Flip-flop Rate Research Articles

1H NMR Shows Slow Phospholipid Flip-Flop in Gel and Fluid Bilayers.

We measured the transbilayer diffusion of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) in large unilamellar vesicles, in both the gel (Lβ′) and fluid (Lα) phases. The choline resonance of headgroup-protiated DPPC exchanged into the outer leaflet of headgroup-deuterated DPPC-d13 vesicles was monitored using 1H NMR spectroscopy, coupled with the addition of a paramagnetic shift reagent. This allowed us to distinguish between the inner and outer bilayer leaflet of DPPC, to determine the flip-flop rate as a function of temperature. Flip-flop of fluid-phase DPPC exhibited Arrhenius kinetics, from which we determined an activation energy of 122 kJ mol–1. In gel-phase DPPC vesicles, flip-flop was not observed over the course of 250 h. Our findings are in contrast to previous studies of solid-supported bilayers, where the reported DPPC translocation rates are at least several orders of magnitude faster than those in vesicles at corresponding temperatures. We reconcile these differences by proposing a defect-mediated acceleration of lipid translocation in supported bilayers, where long-lived, submicron-sized holes resulting from incomplete surface coverage are the sites of rapid transbilayer movement.

Bilayer Defects Facilitate DPPC Flip-Flop

We measured the flip-flop rate of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) in large unilamellar vesicles (LUVs) as a function of temperature. The transbilayer distribution of headgroup-protiated DPPC exchanged into the outer leaflet of headgroup-deuterated DPPC vesicles was monitored using 1H NMR spectroscopy coupled with the addition of a paramagnetic shift reagent, which allowed us to distinguish between inner and outer leaflet lipids. After careful determination of structure and thermotropic behavior of this system, we determined the fluid-phase flip-flop activation energy Ea to be 123 kJ/mol. This is the first report of probe-free fluid phase flip-flop kinetics for DPPC in freely floating vesicles. No flip-flop was observed over the course of 6 days when DPPC was incubated below the main transition temperature, and consequently gel phase thermodynamic values could not be determined in LUVs. This result is in contrast with previous studies using supported bilayers that reported fast flip-flop in the gel phase. To further investigate this discrepancy, we measured DPPC LUVs incubated within the main transition temperature, and found accelerated flip-flop (i.e., faster rates than were found just above the main transition temperature). We conclude that bilayer defects such as gel/fluid domain boundaries accelerate lipid flip-flop. We speculate that sample environment and measurement conditions that can alter the physical properties of bilayers have contributed to flip-flop discrepancies in literature.

Structure-Kinetic Relationships of Passive Membrane Permeation from Multiscale Modeling.

Passive membrane permeation of small molecules is essential to achieve the required absorption, distribution, metabolism, and excretion (ADME) profiles of drug candidates, in particular intestinal absorption and transport across the blood-brain barrier. Computational investigations of this process typically involve either building QSAR models or performing free energy calculations of the permeation event. Although insightful, these methods rarely bridge the gap between computation and experiment in a quantitative manner, and identifying structural insights to apply toward the design of compounds with improved permeability can be difficult. In this work, we combine molecular dynamics simulations capturing the kinetic steps of permeation at the atomistic level with a dynamic mechanistic model describing permeation at the in vitro level, finding a high level of agreement with experimental permeation measurements. Calculation of the kinetic rate constants determining each step in the permeation event allows derivation of structure-kinetic relationships of permeation. We use these relationships to probe the structural determinants of membrane permeation, finding that the desolvation/loss of hydrogen bonding required to leave the membrane partitioned position controls the membrane flip-flop rate, whereas membrane partitioning determines the rate of leaving the membrane.

The Ins and Outs of Lipid Flip-Flop.

