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Flip-Flop of Oleic Acid in a Phospholipid Membrane: Rate and Mechanism Chenyu Wei, and Andrew Pohorille J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp508163e • Publication Date (Web): 16 Oct 2014 Downloaded from http://pubs.acs.org on October 24, 2014

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The Journal of Physical Chemistry

Flip-Flop of Oleic Acid in a Phospholipid Membrane: Rate and Mechanism

Chenyu Wei1,3* and Andrew Pohorille2,3* 1

NASA Ames Research Center, Mail Stop 229-1, Moffett Field, CA 94035, USA

2

NASA Ames Research Center, Mail Stop 239-4, Moffett Field, CA 94035, USA

3

Department of Pharmaceutical Chemistry, University of California San Francisco

*Corresponding authors: [email protected]; [email protected]

ACS Paragon Plus Environment


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Abstract

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 towards 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.

Keywords: flip-flop process, fatty acid, lipid membrane, vesicle, proton transport


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Introduction

Flip-flop of amphiphilic molecules in bilayer membranes is their traverse motion from one leaflet to the other accompanied by a mirror-image change of orientation.1 It is a key step in the transport of fatty acids across cell membrane walls that is involved in a number of cellular functions, and in particular in generating energy for metabolic processes inside cells.2-4 It also provides a path to fatty acid-mediated proton transfer through membranes, whereby the hydroxyl proton from a protonated fatty acid molecule in the outer leaflet is released to the cell interior following flip-flop to the inner leaflet.5-10 Flip-flop of fatty acids has also been found to play a role in determining shapes of vesicles.11

Even though the kinetics of fatty acid flip-flop has been a subject of extensive studies, the debate regarding whether this process is fast or slow continues,7,12-17 and the exact flipflop rate is not clear. Recent experiments by Thomas et al.14 suggest that flip-flop of protonated fatty acid molecules is very fast with the half time t1/ 2 < 5 ms for oleic acid. Similar estimates ( t1/ 2 < 10-25 ms) follow from studies of Kamp et al.13 and Simard et al.15 Measurements by Carley and Kleinfeld,17 however, suggest a markedly slower flipflop rate (k ~ 4s-1). Discrepancies in the measured rate seem to be due to difficulties in tracking molecular motions on fast time scales and interpretations of measurements. Understanding the kinetics and thermodynamics of flip-flop is essential for assessing whether this process or desorption from the membrane surface is the rate limiting step in fatty acids transport, an issue that remains controversial.16, 17 Further, it helps to establish



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whether this transport is fully unassisted or, alternatively, is mediated by membrane proteins, as fast flip-flop rates would argue for the former.3

Recently, a number of influential papers have indicated that flip-flop of fatty acids might have played a role in the emergence of Darwinian evolution at the origin cellular level.10,18-22 Several lines of evidence indicate that ancestors of cells were built of membranes simpler than phospholipid bilayers, most likely containing a considerable fraction of fatty acids.23-25 A number of processes inducing competitive growth and subsequent division have been identified in such vesicles, such as by stressing vesicles osmotically with encapsulated replicator of nucleic acids,19 adsorption of small peptides generated inside vesicles,22 photochemically driven redox chemistry,21 or incorporation of a small amount of phospholipids into the vesicle membrane.20 All vesicle-growth processes would involve adsorption of fatty acids from the environment and their subsequent flip-flop to equilibrate the composition of both leaflets of the bilayer. The kinetics of flip-flop compared to the kinetics of other, competitive processes determines whether vesicle growth actually occurs.

Computer simulations can help to answer the question about the rates and mechanisms of fatty-acid flip-flops in membranes. So far, however, they have been mainly used to aid to our understanding of this process for steroids.26-31 In those studies, the flip-flop rates were determined indirectly through free energy calculations29-31 or were obtained from coarse grained molecular dynamics (MD) simulations28 that employed a simpler, less accurate descriptions of molecular interactions than atomic-level MD.


To overcome these

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shortcomings, we investigate the flip-flop process of oleic acid (OA), one of the most abundant fatty acids in nature, in a phospholipid bilayer through atomic-level MD simulations that extend to time scales of several microseconds. This is sufficient to observe a considerable number of flip-flop events and determine the free energy profile for this process.

