## 1 Introduction  
Nanoelectromechanical systems, nanomachines, and nanorobots represent a challenging and future-orientated research area in biomedical engineering. A nanoelectromechanical system (NEMS) is a device that combines electrical and mechanical system behavior at the nanoscale level. The NEMS has electromechanical parts that have been developed on the nanoscale level, such as sensors, actuators, controllers, and drives [1]. Nanorobots are nanoelectromechanical or nanomechatronic systems, which are innovative devices expected to have revolutionary applications in health care, cancer therapy, monitoring, and drug delivery [2]. These nanoelectromechanical systems and nanorobots represent miniaturizations of microelectromechanical systems and microrobots that travel in the human body and can be used in applications to monitor, interact, and control processes at a cellular level. In particular, these robotic applications involve sensing, control, actuation and propulsion, communications, interfacing, programming and coordination at macro, micro, and nano-levels [2]. In the field of biomedical engineering and medicine, microelectromechanical/ nanoelectromechanical systems (MEMS/NEMS) are also called bioMEMS/bioNEMS [3, 4]. with almost unlimited practical applications, e.g., in surgery, drug delivery, or gene therapy [4; 5; 6; 7; 8]. Figure 1 shows a schematic nanoscale comparison of different items in nature, adapted based on material published in [3; 9]. In this work, we chose a voltage-gated potassium ion channel as an example of a biological system at a nanoscale. Ion channels are membrane proteins the size of about 4 nm that enable the passive transport of ions through the cell membrane [10; 11]. Based on the scale depicted in Figure 1, we assumed that the dynamic behavior of the ion channel could be measured and controlled with MEMS/NEMS and/or nanorobots. Depending on the gating mechanism, three main types of ion channels are classified as: voltage-gated, receptor/ligand-gated, and second messenger gated channels [12]. Cells usually express a variety of ion channel types, e.g., there are more than 300 different ion channels in an inner ear cell alone [13]. We here selected a single channel from a voltage-gated ion channel family representing the biological system. Voltage-gated ion channels open (activate) and close depending on the cell membrane potential. Subtypes of voltage-gated ion channels (Nav, Cav, Kv, CLC, and Hv) are specifically selective for sodium (Na\({}^{+}\)), calcium (Ca\({}^{2+}\)), potassium (K\({}^{+}\)), chloride (Cl\({}^{-}\)), and proton (H\({}^{+}\)) channels. Voltage-gated potassium channels are referred to as the giant subtype and denoted as Kv. These Kv channels encode more than 100 human genes [14]. Potassium channels represent the most complex class of voltage-gated channels [15] and are found in basically all types of mammalian cells, such as cells in the nervous, muscular, and immune systems, among others [15; 16; 17; 18]. Each ion channel exhibits a specific dynamic behavior with different physiological and pharmacological properties [15]. In particular, aberrant expression and functionality of various Kv channels in cancer cells have been associated with tumor development and progression. The voltage-gated Kv10.1 potassium channel, encoded by the gene KCNH1 (subfamily H member 1, known as EAG1 or Ether-a-go-go 1), is implicated in various cellular processes, including, for example, cell proliferation [15]. Figure 1: Scales in nature, ranging from micro-systems to nano-systems. An analysis of Kv channel expression in human cancer cells [18] revealed an up-regulation of Kv10.1 in a variety of tumors and can be found in blood, bone, brain, breast, stomach, colon, cervix cancer, and prostate cancers cells, thus providing a novel biomarker candidate and potential oncological target for cancer [5; 19; 20]. For single-channel modeling, we finally selected the Kv10.1 ion channel, as it represents a significant ion channel in cancer development and progression.