Urea-mediated anomalous diffusion in supported lipid bilayers

Abstract

Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the time scale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous diffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatized with polyethylene glycol. Here, we extend this work, using urea to induce anomalous diffusion in SLBs. By tuning incubation time and urea concentration, we produce bilayers that exhibit anomalous behaviour on the same scale as that observed in biological membranes.

1. Introduction

Diffusion is a vital process that underpins many cellular functions, including protein organization [1], signalling [2,3] and cell survival [4]. In living systems, diffusion rarely follows the Brownian motion predicted by a simple random walk model but instead exhibits ‘anomalous’ diffusion, whereby the rate of diffusion is dependent on the time scale of observation [5]. Anomalous diffusion has been observed in three dimensions in the cytosol [6] and in two dimensions in plasma membranes [7–9]. The underlying mechanism for anomalous diffusion in membranes is thought to involve molecular crowding [10], with contributions from slower-moving obstacles [11,12], pinning sites and compartmentalization [8,10,13]; this is reviewed comprehensively elsewhere [14]. The notion that the cell membrane is a homogeneous entity in which lipids and proteins are free to diffuse unhindered, as per the ‘fluid mosaic model’ [15], has in recent years been re-evaluated to accommodate increased levels of complexity [10].

Anomalous diffusion can be modelled by a power law,

1.1

where the conventional diffusion coefficient D is replaced by an anomalous transport coefficient Γ, whose dimensions change for different degrees of anomalous behaviour. The anomalous exponent α defines whether the diffusion is normal (α = 1), sub-diffusive (α < 1) or super-diffusive (α > 1). The units of Γ vary with the degree of anomalous behaviour, which presents a challenge of interpretation. However, by de-dimensionalizing the observation time [5] with a ‘jump time’ τ,

1.2

the length scale λ associated with the two-dimensional anomalous behaviour can be defined (). It should be noted, however, that this only applies in cases where geometry is the direct cause of anomalous diffusion, such as in the case of obstacles. There will be no associated length scale where the cause is transient binding events [16].

Artificial bilayers have been critical in furthering our understanding of anomalous diffusion [17–22]. In supported lipid bilayers (SLBs), phase separation [18], protein binding [19] and defect formation [23] have been used to generate anomalous diffusion. Simulations have also played a vital role [5,24–31]; in particular, those linking the role of mobile and immobile obstacles within the bilayer to the phenomenon [11,12]. Simulations have also provided the means to better interpret single particle tracking (SPT) data [32], as well as methods for discriminating between distinct classes of anomalous diffusion [33].

To elucidate the specific molecular mechanisms giving rise to anomalous diffusion in vivo, there is a need for experimental models which are able to exhibit readily tuneable anomalous diffusion of a biologically relevant magnitude [14]. Recently, we used SPT to sample anomalous behaviour over four orders of magnitude of time by forming SLBs containing varying mole fractions of lipids functionalized with polyethylene glycol (PEG), thereby controlling nanoscale obstacle formation [23]. Here, we make use of urea as a chaotropic agent (hydrogen bond disrupter), with reported ability to alter the physical properties of lipid bilayers [34–37]. Urea is present at high concentrations in the tissues of deep-sea elasmobranchs (sharks, skates, rays) [38] and is also part of the natural moisturizing factor in skin [39], where it is thought to offer cell membranes protection from osmotic shock due to highly saline or dehydrating conditions by stabilizing the lamellar liquid phase. Here, we use single-molecule total internal reflection fluorescence (smTIRF) and perform SPT to evaluate urea as a means to induce anomalous diffusion in pre-formed SLBs.

2. Material and methods

2.1. Materials

1,2-dicapryl-sn-glycero-3-phosphocholine (DCPC) was purchased from Avanti Polar Lipids (Alabaster, AL). Texas Red 1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine triethylammonium salt (TR-DHPE) and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethylene glycol)–5000] ammonium salt (PEG(5K)-DPPE) were purchased from Lipoid (Ludwigshafen, Germany). Unless stated, all other chemicals were purchased from Sigma-Aldrich. All aqueous solutions were prepared using doubly deionized 18.2 MΩ cm MilliQ water.