From a theoretical standpoint, the flip-flop process is an interesting case to test the applicability of diffusion models, such as the ones based on the Fokker-Planck or Smoluchoski equations.32 These models have been widely applied to biophysical systems, in which the kinetics of a process of interest is described as a stochastic one on a free energy landscape defined by only a few chosen coordinates. Not only do they lead to a better understanding of rare events on multi-dimension free energy landscapes but also can be used, in combination with atomic-level simulations, to obtain improved estimates of kinetic parameters. From diffusion models, a number of dynamic properties can be obtained, including transition rates between (meta)stable states of the system, calculated for example by way of Kramers’ escape rate,33 and the most probable transition path.34-36 Application of diffusion models to membrane-related phenomena include calculations of permeability of membranes to solutes,37-41 ion transports through protein channels42-44 and flip-flop of steroids.28-31 In this study, transition rates and the most probable transition path predicted from a simple diffusion model are compared with the rates and paths obtained from MD simulations, thus providing a direct test of this model.



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Methods Molecular dynamics simulation Two 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membrane systems containing a small fraction of OA molecules were simulated. One system, further abbreviated POPC-10-OA, had 3% mole fraction of OA, and included 264 POPC molecules, 10 OA molecules, and 16228 water molecules. In the second system, called POPC-68-OA, the molar fraction of OA was equal to 25, which contained 206 POPC molecules, 68 OA molecules, and 16228 water molecules. Including the POPC-68-OA system, which contained a larger fraction of OA molecules, allowed for (1) investigating the dependence of the flip-flop process on OA concentration and (2) improving the statistics of flip-flop events observed in the MD simulations.

The recently updated version of CHARMM potentials for phospholipids45-47 and the TIP3P model48 of water were used to describe inter-atomic interactions in the system. All OA molecules were in the protonated (uncharged) state. The unprotonated form of OA was not considered in this study even though its fraction in the membrane is close to 0.5 at neutral pH. This is because flip-flops of negatively charged OA molecules are much slower than flip-flops of neutral species due to the high electrostatic barrier associated with this process, and therefore contribute negligibly to the total flip-flop rate. Electrostatic interactions were calculated using the Particle Mesh Ewald approach with a grid size of 100×100×90. The cutoff distance of 12 Å was used for van der Waals (VDW) interactions, and the pair list distance for the non-bonded (VDW and electrostatic) interactions was 13.5 Å. The systems were initially relaxed in short simulations, 5 ns in


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length, carried out in the NPT ensemble using the NAMD simulation package.49 Further simulations were performed on the Anton computer50 at Pittsburgh Supercomputer Center. After 100–200 ns of initial relaxation that was carried out in the NPT ensemble with the aid of Berendsen thermostat and barostat, production trajectories were generated in the NVT ensemble with the aid of Nose-Hoover thermostat. Their lengths were 5.25 and 2.22 µs for the POPC-10-OA and POPC-68-OA systems, respectively. The equilibrated unit cell size is ~ 93×93×94 Å and 87×87×101 Å, for POPC-10-OA and POPC-68-OA system, respectively. The results presented in this study were averaged over these trajectories. In all simulations the temperature was kept at 303 K. The multiple time-step RESPA algorithm was used with the short and long time step set to 2 fs and 6 fs in the simulations on Anton, and 1 fs and 4 fs in NAMD.

Results

Density of OA inside membrane

The number densities of O1 atoms in the head group of OA molecules (schemetic plot of which shown in the insert of Figure 1), atoms of POPC molecules and water molecules along the z-direction normal to the membrane surface are shown in Figure 1. The density profiles of POPC and water overlap markedly in the head group region. Near the middle of the membrane, where two leaflets forming the bilayer meet, the POPC density drops somewhat, which points to the increased disorder at the tail end of phospholipid molecules. Such density profiles are typical to hydrated, pure phospholipid



