Response to “How Slow Is the Transbilayer Diffusion (Flip-Flop) of Cholesterol?”.

In their comment (1) on our recently published article discussing the kinetics of cholesterol transport using small angle neutron scattering as a noninvasive probe (2), Steck and Lange raise several questions regarding the analysis and interpretation of our data. They are particularly concerned with our very slow intramembrane flipping rates and wonder whether the data might not be equally well interpreted with very fast cholesterol flipping. Indeed, although we are certainly not the first to report slow flipping rates, fast flipping rates are now generally accepted (3,4). Fundamentally, all the questions or comments fall into two categories: questions relating to the analytical formalisms that leads to a two-process model, and questions relating to the interpretation of the origin of a second process. We thus structure our response accordingly. Steck and Lange first raise the reasonable question of whether a single-process model would actually be adequate after all, and if not, whether a stretched exponential might be more appropriate than a two-process model. Fig. 1 clearly demonstrated that our original single-process assumption was incorrect. The second part of the question was precisely what we wished to answer when devising the cholesterol sulfate experiment. We believe the successful separation of the two time constants clearly demonstrates, independently of any modeling, that two distinct processes are indeed involved rather than a series of processes or a single process with a distribution of decay constants. Figure 1 Normalized intensity decay curves for cholesterol transport between donor and acceptor vesicles at 50°C. (Solid line) Fit assuming only an intermembrane exchange process; (dashed line) fit accounting for both an intramembrane (flipping) and intermembrane ... Steck and Lange also suggest we fit the data to a “simple biexponential” as per Gutfreund (5) to determine the pool sizes responsible for the two processes independently of whether they are sequential or parallel. Although a full discussion of the details of the analysis will be part of a forthcoming article, the key point here is that the normalized intensity decay curves are not directly proportional to the concentration loss in the donor vesicles because all the cholesterol, both in the donor and acceptor vesicles, contributes to the measured intensity all the time. Thus we indeed begin by setting up the differential equations as per Gutfreund, though in our particular model four such equations are necessary rather than three (Eqs. 1–4 of our article). As shown by Gutfreund, the differential equations can be solved analytically to yield a series of double exponential equations for each time-dependent concentration. However, those results must be substituted into Eqs. 8 and 9 in our original article to relate those concentration changes to the intensity. The term x in Eq. 9 of our article then would be a four-exponential term that, when substituted into Eq. 8 of our article, will come into the measured intensity as a squared as well as linear term. Thus, setting up the differential equations depends on the kinetic model assumed, including how many processes are involved, and whether they are serial or parallel, preventing an independent measurement of pool sizes. However, the cholesterol sulfate experiment, by completely separating the time constant for the two processes, demonstrates, independently of any model, that 25% of the cholesterol migrates to the acceptor vesicles in the first process and that the other 25% migrates in the second process, indicating that the two pool sizes are identical. Of course we agree that establishing the existence of two distinct processes does not prove what those processes are. Although the first process must be the exchange between vesicles due to the experimental method used, we explored a number of hypotheses besides flipping to account for the second process, including the two suggested here. The following experimental evidence argues against these hypotheses. The first hypothesis suggested by Steck and Lange was the existence of a significant fraction of multilamellar vesicles with cholesterol in the inner bilayers constituting the second pool of cholesterol leading to the second process measured. The first problem with this scenario is that the second process is, in fact, exactly the same as the first: cholesterol exits the bilayer, traverses the aqueous medium somehow, and enters the next membrane it encounters. Thus the rate constants should be the same, which is only true for the DHE case (see Table 1 in Garg et al. (2)). More importantly, multilamellar vesicles are rather easy to identify experimentally with scattering techniques due to the sharp Bragg peak at a q ≈ 0.1 A−1. None of our systems exhibits any such peak, cleanly eliminating this hypothesis. With respect to the suggestion of utilizing sonication rather than extrusion, both are widely used to provide unilamellar vesicles (6–8). We avoid sonication mainly because, to our knowledge, it does not allow for independent control of the size and the polydispersity. Such control greatly simplifies the data analysis and is essential for some of our studies. With respect to the possibility that there is a single process with a cholesterol-concentration-dependent transport rate, we first note that to be consistent with the two-step process, the rates cannot vary continuously with concentration. Instead, they must be constant, with concentration in two different concentration regimes having an abrupt change at some concentration. As suggested by Steck and Lange, the ideal experiment would be to have the acceptor population equally full of invisible cholesterol. As these authors also note, it is unclear whether such an experiment can be successfully carried out, though we have plans to try doing so using the highest-powered source available. However, we have measured the rates with different starting concentrations of cholesterol and have been unable to identify any significant change in transport rates. Thus, the current evidence argues against any concentration dependence in the rates. Other concerns listed are that: a), the ratio kex/kf does not change significantly except for cholesterol sulfate; b), the flipping rate does not increase in the cholesterol sulfate system; c), the activation energy for flipping seems excessively large; and d), cyclodextrin (CD) should not affect the flipping rate. The first point suffers from statistics of small numbers. In fact, we have measured a large number of systems and see many ratios, spanning no detectable flipping (ratio of 0) (S. Garg, L. Porcar, P. Butler, and U. Perez-Salas, unpublished) to the extreme case of cholesterol sulfate with a ratio of 40. Indeed, even in the small set presented in our first article, addition of CD only marginally increases the ratio from 2.3 to 2.6, but replacing cholesterol with DHE drops the ratio by a factor of 2 (ratio = 1.1), whereas replacing it with cholesterol sulfate increased it by a factor of 17. Note that in a set of serial processes such as this, and different from a set of parallel processes, the first process will significantly slow the overall process even if the rate constants for the two processes are the same (i.e., kex/kf = 1). Whether ratios <1 are still measurable with this technique will be the subject of a future article. The second and third points make the assumption that hydrophobic effects completely dominate the barrier to flipping. Although this is a reasonable a priori assumption (and indeed was ours), it is possible for other forces (e.g., steric interactions, van der Waals, etc.) to dominate as was expressed in our original article. The fourth point is based on the assumption that CD cannot affect the flipping. We note that we are not the first to suggest that CD may affect lipid behavior in membranes (9). Further, it is a well-established principle in colloid and interface science that the addition of a small amount of a “foreign” substance can alter self-assembling systems, sometimes dramatically. As a final comment, Steck and Lange point to experiments showing the short transport time of minutes from introduction to the outer leaflet of the plasma membrane to intracellular compartments as being at odds with our flipping rates. In fact, those experiments would suggest that both flipping and exchange occur much more rapidly than in our system. However, one of the primary conclusions of our study is that the entire system is energetically driven and any small perturbation to the energy landscape will alter the behavior. Thus there are many pieces to the puzzle, of which this study is only one, that must come together to begin to understand the full complexity of the living system. We thus believe the evidence so far favors our current interpretation over the alternatives. We accept, however, that more needs to be done to thoroughly test these ideas. Indeed, we have already begun tackling a number of these questions and look forward to a robust discussion as further experimental results, from our lab and others, become available from these very complex systems.