Our current view of cellular membranes centers on the fluid-mosaic model, which envisions the cellular membrane as a "liquidlike" bilayer of lipids, cholesterol, and proteins that freely diffuse in two dimensions. In stark contrast, the exchange of materials between the leaflets of a bilayer was presumed to be prohibited by the large enthalpic barrier associated with translocating hydrophilic materials, such as a charged lipid headgroup, through the hydrophobic membrane core. This static picture with regard to lipid translocation (or "flip-flop" as it is affectionately known) has been a long-held belief in the study of membrane dynamics. The current accepted membrane model invokes specific protein flippase (inward moving), floppase (outward moving), and scramblase (bidirectional) enzymes that assist in the movement of lipids between the leaflets of cellular membranes. The low rate of protein-free lipid flip-flop has also been a cornerstone of our understanding of the bilateral organization of cellular membrane components, specifically the asymmetric distribution of lipid species found in the luminal and extracellular leaflets of the plasma membrane of eukaryotic cells. Much of the previous work contributing to our current understanding of lipid flip-flop has utilized fluorescent- or spin-labeled lipids. However, there is growing evidence that these lipid probes do not accurately convey the dynamics and thermodynamics of native (unlabeled) lipid motion. This Account summarizes our research efforts directed toward developing a deep physical and chemical understanding of protein-free lipid flip-flop in phospholipid membrane models using sum-frequency vibrational spectroscopy (SFVS). Our use of SFVS enables the direct measurement of native lipid flip-flop in model membranes. In particular, we have explored the kinetic rates and activation thermodynamics of lipid translocation as a means of deciphering the underlying chemical and physical directors governing this process. By means of transition state theory, the contributions from enthalpy and entropy on the activation energy barrier to lipid flip-flop have been explored in detail for a variety of lipid species and membrane compositions. Specifically, the effect of lipid structure and packing and the inclusion of cholesterol and transmembrane peptides on the rates and thermodynamics of lipid translocation have been investigated in detail. It is our hope that these studies will provide a new perspective on lipid translocation in biological membranes and the role of lipid flip-flop in generating and maintaining cell membrane lipid asymmetry.

Transport and Organization of Cholesterol in a Planar Solid-Supported Lipid Bilayer Depend on the Phospholipid Flip-Flop Rate

Understanding the transport behavior of the cholesterol molecules within a cell membrane is a key challenge in cell biology at present. Here, we have applied sum frequency generation vibrational spectroscopy to characterize the transport and organization of cholesterol in different kinds of planar solid-supported lipid bilayers by combining achiral- and chiral-sensitive polarization measurements. This method allows us to distinguish the organization of cholesterol in tail-to-tail, head-to-tail, head-to-head, and side-by-side manners. It is found that the movement of cholesterol in the lipid bilayer largely depends on the flip-flop rate of the phospholipid. The flip-flop dynamics of the phospholipid and cholesterol are synchronous. In the solid-supported zwitterionic phosphocholine lipid bilayer, the cholesterol molecules flip quickly from the distal leaflet to the neutral proximal leaflet of the bilayer and form tail-to-tail organization on both leaflets. The phosphocholine lipid and cholesterol show the same flip-flop rate. However, when the proximal leaflet is prepared using negative glycerol phospholipids, cholesterol organizes itself by mainly forming an α-β structure on the distal leaflet. Because of the strong interaction between the glycerol phospholipid and the substrate, no or only partial cholesterol molecules flip from the distal leaflet to the negatively charged proximal leaflet. However, the cholesterol molecules undergo flip-flop in the presence of salt solution because the ions weaken the interaction between the negative phospholipid and the substrate.

Direct Measurement of the Flip-Flop Rate of Electron Spins in the Solid State

Direct Measurement of the Flip-Flop Rate of Electron Spins in the Solid State

Optical nuclear spin polarization in quantum dots**Project partially supported by the National Natural Science Foundations of China (Grant Nos. 11374039 and 11174042) and the National Basic Research Program of China (Grant Nos. 2011CB922204 and 2013CB632805).

Hyperfine interaction between electron spin and randomly oriented nuclear spins is a key issue of electron coherence for quantum information/computation. We propose an efficient way to establish high polarization of nuclear spins and reduce the intrinsic nuclear spin fluctuations. Here, we polarize the nuclear spins in semiconductor quantum dot (QD) by the coherent population trapping (CPT) and the electric dipole spin resonance (EDSR) induced by optical fields and ac electric fields. By tuning the optical fields, we can obtain a powerful cooling background based on CPT for nuclear spin polarization. The EDSR can enhance the spin flip–flop rate which may increase the cooling efficiency. With the help of CPT and EDSR, an enhancement of 1300 times of the electron coherence time can be obtained after a 10-ns preparation time.