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membranes,51,52 which means that the addition of OA molecules does not cause major structural disruptions of the bilayer. This is consistent with an earlier simulation of OA in a phospholipid bilayer in which it has been found that OA molecules disperse homogeneously in the bilayer at all concentration studied without causing significant perturbations in the membrane.53 The densities of OA headgroups peak inside the density profiles of POPC headgroups indicating that OA molecules are buried in the membrane. Radial distribution functions (RDF) between O1 atoms of OA and the phosphate or oxygen atoms of the carboxylic acid group of POPC, plotted in the inset of Figure 1, confirm this observation. They peak at 5 Å and 2.75 Å, respectively, which means that the OA head groups are, on average, close to the carboxylic groups, but not to the phosphate groups, of POPC. OA and POPC headgroups interact mostly through O-H…O hydrogen bonds, and the time-averaged number of such bonds is 0.29 per OA molecule. O-H…O hydrogen bonds are also formed between O1 of OA and water molecules that penetrate the head group region of the membrane. The average number of such hydrogen bonds is 1.8. Hydrogen bonds with both water and lipids have to be broken when the OA molecule moves inside the membrane, contributing to the free energy barrier of the flipflop process.

Flip-flop process observed in MD simulations

During our MD simulations, flip-flop events are observed directly. In the POPC-10-OA system, there are 15 single-molecule flip-flop events in 5.25 µs, whereas 33 such events are observed in the POPC-68-OA system simulated for 2.22 µs. The corresponding flipflop rate, defined as k = N/(ttot M), where N is the number of events, M is the number of


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OA molecules in membrane, and ttot is the total simulation time, is equal to 0.28 and 0.22 µs −1 for POPC-10-OA and POPC-68-OA, respectively. This yields the average time, τ, of 3.5 – 4.5 µs for flip-flop of a single OA in these two systems. Trajectories of OA molecules along z are plotted in Figure S1.

If flip-flop events are independent of each other and stationary in time the probability distribution of waiting times between two consecutive events should follow the Poisson statistics. This means that the cumulative probability distribution, Pcum(t), that an observed waiting time is longer than t, is given by an exponential decay function e-λt with rate parameter λ. As can be seen in Figure 2, the fit of Pcum(t) to an exponential function is very good, indicating that flip-flops of single OA molecules in phospholipid membranes are, indeed, distributed according to the Poisson statistics. The rate parameter λ is equal to 1/330 ns-1 and 1/70 ns-1 for the POPC-10-OA and POPC-68-OA system, respectively. Considering that these systems contain 10 and 68 OA, the corresponding average time for flip-flop is equal to 3.3 µs and 4.6 µs, in a very good agreement with the values of τ obtained from the direct count of flip-flop events. For Poisson distribution, statistical errors for τ can be readily calculated. They are equal to 0.85 and 0.80 µs for the POPC-10-OA and POPC-68-OA system, respectively. With these statistical errors, there is insufficient basis to reject (p < 0.05) a hypothesis that the flip-flop rates in these two systems are identical.

In addition to flip-flops of single OA molecules, two OA molecules, hydrogen bonded through their carboxylic acid headgroups, occasionally flip-flop in concert. Only one



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such event is observed during the simulation of the POPC-10-OA system, whereas four such events occur during the simulations of the POPC-68-OA system. Trajectories of two OA molecules undergoing the concerted flip-flop in the POPC-10-OA system are shown in Figure S2. A snapshot of these molecules immediately before the flip-flop is also shown in this figure. Double flip-flop can take place only if headgroups of two OA molecules are directly in contact. The averaged number of OA pairs for which the distance between C1 atoms of the head-group, |rC1-C1 |, is smaller than 5 Å is only 0.01 in the POPC-10-OA system and 0.12 in the POPC-68-OA system. It would appear that the ratio of double- to single-molecule flip-flops increases slightly in the system with the larger concentration of OA in the membrane, a result that would be predicted on combinatorial basis. However, the statistics are insufficient to draw firm conclusions in this regard. The only statistically supported conclusion is that concerted flip-flops provide only a minor contribution to the overall flip-flop rate at fatty acid concentrations studied here or in experiments, largely due to a small probability of forming hydrogen-bonded pairs between OA molecules.

