## 1 Introduction  
The introduction of carbon nanoparticles into the biotechnological and biomedical fields has opened a large number of applications, such as biosensors and drug carriers [1; 2; 3; 4; 5; 6; 7; 8]. One such kind of nanomaterial is the carbon nanotube (CNT), which can deliver peptides [6; 8], proteins [4], and nucleic acids [5] to different cells. Ahead of these applications, understanding the interactions between CNTs and phospholipid membranes is fundamentally essential for avoiding its adverse effects, since CNTs may be toxic. Therefore, present studies are mainly focused on cytotoxicity and its interactions with cell membranes [9; 10; 11; 12]. For example, experiments have demonstrated that CNTs induce oxidative damage to lipids in lung membranes [13] and the formation of reactive oxygen species in vivo and in vitro [14; 15]. CNTs have also been found to enter both animal and plant cells [16; 17], but the internalization mechanism is still not clear. Two very recent works show that short CNTs can transport water, protons, and small ions after the spontaneous insertion into the live cell membranes [18]. Meanwhile, the embedded CNTs possess ion selectivity that can be tuned by pH values and ion concentrations [19]. These reports demonstrate that CNTs in the membrane can transport small molecules through their hollow channels [20].  
In recent years, molecular dynamics (MD) simulation has been employed to explore the interactions between carbon nanoparticles and lipid membranes [21; 22; 23; 24; 25]. Particularly, how CNTs land on, bind to, and translocate through cell membrane are systematically studied by MD simulations [26; 27; 28]. For example, [PERSON] and [PERSON] performed steered MD with a coarse-grained model to simulate the penetration of the dipalmitoylphosphatidylcholine (DPPC) bilayer by CNTs, and they observed that lipids were extracted from the bilayer and blocked the tube [23]. However, the penetration was not spontaneous but exerted by an external force to pull the nanotube through the bilayer. [PERSON] et al. reported the presence of CNTs in the bilayer reduced the mobility of lipids and perturbed the structure of interfacial water, using all-atom MD simulations [24]. It should be noted that the CNTs are initially embedded in the lipid bilayer. [PERSON] et al. performed MD simulations to explore the internalization of functionalized CNTs (FCNTs) into a model lipid bilayer as a function of their length [26; 27]. They found the hydrophobicity was one of the key factors responsible for the insertion process. However, experiments conducted by [PERSON] et al. showed that electrostatic interactions between the hydrophilic and charged functional moieties of FCNTs and the polar headgroups of the lipid membranes were the major contributors to the insertion process [28]. Obviously, they are contradictory.  
In this work, we first repeated the simulations on the interactions between CNTs and lipid membranes. Then, we studied the effects of CNTs on membrane structure and membrane protein. Finally, we performed MD simulations to investigate the transport properties of CNTs when embedded in the bilayer center. We observed that pristine CNT (PCNT) could readily enter the membrane and stay therein without specific orientation. When functionalized CNT (FCNT) was embedded in the membrane, FCNT preferred to locate vertically. CNTs in the lipid bilayer may block membrane proteins. However, CNTs can act as artificial channels to transport water, ions, and small molecules. Taking carbon dioxide (CO\({}_{2}\)) and urea as model small molecules, we found CO\({}_{2}\) could enter both PCNT and FCNT hollow channels because of their hydrophobic interior, while urea molecules were found it much difficult to fill the FCNT.