The Flip-Flop Diffusion Mechanism across Lipids in a Hybrid Bilayer Membrane

In this study, we examine the mechanism of flip-flop diffusion of proton carriers across the lipid layer of a hybrid bilayer membrane (HBM). The HBM consists of a lipid monolayer appended on top of a self-assembled monolayer containing a Cu-based O2 reduction catalyst on a Au electrode. The flip-flop diffusion rates of the proton carriers dictate the kinetics of O2 reduction by the electrocatalyst. By varying both the tail lengths of the proton carriers and the lipids, we find the combinations of lengths that maximize the flip-flop diffusion rate. These experimental results combined with biophysical modeling studies allow us to propose a detailed mechanism for transmembrane flip-flop diffusion in HBM systems, which involves the bending of the alkyl tail of the proton carrier as the rate-determining step. Additional studies with an unbendable proton carrier further validate these mechanistic findings.

Dynamic and mechanical properties of supported lipid bilayers.

Supported lipid bilayers (SLBs) offer an excellent model system for investigating the physico-chemical properties of the cell membrane. In this work, dynamic and mechanical properties of SLBs are explored by dissipative particle dynamics simulations for lipids with different architectures (chain length, kink, and asymmetry associated with lipid tails). It is found that the lateral diffusivity (Dx) and flip-flop rate (FF) grow with increasing temperature in both gel and liquid phases and can be described by an Arrhenius-like expression. Three regimes can be clearly identified for symmetric and asymmetric saturated lipids but only two regimes are observed for kinked lipids. Both Dx and FF grow with decreasing tail length and increasing number of kinks. The stretching (KA) and apparent bending (KB) moduli exhibit concave upward curves with temperature and the minima are attained at Tm. In general, the minima of KA and KB decrease with the chain length and increase with number of kinks. The typical relation among the bending modulus, area stretching modulus, and bilayer thickness is still followed, KB = βKAh(2) and β is much smaller in the gel phase. The dynamic and mechanical properties of lipids with asymmetric tails are found to situate between their symmetric counterparts.

Structural Origins of Cholesterol Accelerated Lipid Flip-Flop Studied by Sum-Frequency Vibrational Spectroscopy.

The unique structure of cholesterol and its role in modulating lipid translocation (flip-flop) were examined using sum-frequency vibrational spectroscopy (SFVS). Two structural analogues of cholesterol--cholestanol and cholestene--were examined to explore the influence of ring rigidity and amphiphilicity on controlling distearoylphosphocholine (DSPC) flip-flop. Kinetic rates for DSPC flip-flop were determined as a function of sterol concentration and temperature. All three sterols increased the rate of DSPC flip-flop in a concentration-dependent manner following the order cholestene > cholestanol > cholesterol. Rates of DSPC flip-flop were used to calculate the thermodynamic activation free energy barrier (ΔG(‡)) in the presence of cholesterol, cholestanol, and cholestene. The acyl chain gauche content of DSPC, mean lipid area, and membrane compressibility were correlated to observed trends in ΔG(‡). ΔG(‡) for DSPC flip-flop showed a strong positive correlation with the molar compression modulus (K*) of the membrane, influenced by the type and concentration of the sterol added. Interestingly, cholesterol is distinctive in maintaining invariant membrane compressibility over the range of 2-10 mol %. The results in this study demonstrate that the compression modulus of a membrane plays a significant role in moderating ΔG(‡) and the kinetics of native, protein-free, lipid translocation in membranes.

Assessing Asymmetry in Detergent-Lipid Interactions with Isothermal Titration Calorimetry

Most of the extensively characterized detergents redistribute rapidly between the two membrane leaflets after partitioning into the membrane bilayer. Interactions between such detergents and the membrane are classically described by the three-stage model: with increasing detergent content, a saturation boundary marks the appearance of micelles and a solubilization boundary marks the absence of vesicles. These boundaries are commonly probed by methods such as turbidimetry, NMR, fluorescence spectroscopy, and isothermal titration calorimetry (ITC). However, many important detergents do not translocate easily in the bilayer and thus have slow flip-flop rates. Mechanisms such as “cracking in,” “micellar solubilization,” and “shedding” have been proposed to explain their solubilization of lipid membranes. The asymmetric distribution of detergents in the membrane has been quantified by ITC uptake and release experiments, NMR, and zeta potential measurements. Here we present ITC solubilization experiments as another approach to characterize detergents with such asymmetry. POPC and 12:0 lysophosphocholine are used as a model system where parameters such as the partition coefficient, enthalpy of detergent transfer from the aqueous to the bilayer phase, and the maximum fraction of detergent supported by the bilayer are determined. Understanding the interactions between these non-equilibrating detergents and the membrane is of fundamental importance as many of these detergents are involved in key biological processes and in membrane protein studies.