Orientation and dynamics of OA molecules inside membrane

Other than the usually analyzed orientational ordering SCD for alkyl tails, discussed in the Supplementary Material and in Figure S3, one structural parameter that is directly relevant to the flip-flop process is orientation of OA molecules with respect to the membrane. As there is a double bond between atoms C9 and C10, we analyze the orientation of two segments of OA molecules, comprising atoms C1-C8 and C11-C18. The distribution of angle θ between the Z-axis and the vector rC1-C8 or rC11-C18 pointing


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from atom C8 to C1 and from C18 to C11, respectively, is shown in Figure 3a - d for three regions in the membrane, corresponding to the position of O1 in the ranges 0 < |z| < 5 Å, 5 < |z| < 10 Å and 10 < |z| < 17 Å. Decreasing values of z correspond to progressive shift of O1 from the surface to the center of the membrane. A large fraction of molecules located in the innermost region are in the process of flip-flop. All distributions are similar for the POPC-10-OA and POPC-68-OA systems. The distributions of the tail segment are always broader than the distributions of the head segment, reflecting larger flexibility of OA tails. For both segments, the shape of the distributions correlates with the position of OA molecules in the membrane, which suggests coupling between translational and rotational motions during flip-flop. As OA head groups move inside the bilayer, the distributions broaden and their peaks shift toward larger values of θ. Specifically, when OA head groups are located near the interface (10 < |z| < 17 Å) the distribution of θ for the head segment C1-C8 peaks at approximately 30o, indicating that this segment of OA molecules is nearly perpendicular to the membrane surface. In contrast, near the center of the membrane (0 < |z| < 5 Å), the peak is located at approximately 60o . In this region, all values of θ are appreciably populated. This means that OA molecules located in the center of the bilayer, but not molecules near the surface, have considerable orientational freedom and can readily rotate inside the bilayer experiencing a low free energy barrier.

To investigate in more details the rotational dynamics of OA in the middle of the bilayer, we generated a MD trajectory 90 ns in length in which O1 atom of one OA molecule was constrained in the plane z = 0 Å at the center of the membrane. In the starting configuration the molecule was orientated parallel to the membrane surface. The



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evolution of angle θ between the vector rC1-C8 and the Z-axis is plotted in Figure 4a. As can be seen from this figure, the angle fluctuates in the full range between 0o and 180 o . This confirms the earlier observation that OA molecules have considerable rotational freedom in the middle of the bilayer. As shown in Figure 4b, the autocorrelation function f (t ) =< rˆ (t ) ⋅ rˆ (0) > of the unit vector rˆ =

rC1−C 8 decays exponentially with the decay rC1−C 8

time τr ≈ 1 ns.

The observed exponential decay resembles rotational dynamics of a rigid rod in polymer solutions.54 This is not surprising, since the C1-C8 segment can be approximated as a rod, due to its short length. According to Flory’s model of a freely joint polymer chain,55 the persistence length l p , defined as the maximum length for which a polymer chain can be considered as rod-like, is ~ 10 lb , where lb is bond length. With only 8 units in the C1-C8 segment, the rod-like condition is satisfied. For Brownian motion of a rod in solution, the autocorrelation function of the end-to-end unit vector, rˆ(t ) , is related to the rotational diffusion coefficient of the rod, Dθ , through the following equation,54

〈 rˆ(t ) ⋅ rˆ(0)〉 = exp(−2 Dθ t ) (1).

This relation applies if there is no (i) position dependent external velocity field in the solution, and (ii) orientation-dependent potential field acting on the rod. Since the tail OA segment (C11-C18) is not expected to induce any position- or orientation-dependent fields, eq 1 should be valid for the C1-C8 segment. Accordingly, the rotational diffusion


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coefficient of the head segment of OA is estimated as Dθ = 1 2τ r ≈ 0.5 × 10 −9 s −1 at z = 0 Å, using the decay time τr ≈ 1 ns, calculated above.