2.2. Supported lipid bilayers

SLBs were prepared on glass coverslips by fusion of small unilamellar vesicles (SUVs) [40] made from 1.77 mM DCPC doped with 1.0 mol% PEG(5K)-DPPE and 3 × 10⁻⁶ mol% TR-DHPE (see electronic supplementary material, figure S1, for the light scattering plot). The addition of PEG-functionalized DPPE (below the mol% required to induce anomalous diffusion [23]) helps improve bilayer fluidity by raising the bilayer, thereby reducing interactions between the lipids in the lower leaflet and underlying glass [41]. Texas Red-labelled DHPE was also included as the fluorescent agent in order to assess the diffusive properties of the bilayer using smTIRF.

Lipid mixtures were first dried with nitrogen and placed under vacuum overnight. The dried lipids were hydrated with water and vortexed before tip sonication (Vibracell VCX130PB with CV188 tip; Sonics & Materials, Newtown, CA) for 15 min at 25% amplitude. The resulting clear vesicle suspension was centrifuged (3 min; 14000g) before the supernatant was retained and any titanium residue (from the sonicator probe) was discarded. SUV preparations were stored at 4°C for up to 48 h.

Glass coverslips were rigorously cleaned using stepwise bath sonication with DECON-90, MilliQ water, and propan-2-ol for 20 min each. Immediately before use, the glass was dried under nitrogen and cleaned with oxygen-plasma treatment for 3 min (Diener Electronic, Femto). A well was created on each coverslip using vacuum grease (Dow Corning). The coverslip was heated to 37°C before 50 μl of SUV stock was diluted 1 : 1 in buffer (250 mM NaCl, 10 mM EDTA, 20 mM Tris, pH 7.0) and added to the chamber immediately. DCPC SLBs were produced by fusion of the SUVs onto the glass coverslip. The vesicles were incubated for 30 min before the membranes were washed thoroughly with degassed MilliQ water followed by buffer.

Urea was added (or removed) by buffer exchange via pipetting; all but 50 μl of fluid above the SLBs was replaced with 200 μl of the new buffer (containing 0.2, 0.5 or 1 M urea), a minimum of five times. Bilayers were imaged 15 s after buffer exchange.

2.3. Total internal reflection fluorescence microscopy

A 532 nm continuous-wave laser light was focused at the back aperture of an objective lens (60× TIRF, oil-immersion NA 1.49, Nikon, approx. 1.4 kW cm⁻²) such that total internal reflection occurred at the coverslip/sample interface. The excited TR-DHPE fluorescence was transmitted through 545 nm dichroic and 550 nm longpass filters before being imaged with an electron-multiplying CCD camera (Andor iXon). The inverted microscope objective was heated to maintain 37°C at the sample throughout imaging; this was above the transition temperature for this lipid to ensure the bilayer was in the liquid phase. Bilayers were imaged at an exposure time of 20 ms for 5000 frames.

2.4. Single particle tracking

SPT was performed using TrackMate [42], a plugin for ImageJ [43]. The space–time co-ordinates of the output tracks were used to calculate mean-squared displacements calculated for different observation times using custom-written procedures in Matlab (MathWorks) as described previously [23].

3. Results

Diffusion of TR-DHPE in the DCPC SLBs was fast (6 μm² s⁻¹) and normal (α = 1.01 ± 0.01) in the absence of urea (figure 1a,b). In the presence of 1 M urea, the diffusion became slower and more anomalous over time (figure 1c). α was sampled by recording short videos of the diffusion at various time points after the addition of urea, and decreased roughly linearly to 0.38, and the transport coefficient (Γ) showed an approximately exponential decrease to 0.02 μm² s^−α (figure 1d) over a 10 min period. Although Γ values cannot be directly compared (because they depend on α, which is also changing), a linear change in α would be expected to cause an overall exponential change in Γ, as we report.

Figure 1.

Time dependence of anomalous behaviour induced by 1 M urea. (a) Spot locations of tracked TR-DHPE in the absence of urea (left) and after the addition of 1 M urea at four time points. Urea was removed by buffer exchange at 200–300 s. Image size: 3 × 3 μm. (b) Anomalous diffusion increases over time from 15 s (turquoise) to 10 min (dark blue). (c) Linear decrease of α over time, at a rate of 9.7 × 10⁻⁴ s⁻¹. (d) Exponential decrease of Γ over time, t_1/2 = 69 s. Error bars throughout represent standard errors from a minimum of 250 tracks. (Online version in colour.)