Integrating DIY and Traditional Biochemical Laboratory Experiences into an Undergraduate Biophysics Course

Many undergraduate physics majors will go directly to industry after graduation. Incorporating laboratory research into senior level courses facilitates the teaching of interdisciplinary skills such as designing experiments, careful measurement, and troubleshooting experimental difficulties. In addition to these skills hacking and making are also valuable for physics majors seeking employment directly after graduation. Two experiments were utilized to engage students in building these skills. In the first, traditional biochemical studies of phase behavior in lipid membranes was done with fluorescent probes. Fluorescence spectroscopy assays were used to measure main chain phase transitions in lipid bilayers and transbilayer flip-flop rates for phospholipid/cholesterol liposomes. Results from both assay experiments were compiled across teams of students. Each student was also responsible for producing a technical written lab report focusing on the experimental methods and results. In a second experience students attempted to build a Brewster Angle microscope using 3D printed parts and a simple cell phone camera. This project introduced students to CAD software and 3D printing.

Enzyme-coupled assays for flip-flop of acyl-Coenzyme A in liposomes

Acyl-Coenzyme A is made in the cytosol. Certain enzymes using acyl-CoA seem to operate in the lumen of the ER but no corresponding flippases for acyl-CoA or an activated acyl have been described. In order to test the ability of purified candidate flippases to operate the transport of acyl-CoA through lipid bilayers in vitro we developed three enzyme-coupled assays using large unilamellar vesicles (LUVs) obtained by detergent removal. The first assay uses liposomes encapsulating a water-soluble acyl-CoA:glycerol-3-phosphate acyl transferase plus glycerol-3-phosphate (G3P). It measures formation of [3H]lyso-phosphatidic acid inside liposomes after [3H]palmitoyl-CoA has been added from outside. Two other tests use empty liposomes containing [3H]palmitoyl-CoA in the inner membrane leaflet, to which either soluble acyl-CoA:glycerol-3-phosphate acyl transferase plus glycerol-3-phosphate or alkaline phosphatase are added from outside. Here one can follow the appearance of [3H]lyso-phosphatidic acid or of dephosphorylated [3H]acyl-CoA, respectively, both being made outside the liposomes. Although the liposomes may retain small amounts of detergent, all these tests show that palmitoyl-CoA crosses the lipid bilayer only very slowly and that the lipid composition of liposomes barely affects the flip-flop rate. Thus, palmitoyl-CoA cannot cross the membrane spontaneously implying that in vivo some transport mechanism is required.

Qualitative and Quantitative Analyses of the Molecular-Level Interaction between Memantine and Model Cell Membranes

Sum frequency generation (SFG) vibrational spectroscopy was employed to study the interaction between memantine (a water-soluble drug for treating Alzheimer’s disease) and lipid bilayers (including zwitterionic PC and negatively charged PG lipid bilayers) at the molecular level in real time and in situ. SFG results revealed how the memantine affected these lipid bilayers in terms of the lipid dynamics, average tilt angle (θ), as well as angle distribution width (σ). It was found that memantine could adsorb onto the zwitterionic PC surface but did not affect the flip-flop rate of the PC bilayer even in the presence of 5.0 mM memantine, indicating the negligible interaction between memantine and the PC bilayer. However, for the negatively charged PG bilayer, it was found that the outer PG leaflet could be significantly destroyed by memantine at a relatively low memantine concentration (1.0 mM), while the inner PG leaflet remained intact. Besides, the θ and σ of CD3 groups in the outer PG lipid leaflet were calculated to be ∼82.0° and ∼19.5° after adding 5 mM memantine, respectively, indicating that these CD3 groups were prone to lie down at the membrane surface (versus the surface normal) with the addition of 5 mM memantine while nearly standing up without the addition of drug molecules. These monolayer- and molecular-level results could hardly be obtained by other techniques. To the best of our knowledge, this is the first experimental attempt to quantify the drug-induced orientational changes of lipid molecules within a lipid bilayer. The present work provided an in-depth understanding on the interaction between memantine and model cell membranes, which will potentially benefit the development of new drugs for neurodegenerative diseases involving drug–membrane interaction.