2-Dimensional potential of mean force for the flip-flop process

The flip-flop process involves both translation and rotation of an OA molecule. This suggests that, in order to capture the details of this process, an order parameter associated with each of these motions should be included in the potential of mean force. Similar variables were used to study flip-flop of cholesterol in phospholipid membranes.29 In restricting ourselves to a 2-dimensional, reduced representation of the process we implicitly assume that equilibration along other, orthogonal degrees of freedom in the system is sufficiently fast to yield correctly converged ensemble averages. If this is not the case, hidden barriers may exist in the system. Their presence would lead to inaccurate estimates of free energy differences. Examples of such situations include slow equilibration of conformational degrees of freedom in nucleosides,56 dipeptides,57 and drug molecules58 peameating membranes, and interactions of ions38 or analogs of amino acid residues57,59 with water molecules or phosphilipids head groups in membranes.

During flip-flop of OA molecules, neither intramolecular degrees of freedom nor interactions with other component of the system are expected to create hidden barriers. As shown in Figure S4, OA exists mostly in the extended form in which the end-to-end distance is approximately equal to 17.2 Å. The small peak around 5.4 Å corresponds to the bent conformation in which, together with the double bond C9-C10, the dihedral



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angle of C11-C12-C13-C14 is also in the cis state. Considering the small population and a short lifetime (< 0.2 ns) of the bent conformation, it is unlikely that this conformation will be responsible for a hidden barrier. Furthermore, no significant water-OA interactions are found during the flip-flop process, as a water molecule accompanied an OA molecule into the membrane in only 4% of the flip-flop events, and stays bonded to the OA headgroup for only 0.4 ns, on average. Similarly, no strong interations between neighboring OA molecules or their entanglement that might slow flip-flop was observed. Taken together, these arguments suggest the absence of additional degrees of freedom that might be responsible for hidden barriers.

Given these considerations, we focus on the potential of mean force, A(z,θ), with two order parameters, z and θ, where z is the position of O1 along the axis normal to the bilayer and θ is the angle between the vector rˆ (C1-C8) and the normal. The orientation of the head segment (C1 to C8) of the OA molecule is used here to represent the molecular orientation, as the tail segment (C11 to C18) is more disordered, as discussed above. The free energy A(z,θ) is calculated according to the Boltzmann distribution P ( z , θ ) ∝ e − A ( z ,θ ) / kBT , using the probability density,

P ( z , θ ) , obtained from the

simulations.

A(z,θ) for POPC-68-OA, plotted in Figure 5a, is similar to that for POPC-10-OA (shown in Figure S5). Since the structure and dynamics of OA molecules dissolved in the membrane are also similar in both systems, we further analyze the flip-flop process only for POPC-68-OA system because more statistics on flip-flop events is available for this


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system. As can be seen from Figure 5a, A(z,θ) is symmetric with respect to z, which reflects the symmetry of the bilayer. The largest asymmetry in A(z,θ), equal to 0.6 kcal/mol, is in the center region (see Figure S6), and decreases towards the membrane surfaces, as statistics improves in these directions. This points to a good convergence of the simulations. Two symmetric, stable states at (z = -14.5 Å, θ = 157.5o) and (z = 14.5 Å, θ = 22.5o) near the membrane surfaces have been identified from the free energy map, with a barrier of ∆A ≈ 4.2 ± 0.3 kcal/mol in the saddle point located at the center of the bilayer (z = 0 Å and θ = 90o). As shown in Figure S7, this point is at the bottom of a shallow (only 1.0 kcal/mol in depth) potential well along θ. This confirms our previous observation that OA molecules located near the center of the bilayer are free to rotate.

An ensemble of flip-flop paths on the 2D free energy landscape is available to an OA molecule. Under over-damped conditions, the most probable path coincides with the minimum energy path (MEP) that connects the two minima on the energy map A(z,θ).60 To calculate MEP, we use the updated version35,61 of the string method developed by E. et al.34,35 in which a string of configurations along a curve that connects two stable states evolves iteratively according to v n = −(∇A) ⊥ , where vn is the velocity in the direction

normal to the curve. Initially, twenty evenly distributed configurations were set along the linear path connecting the stable states, (z = -14.5 Å, θ = 157.5o) and (z = 14.5 Å, θ = 22.5o). A string of these configurations was evolved until convergence after 10000 iterations. The calculated MEP is plotted in Figure 5a and a series of snapshots of an OA molecule flip-flopping along this path is shown in Figure 5b. As can be seen from the figure, the OA molecule gradually rotates as it moves to the center of the membrane and



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continues to rotate to complete the flip-flop when it leaves the central region and moves toward the other leaflet of the membrane. This path is consistent with the previously described orientational preferences of OA molecules, which change with the position in the membrane. It should be kept in mind, however, that the MEP is just the most likely path, and the distribution of actual paths is markedly broader, as shown in Figure S8.