Increasing the urea concentration of the buffer surrounding the SLBs incrementally from 0 to 1 M, with a fixed short incubation time (15 s), resulted in increasingly slower diffusion (figure 2a). The behaviour remained largely normal at short times after adding urea (though this was observed to decrease significantly at longer times), with only a modest decrease of α (to 0.94) at the highest concentration tested (figure 2b). An exponential decrease in Γ with increasing urea concentration was observed (figure 2c). From the linear relationship between log₁₀(Γ/D) and α (figure 2d) and assuming a single obstacle size, the characteristic length scale (λ) associated with the system was calculated to be 45.1 nm, with a jump time (τ) of 86.1 μs.

Figure 2.

Effect of urea concentration on lipid diffusion in an SLB. (a) Diffusion of lipids becomes slower as urea concentration of the surrounding buffer is increased from 0 (black) to 1 M (red). (b) Decrease of α with increasing urea concentration. (c) Exponential decrease of Γ with increasing urea concentration. (d) Plot of log₁₀ (Γ/D) versus α with linear fit. Blue: data from 1 M urea time course (figure 1); orange: data from urea titration (this figure). Error bars represent standard errors. (Online version in colour.)

4. Discussion

We observe that urea causes diffusion in DCPC SLBs to become irreversibly slower and more anomalous in a time and concentration-dependent manner. Given our previous experiments reporting defect-mediated anomalous diffusion using PEG doping of SLBs [23], it is appealing to suggest that a similar mechanism must operate for urea. For this case, urea would associate with the bilayer, where its chaotropic nature would act to induce the removal of bilayer patches from the glass coverslip surface, producing defects visible as excluded areas of the surface corresponding to those observed in figure 1a. However, there is little evidence that urea acts directly to solubilize or otherwise permeabilize lipid bilayers [35], and this hypothesis would rely on urea acting at the glass–lipid interface.

An alternative explanation for our results would be the action of urea to alter lipid phase behaviour, inducing phase coexistance phases [34]. Unfortunately, the evidence supports a mode of action whereby urea stabilizes the liquid disordered phase [34,35], suppressing phase separation, rather than encouraging it. In our experiments, we observe a decrease in the area fraction of mobile lipids, which is the opposite trend.

A final hypothesis would be the action of urea not on the bilayer, but on the PEG-DHPE. A chaotropic effect on the PEG might act to increase the area fraction occupied by the PEG, which would then again drive the formation of defects in the membrane [23].

The effect that urea has on diffusion appears not only irreversible but also appears to progress even once urea is removed from the bulk solution. The half-life for this process at 1 M urea was short (69 s) and was finished after approximately 500 s. We speculate that either our (1000-fold dilution) washing procedure must be ineffective or there is a more long-lived, direct interaction between urea and the bilayer. Given the low partition coefficient for urea in lipid bilayers [44] and the evidence from studies of multi-lamellar phases that it remains primarily in the aqueous layers between bilayers [35], it is difficult to rationalize this as a possible mechanism.

We note that anomalous diffusion can arise from a variety of phenomena; simulations have shown a crossover to normal diffusion after around 10 ns at smaller length and experiment scales (e.g. equivalent to the size of a head group on a confined lipid) [45–47], whereas a further crossover (from normal to anomalous) is reported at the microsecond to millisecond time scale (e.g. equivalent to diffusion between obstacles in the bilayer) [16,48,49]. Our model is appropriate to this longer length scale.

Further work is needed to distinguish between these different possible mechanisms either by viewing the defects directly (e.g. by atomic force microscopy) or by restoring the defects by addition of fresh SUVs. There are many ways discussed in the literature [16,33,50–53] for characterizing the nature of the anomalous diffusion seen. For example, it is possible to observe whether the diffusion is Gaussian or non-Gaussian via the fourth moment [47], or to test for ergodicity [50]. Such analysis could form part of future studies on this and similar systems.

5. Conclusion

We have presented preliminary findings demonstrating a novel approach to controlling anomalous diffusion in SLBs on a scale relevant to biological systems [13,17] by incorporating urea into the aqueous medium surrounding an SLB. Although this work involved the use of DCPC, it would be interesting to extend the method to other, more biologically relevant lipid compositions. As a complementary method to the inclusion of PEG lipids, we see potential for this approach for producing a simple membrane model with defined anomalies.

Data accessibility

This article has no additional data.

Authors' contributions

E.E.W. performed the experiments, H.L.E.C. and M.R.C. performed the analysis, M.I.W. secured the funding; all authors wrote and reviewed the manuscript.

Competing interests

We declare we have no competing interests.

Funding

We thank the European Research Council for providing funding for this work (ERC-2012-StG-106913, CoSMiC).