Understanding Miltefosine-Membrane Interactions Using Molecular Dynamics Simulations.

Coarse-grained molecular dynamics simulations are used to calculate the free energies of transfer of miltefosine, an alkylphosphocholine anticancer agent, from water to lipid bilayers to study its mechanism of interaction with biological membranes. We consider bilayers containing lipids with different degrees of unsaturation: dipalmitoylphosphatidylcholine (DPPC, saturated, containing 0%, 10%, and 30% cholesterol), dioleoylphosphatidylcholine (DOPC, diunsaturated), palmitoyloleoylphosphatidylcholine (POPC, monounsaturated), diarachidonoylphosphatidylcholine (DAPC, polyunsaturated), and dilinoleylphosphatidylcholine (DUPC, polyunsaturated). These free energies, calculated using umbrella sampling, were used to compute the partition coefficients (K) of miltefosine between water and the lipid bilayers. The K values for the bilayers relative to that of pure DPPC were found to be 5.3 (DOPC), 7.0 (POPC), 1.0 (DAPC), 2.2 (DUPC), 14.9 (10% cholesterol), and 76.2 (30% cholesterol). Additionally, we calculated the free energy of formation of miltefosine-cholesterol complexes by pulling the surfactant laterally in the DPPC + 30% cholesterol system. The free energy profile that we obtained provides further evidence that miltefosine tends to associate with cholesterol and has a propensity to partition into lipid rafts. We also quantified the kinetics of the transport of miltefosine through the various bilayers by computing permeance values. The highest permeance was observed in DUPC bilayers (2.28 × 10(-2) m/s) and the lowest permeance in the DPPC bilayer with 30% cholesterol (1.10 × 10(-7) m/s). Our simulation results show that miltefosine does indeed interact with lipid rafts, has a higher permeability in polyunsaturated, loosely organized bilayers, and has higher flip-flop rates in specific regions of cellular membranes.

Characterization of thylakoid lipid membranes from cyanobacteria and higher plants by molecular dynamics simulations

The thylakoid membrane is mainly composed of non-common lipids, so called galactolipids. Despite the importance of these lipids for the function of the photosynthetic reaction centers, the molecular organization of these membranes is largely unexplored. Here we use multiscale molecular dynamics simulations to characterize the thylakoid membrane of both cyanobacteria and higher plants. We consider mixtures of up to five different galactolipids plus phosphatidylglycerol to represent these complex membranes. We find that the different lipids generally mix well, although nanoscale heterogeneities are observed especially in case of the plant membrane. The fluidity of the cyanobacterial membrane is markedly reduced compared to the plant membrane, even considering elevated temperatures at which thermophilic cyanobacteria are found. We also find that the plant membrane more readily undergoes a phase transformation to an inverted hexagonal phase. We furthermore characterized the conformation and dynamics of the cofactors plastoquinone and plastoquinol, revealing of the fast flip-flop rates for the non-reduced form. Together, our results provide a molecular view on the dynamical organization of the thylakoid membrane.

Computer Simulations of Lipid Flip-Flop and Membrane Asymmetry

Computer simulations of model membranes give detailed information about the structure and dynamics of lipids. Although typical phospholipids have very slow flip-flop rates compared to molecular dynamics time scales of microseconds, flip-flop can be simulated by a combination of free energy calculations and kinetic information. Less polar lipids and sterols have flip-flop rates that are within direct reach of coarse-grained simulations with the Martini model. Flip-flop of phospholipids involves significant defects in membranes that are also relevant for other transport properties and the mechanism of membrane perturbing peptides. I will summarize the results of a substantial body of simulations in this area and highlight a number of current directions.