Diffusion model for the flip-flop process

The flip-flop process can be regarded as diffusion between the two stable states on the 2D surface given by the minima in A( z , θ ) and, therefore, can be described by the Smoluchowski equation, ∂ t P ( z , θ , t ) = ∇De − β A( z ,θ )∇e− β A( z ,θ ) P ( z , θ , t ) , where P ( z , θ , t ) is the probability density function of finding an OA molecule in position z and orientation θ at time t, D is diffusion coefficient.32 Due to complications in the treatment of boundary conditions, general solution to the diffusion equation in more than one dimension cannot easily obtained.33 Moro et al.62,63 circumvented this difficulty by reducing the continuous Smoluchowski diffusion equation to a special Master equation,

∂Pm (t ) = −∑ Wmn Pn (t ) , ∂t n

for a discrete set of populations Pm (t ) for each stable state m, where the transition rate

Wmn from state m to n is expressed as a function of diffusion coefficients besides the free energy profile. Such reduction is valid for an intermediate to high barrier ( ∆ A / k B T > 2 ) between the states of interest. This condition is satisfied here, as ∆A = 4.18 kcal/mol and −1

thus ∆ A / k B T ~ 7 . The transition time ( Wmn ) between state m and n is given as,62,63


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1/ 2

1 2π  det[(2π k BT ) −1 U s ]  = τ=   Wmn λ1  det[(2π k BT )−1 U m ] 

∆A

e kBT , (2)

where λ1 is a vibration frequency constant, and U s and U m is the 2x2 Hessian matrix of A(z, θ) at the saddle point s (between state m and n) and at the minimum point for the state m, respectively. The value of λ1 is the negative eigenvalue of the 2x2 matrix of Ds ⋅ U s , where D s = ( Dzz , Dzθ );( Dθ z , Dθθ )  is the diffusion tensor at the saddle point. The transition rate expressed in eq 2 is identical to the extension of Kramers’ escape rate for multi-dimension cases, previously derived by Langer.33,64

To apply eq 2 to the flip-flop process, we first calculated the translational diffusion coefficient of an OA molecule at the center of the POPC membrane from the autocorrelation function of random force through the fluctuation-dissipation theorem:65

Dzz =

(k BT ) 2

∫

∞

0

〈δ Frs (t )δ Frs (0)〉 dt

, (3)

where δ Frs (t ) is the random force acting on the molecule along the z direction at time t at the saddle point s. This random force was obtained from simulations in which the OA molecule was constrained to the x, y-plane at z = 0, with its orientation parallel to the membrane surface (θ = 90o). The translational diffusion coefficient, calculated from eq 3, is equal to Dzz ≈ 1.1×10 −6 cm 2 / s , which is in good agreement with the value of 0.3 × 10−6 cm2 / s obtained experimentally for an octadecane molecule in lipid bilayer



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environments.66,67 Together with the previously obtained rotational diffusion coefficient Dθθ ≈ 0.5 × 10 −9 / s and neglecting the off-diagonal terms in the diffusion tensor (as the

direction of rotation of the molecule is not expected to be coupled to its diffusion along Z-axis), the vibration constant λ1 calculated by way of diagonalizing the matrix D s ⋅ U s is 1/ 2

 det[(2π k BT )−1 U s ]  equal to -0.34 ns . The ratio of   in eq 2 is equal to ≈ 0.2. This −1  det[(2π k BT ) U m ]  -1

yields the average flip-flop time of an OA molecule equal to 2.4 µs, which is similar to 3 - 4 µs obtained from counting the number of flip-flop events in the MD simulations. This

good agreement means that the flip-flops process can be satisfactorily described as a diffusive process on the 2D potential of mean force, adding other example to the many successful applications of diffusion models to biological processes, discussed in the introduction. For comparison, the flip-flop rate λ (1D ) has been also estimated with the L/2  L/2 1  simpler 1D PMF, A(z), as λ (1D ) = 1/  ∫ e A( z ) / kBT dz ∫ e − A( z′) / kBT dz ′  ,32 in which z  0 Dzz ( z ) 

