11Measurements of membrane protein structure and function often rely on reconstituting the protein 12 into lipid bilayers through the formation of liposomes. Many measurements conducted in 13 proteoliposomes, e.g. transport rates, single-molecule dynamics, monomer-oligomer equilibrium, 14 require some understanding of the occupancy statistics of the liposome population for correct 15 interpretation of the results. In homogenous liposomes, this is easy to calculate as the act of protein 16 incorporation can be described by the Poisson distribution. However, in reality, liposomes are 17 heterogeneous, which alters the statistics of occupancy in several ways. Here, we determine the 18 liposome occupancy distribution for membrane protein reconstitution while taking into account 19 liposome size heterogeneity. We calculate the protein occupancy for a homogenous population of 20 liposomes with radius r = 200 nm, representing an idealization of vesicles extruded through 400 21 nm pores and compare it to the right-skewed distribution of 400 nm 2:1 POPE:POPG vesicles. As 22 than one protein at higher protein/lipid densities. These results demonstrate that the occupancy 32 distributions of membrane proteins into vesicles can be accurately predicted in heterogeneous 33 populations with experimental knowledge of the liposome size distribution. 34 35 Keywords 36 Liposome size distribution, Poisson, membrane protein, reconstitution, single-molecule 37 photobleaching, CLC-ec1 38 39 Abbreviations 40micelle concentration. From this mixed-micelle condition, the detergent is then slowly removed 63 by dialysis, resulting in the formation of bilayers with the protein incorporated within, that then 64 assemble into self-contained liposomes (4). 65
66One of the benefits of the compartmentalized structure of liposomes is that it enables the 67 establishment of gradients across the membrane, which allows interrogation of the protein's 68 function (5, 6). One limitation, is that dialysis methods typically generate small, unilamellar 69 vesicles (7) that incorporate the protein according to the state in the mixed micelle condition. Since 70 liposomes do not spontaneously exchange with one another on a reasonable time scale, this means 71 that the protein state that is examined in the resultant proteoliposome population may not reflect 72 equilibrium. This presents an issue for considering stoichiometry of the protein, particularly at 73 'Poisson-dilutions' where most of the liposomes are unoccupied or have a single protein species. 74However, this is the range of dilution that is most desirable when considering protein function, as 75 the membrane transport behavior reflects a single-molecule and so unitary transport rates can be 76 estimated (8). Still, when investigating the function of the native assembly, it is advantageous to 77 capture the equilibrium state of the protein in the membrane into single vesicles for further analysis 78 of function and dynamics. 79
80One way of doing this is by taking the small unilamellar liposomes from ...