Phosphatidylglycerol Asymmetry and Translocation in Lipid Membranes

Our current understanding of the structure and dynamics of cellular membranes emerged in the early 1970 's. However, there is still much we do not know about the underlying lipid dynamics in cellular membranes, specifically the process of lipid translocation or flip-flop. The flip-flop rates of only a few lipid species, principally phosphatidylcholines (PCs), have been measured. Anionic lipids, such as phosphatidylseryine (PS), phosphatidylinositol (PI), and phosphatidylglycerol (PG), are known to be play active roles in membrane function, but almost nothing is known of the rates of translocation of these species. While PS and PI are the major anionic lipids of eukaryotic cellular membranes, PG is mainly found in prokaryotic membranes and comprises about 10% of the phospholipid content of the mitochondria membrane in eukaryotes. In the work presented here, the native flip-flop rates of 1,2-diasterol-sn-glycero-3-[phospho-(1′-rac-glycerol)] (DSPG) flip-flop in mixed DSPG: 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) bilayers have been investigated. Using methods of classical surface chemistry coupled with nonlinear optical methods, we have developed a novel analytical approach, using sum-frequency vibrational spectroscopy (SFVS), to selectively probe lipid compositional asymmetry in a planar supported lipid bilayer. This new method allows for the detection of lipid flip-flop kinetics and compositional asymmetry without the need for a fluorescent or spin-labeled lipid species by exploiting the coherent nature of SFVS. Using SFVS, the rates of DSPG flip-flop in a DSPC matrix have been examined for the first time. Analysis of the dynamics provides an assessment of the underlying energetic barrier to PG translocation. The results will be discussed in the framework of the protein-free energetic barriers to PG flip-flop and the role of electrostatics in this process.

Efficient dynamic nuclear polarization of phosphorus in silicon in strong magnetic fields and at low temperatures

Efficient manipulation of nuclear spins is important for utilizing them as qubits for quantum computing. In this work we report record high polarizations of ${}^{31}\mathrm{P}$ and $^{29}\mathrm{Si}$ nuclear spins in P-doped silicon in a strong magnetic field (4.6 T) and at temperatures below 1 K. We reached ${}^{31}\mathrm{P}$ nuclear polarization values exceeding $98%$ after 20 min of pumping the high-field electron spin resonance (ESR) line with a very small microwave power of 0.4 $\ensuremath{\mu}\mathrm{W}$. We evaluate that the ratio of the hyperfine-state populations increases by three orders of magnitude after 2 hours of pumping, and an extremely pure nuclear spin state can be created, with less than 0.01 ppb impurities. A negative dynamic nuclear polarization has been observed by pumping the low-field ESR line of ${}^{31}\mathrm{P}$ followed by the flip-flip cross relaxation, the transition which is fully forbidden for isolated donors. We estimate that while pumping the ESR transitions of ${}^{31}\mathrm{P}$ also the nuclei of $^{29}\mathrm{Si}$ get polarized, and polarization exceeding $60%$ has been obtained. We performed measurements of relaxation rates of flip-flop and flip-flip transitions which turned out to be nearly temperature independent. Temperature dependence of the ${}^{31}\mathrm{P}$ nuclear relaxation was studied down to 0.75 K, below which the relaxation time became too long to be measured. We found that the polarization evolution under pumping and during relaxation deviates substantially from a simple exponential function of time. We suggest that the nonexponential polarization dynamics of ${}^{31}\mathrm{P}$ donors is mediated by the orientation of $^{29}\mathrm{Si}$ nuclei, which affect the transition probabilities of the forbidden cross-relaxation processes.

Flip-flop of oleic acid in a phospholipid membrane: rate and mechanism.

Flip-flop of protonated oleic acid molecules dissolved at two different concentrations in membranes made of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine is studied with the aid of molecular dynamics simulations at a time scale of several microseconds. Direct, single-molecule flip-flop events are observed at this time scale, and the flip-flop rate is estimated at 0.2-0.3 μs(-1). As oleic acid molecules move toward the center of the bilayer during flip-flop, they undergo gradual, correlated translational, and rotational motion. Rare, double-flipping events of two hydrogen-bonded oleic acid molecules are also observed. A two-dimensional free energy surface is obtained for the translational and rotational degree of freedom of the oleic acid molecule, and the minimum energy path on this surface is determined. A barrier to flip-flop of ~4.2 kcal/mol is found at the center of the bilayer. A two-dimensional diffusion model is found to provide a good description of the flip-flop process. The fast flip-flop rate lends support to the proposal that fatty acids permeate membranes without assistance of transport proteins. It also suggests that desorption rather than flip-flop is the rate-limiting step in fatty acid transport through membranes. The relation of flip-flop rates to the evolution of ancestral cellular systems is discussed.