is a vital element in treating bacterial infections. Nonetheless, a significant hurdle in achieving this goal is the low permeability of antibiotics and the need for high doses to reach the intended target. This can result in off-target effects. To address this challenge, a thorough understanding and quantification of the permeability barrier of Gram-negative bacteria are imperative [7; 24; 29; 36; 37]. Measuring the uptake of antibiotics across the cell envelope of Gram-negative bacteria is a complicated process [24; 29]. Various experimental techniques have been employed to quantify this process, such as mass spectrometry and fluorescence, which measure uptake at a cellular level, and electrophysiology, which measures uptake at a single-channel stage (see Figure 2). For antibiotics with channel-limited permeation, the flux across a single OmpF or OmpC channel has been measured, with the results indicating uptake rates varying from one to a few hundred molecules per second [37; 38; 39; 40; 54; 164]. However, the lack of appropriate direct assays to measure permeability presents a significant challenge in understanding this barrier. To assist researchers, critical information has compiled in Table 2, including data from different studies involving various membrane proteins from different Gram-negative bacterial species. A larger dataset of single-channel permeabilities under various conditions would be a powerful tool. Additionally, real-time flux rate data across different membrane proteins measured using reversal potential measurements have compiled in Table 3[38; 39; 165; 164; 166]. Further, this electrophysiology assay offers an essential methodology for quantifying the flux of charged antibiotics and antimicrobials through the bacterial cell membrane proteins [37; 40]. This methodology entails the incorporation of one or more membrane channels into classical experiments utilizing an artificial planar lipid bilayer and utilizing the transmembrane potential-driven ion current as a detection probe [37; 38; 39; 40; 54; 163; 164; 165]. An overview of this methodology is provided in Figure 2B. The electrophysiological characteristics of the membrane channels, such as their size, single-channel conductance, channel ion selectivity, and channel gating dynamics, have been well-characterized and provide valuable information for comprehending the transport of small molecules across the bacterial cell membrane [37; 40]. Moreover, the size of the membrane channels plays a crucial role in transporting molecules through the channel and, thus, in antibiotic susceptibility. Developing antibiotics that effectively target Gram-negative bacteria is a complex and challenging undertaking due to the multi-layered cell envelope and the various obstacles active compounds must overcome. Understanding and quantifying the permeability barrier is vital for designing and developing new antibiotics, and compiling experimental data, including electrophysiology measurements, can play a critical role in this process. Figure 2A,B depicts how membrane channels get inserted into a planar lipid bilayer. Figure 2C,D clearly distinguishes when a channel interacts with a particular compound. Please be advised that Figure 2A-D is a unique representation created solely for explanatory purposes. For a comprehensive understanding of the research, kindly refer to the cited sources [40; 54]. Furthermore, the sizing of membrane channels using electrophysiology can provide insights into the maximum size of the molecule it can transport and help evaluate the inner structure, including the constriction site [24; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 83]. In addition, the electrophysiological technique enables the real-time quantification of the transport rate of individual molecules, which is a potent approach for exploring the kinetics of the transport process [15; 83].