A(z) (shown in Figure S9) has been obtained from the probability distribution, P(z), according to Boltzmann distribution P ( z ) = e− A( z ) kBT . Taking the distance L = 29 Å between the two minima in A(z) and Dzz ≈ 1.1×10 −6 cm 2 / s , is has been found that flipflop rate (1/ λ (1D ) ~ 0.8 µs) is overestimated 3 - 5 fold, compared to the rate obtained from the 2D PMF or direct simulations.

Discussion

Very fast rates for fatty acid flip-flop have been observed in phospholipids membranes1315

and fatty acid vesicles.10,19-22 Thomas et al. measured an upper bound for the half time


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t1/ 2 at 5 ms of a protonated OA molecule flip-flopping in phosphatidylcholine vesicle membrane,14 and a similar threshold ( t1/ 2 < 10 - 25 ms) was obtained by Kamp et al.13 and later by Simard et al.15 While our calculated transition time is below the observed upper threshold, the flip-flop transition time is predicted to be as fast as a few microseconds.

In a recent experiment Bruckner et al.68 estimated that a cholesterol molecule, which is bulkier than an OA molecule, flip-flops in a POPC vesicle on a sub-millisecond to millisecond time scale, with a conservative upper bound for t1/ 2 of 10 ms. The free energy barrier for the process was calculated to be ~ 5.5 - 7 kcal/mol in separated simulation studies.29-31 Such a barrier is 1.5 - 3 kcal/mol higher than the one calculated in this study for the flip-flop of OA, which can be attributed to the larger size and more complex structure of cholesterol. Taking into account the lower barrier, the upper bound on t1/ 2 is estimated to be ~ 90 µs for the flip-flop of OA, which is consistent with the fast transition time calculated above.

Facilitated pathways for fatty acids transport across membrane through membrane-bound transport proteins have been proposed,69,70 but the exact functions of several candidates (such as CD3670 and caveolin-171 etc) are still being investigated.2,3 An alternative pathway was suggested in which the uncharged forms of fatty acid molecules directly diffuse through membranes.3,16 Such a route can be crucially important in early cellular systems where no protein transporters were yet available. Although the fast rate of the flip-flop process found in this study provides support for the direct diffusion pathway, it



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should be noted that a cell membrane is a more complicated system than the pure phospholipids system studied here, and the flip-flop process of fatty acids can be influenced by the complex compositions of cell membranes.2,3,16,72

An important implication of the fast rate of flip-flop is that the rate-limiting step in the diffusive transport of fatty acids across membranes is most likely its desorption from the membrane into the interior of the cell, as suggested by Hamilton et al.,12,13,15 and later by Szostak et al. in their experiments on growth and division of model protocellular systems.10,20,22 In these studies the dissociation rate was measured in the range of milliseconds to seconds. It was further shown that the dissociation rate increased with larger ratio of oleate molecules in the 1,2-Dioleoyl-sn-glycero-3-phosphate (DOPA) membrane.20 These results indicate that the diffusive transport rate of fatty acids can be tuned by varying membrane compositions. The fast flip-flop rate means that this step does not hinder cellular functions dependent on flip-flop of fatty acids, such as proton transport mediated by fatty acids,5-10 or competitive vesicle growth in the presence of free fatty acids in aqueous solution.19,20,22 It has been also shown that vesicle growth leads to spontaneous generation of transmembrane proton gradients most likely by proton transport through flip-flop of protonated fatty acids,10 and the sustainable gradient suggests a fast flip-flop rate to overcome any proton leakage through membranes, which have a permeability ~ 10−4 to 10−6 cm/s.73,74

