PHYSICAL REVIEW E 85, 051910 (2012) Extrusion of small vesicles through nanochannels: A model for experiments and molecular dynamics simulations Martin Bertrand and B´ ela Jo´ os * D´ epartement de Physique, Universit´ e d’Ottawa, Ottawa, Ontario, Canada K1N 6N5 (Received 12 December 2011; revised manuscript received 10 April 2012; published 18 May 2012) We propose a model that predicts the final sizes of lipid bilayer vesicles produced by pressure extrusion through nanochannels and we conduct large-scale coarse-grained molecular dynamics simulations of the phenomenon. We show that, to a first approximation independent of pressure, vesicle size can be predicted by a simple geometrical argument that considers an invariable inner vesicle volume enclosed by a finitely extensible lipid bilayer. The pressure dependence is then incorporated in our model by arguing that the effective channel radius decreases with increasing pressure due to a thickening of the lubrication layer between the vesicles and the channel wall. We fit our model to the experimental data of Patty and Frisken [Biophys. J. 85, 996 (2003)]. We predict that at high pressure, vesicle size significantly depends on channel length and, therefore, flow rate. The CGMD simulations reproduce the physical principles of the model. They also show the build-up of the stress in the vesicle, and typical rupture scenarios as the pressure gradient is increased. DOI: 10.1103/PhysRevE.85.051910 PACS number(s): 87.16.D−, 87.10.Tf, 83.50.−v, 82.70.Uv I. INTRODUCTION Small unilamellar lipid bilayer vesicles (SUVs), or lipo- somes, are often synthesized for research and pharmacological applications [1–3]. One of the most popular techniques to produce such soft objects is the pressure extrusion of a vesicle suspension through an array of nanochannels [2,4–7]. Related to this procedure, a long-standing goal has been to be able to predict the average final size of the extruded liposomes given the parameters of the system, which are: lipid nature, concentration of lipids in suspension, temperature, applied pressure, and radius of the nanochannels. Two models have been proposed: the first by Clerc and Thompson [8] refers to the Rayleigh instability [9] and predicts a final vesicle size larger than observed [5–7] and mostly independent of pressure; the second by Patty and Frisken [7] uses the analogy of blowing a bubble through a hole to describe the initial entry of large vesicles in the smaller nanochannels and derives a prediction from an analysis of the system in static equilibrium. Although this second model successfully fits their data, it requires two free parameters that are not clearly linked to the physics of vesicle pressure extrusion and looks at the problem from a static viewpoint. In contrast to this static description our model includes a dynamic (i.e., rheological) description of the extrusion. Pressure extrusion involves multiple passages through nanochannels, and we can assume that in the final passages, vesicles mostly unilamellar, flow in and out without breaking and their shape goes back and forth between a spheroid outside of the channels and a spherocylinder inside. The spherocylinder has a greater area than the sphere of equal volume. The final vesicles are of a size such that the lipid bilayer can tolerate this area difference. We show that to a first approximation, this prediction is valid. We then incorporate the effects of pressure in our simple geometrical argument using elements of a model of spherocylindrical vesicles flowing in narrow channels developed by Bruinsma [10] to predict * bjoos@uottawa.ca the final sizes of extruded vesicles as pressure is increased. This idea was mentioned by Hunter and Frisken [5] but not exploited. Flow being involved here, it is expected that the length of the channels would be an important parameter in the process. Frisken et al. [6] find that at low pressure, doubling the length of the channels does not significantly influence the final sizes of the produced vesicles. Our model corroborates experimental evidence at lower pressures but predicts that there is a length dependence at high pressure, which suggests further experimental investigation. Our model can also explain the small dependence in lipid concentration observed [6]. In addition to the rheological model, we performed out of equilibrium coarse-grained molecular dynamics simulations of vesicle extrusion to confirm our geometrical argument, to corroborate some main elements of Bruinsma’s theory [10], and to describe the initial entry of a large vesicle in a nanochannel and its subsequent rupture. Although the extrusion of vesicles [11] and erythrocytes [12] has been simulated in the past, to the best of our knowledge, no true bilayer vesicle in an explicit solvent has ever been simulated in such a context. We leverage the computing power of graphical processing units (GPUs) to make this feasible in a relatively short time frame. Our model and study should be useful to experimentalists considering pressure extrusion as a means to produce lipo- somes, but also to the large community studying the flow of diverse cells in and out of narrow channels such as red blood and plasma cells flowing in narrow capillaries. II. EXTRUSION MODEL The production of liposomes or SUVs through pressure extrusion consists in starting with a suspension of large and possibly multilamellar vesicles (MLVs) that is pushed by a pressure drop P multiple times through an array of nanochannels of average radius R p and length L p as seen in Fig. 1 (typically 10–15 times [5–7]). For every passage through the extruder there is an ever-diminishing drop in the average vesicle size (see Fig. 1 in the article by Frisken et al. [6]). 051910-1 1539-3755/2012/85(5)/051910(8) ©2012 American Physical Society