Conclusions


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In this study, the flip-flop process of protonated OA molecule in POPC membranes is investigated by MD simulations on microsecond time scales, and flip-flop events are observed directly. It is further shown that the process can be described sufficiently accurately as diffusion on a two-dimensional surface defined by a translational and an orientational degree of freedom of the molecule. The flip-flop mechanism is characterized by concerted translation and rotation of an OA molecules and its facile reorientation near the center of the bilayer may by typical to permeation of fatty acids and sterols through membranes. Average flip-flop times calculated directly from MD simulations and estimated from Kramers’ escape rate on a two-dimensional free energy map are very similar and approximately equal to 3 – 4 µs. These times are below the upper limit determined experimentally for this quantity and are consistent with the recently measured flip-flop time of cholesterol in phospholipid bilayers. The fast flip-flop rate supports the proposal that fatty acids permeate membranes without assistance of transport proteins.3 It also suggests that desorption rather than flip-flop is the rate limiting step in fatty acid transport through membranes.

Acknowledgements. This work was supported by the NASA Exobiology Program. All

simulations were performed at the NASA Advanced Supercomputing (NAS) Division and on the Anton computer at the Pittsburgh Supercomputer Center.



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Supporting Information

Trajectories of OA molecules and the one involving double flip-flop, order parameter of alky chain of OA molecules, distribution function of end-to-end distance, 2D PMF fin the POPC-10-OA system, difference in PMF, free energy profile along orientation angle pf OA molecule, 2D path of OA molecules in flip-flop process, and 1D PMF of OA molecule in POPC-68-OA and POPC-10-OA system. This material is available free of charge via the Internet at http://pubs.acs.org.


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Figures.

Figure 1. Density of water (black line) and POPC (tail: red dashed line; headgroup: red dotted line; total: red solid line) as a function of distance from the center of the membrane in POPC-10-OA system. The number density (x 6) of the O1 atom on the head group of an OA molecule is also plotted with blue line. Inset: (left) Radial distribution function (RDF) between the O1 atom on OA and oxygen atoms on POPC lipids. Black and red lines are for oxygen atoms on PO4+ head-group and ester groups of POPC lipids, respectively; (right) Space-filling representation of an OA molecule, with the double bond between atom C9 and C10.



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Figure 2. Cumulative probability function Pcum(t) for the waiting time is t. The solid black and red line is for POPC-10-OA and POPC-68-OA system, respectively. The thin dashed lines are their fittings to exponential decay function e-λt.


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Figure 3. Distribution of the OA molecule orientation for (a) the head segment C1-C8 and (b) the tail C11-C18 in the POPC-10-OA system; (c) C1-C8 and (d) C11-C18 in the POPC-68-OA system. Black, red, and blue line is for region of 0 Å < |z(O1)| < 5 Å, 5 Å < |z(O1)| < 10 Å, and 10 Å < |z(O1)| < 17 Å, respectively.



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r

Figure 4. (a) The orientation angle between the vector rC

8 − C1

for the segment C1-C8 on the

OA molecule and the Z-axis, as a function of simulation time. During the simulation the O1 atom of the chosen OA molecule is fixed at z =0 Å. (b) Auto-correlation function r rC8 −C1 , as a function of time. f (t ) =< rˆ (t ) ⋅ rˆ (0) > for the orientational unit vector rˆ = r rC8 −C1


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Figure 5. (a) 2D potential of mean force (kcal/mol) for an OA molecule in POPC membrane as a function of the distance from the center of membrane and the orientation angle of the OA molecule, relative to the normal direction of the membrane. The black thick line is the MEP calculated from the string method. (b) Snapshots of an OA molecule flip-flopping in a POPC membrane, with a gradual rotation of its orientation while translating from one side to the other side of the membrane.



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(74.) Nichols, J. W.; Deamer, D. W. Net Proton-Hydroxyl Permeability of Large Unilamellar Liposomes Measured by an Acid-Base Titration Technique. Proc. Natl. Acad. Sci. U. S. A. 1980, 77, 2038–2042.



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SYNOPSIS TOC


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Flip-Flop of Oleic Acid in a Phospholipid Membrane - American

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