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We use fluorescence microscopy to examine the dynamics of the crowding-induced mixing transition of liquid ordered (Lo)-liquid disordered (Ld) phase separated lipid bilayers when the following particles of increasing size bind to either the Lo or Ld phase: Ubiquitin, green fluorescent protein (GFP), and nanolipoprotein particles (NLPs) of two diameters. These proteinaceous particles contained histidine-tags, which were phase targeted by binding to iminodiacetic acid (IDA) head groups, via a Cu2+ chelating mechanism, of lipids that specifically partition into either the Lo phase or Ld phase. The degree of steric pressure was controlled by varying the size of the bound particle (10-240 kDa) and the amount of binding sites present (i.e. DPIDA concentrations of 9 and 12 mol%) in the supported lipid multibilayer platform used here. We develop a mass transfer-based diffusional model to analyze the observed Lo phase domain dissolution that, along with visual observations and activation energy calculations, provides insight into the sequence of events in crowding-induced mixing. Our results suggest that the degree of steric pressure and target phase influence not only the efficacy of steric-pressure induced mixing, but the rate and controlling mechanism for which it occurs.
In aqueous environments, phospholipids self-assemble to form bilayers that can exist in either a solid or liquid phase.1-4 Structure of the head group (i.e. size and charge), structure of the carbon tails (i.e. length and degrees of unsaturation), and temperature are several of the properties and conditions that determine whether a solid or liquid phase is formed.2, 5 When an appropriate amount of cholesterol is added to a binary solid-liquid phospholipid mixture, the solid and liquid phases become liquid-ordered (Lo) and liquid-disordered (Ld) phases, respectively.1-4 Fluorescent probes and functionalized lipids are capable of selectively partitioning into either of these coexisting, immiscible phases due to their distinct compositions.6-7 The contrast from fluorescent probe partitioning allows for visualization of phase separation via fluorescence microscopy, while functionalized lipids can allow for targeted binding of proteins to specific phases. This type of phenomenon has been of interest for the development of a variety of biological materials, such as high-density arrays, microfluidic networks, and biosensors.8-12 Tethering of proteins to bilayers via functionalized lipids has been previously achieved by several mechanisms, such as disulfide bonds, single-stranded DNA linkages, and biotinylation.13-15 Another mechanism – the method of interest for the work presented here – is metal chelation.16 Lipid head groups functionalized with iminodiacetic acid (IDA) are capable of coordinating divalent transition metals (e.g. Zn2+, Ni2+, Cu2+) through four coordination sites, leaving the two remaining sites exposed.17 Poly-histidine tags that are covalently attached to proteins of interest are then able to bind to these exposed sites. IDA membranes also exhibit reversibility after EDTA is added to the system, as EDTA sequesters metal ions, causing proteins to become unbound.18-19
Dipalmitoyl iminodiaceticacid (DPIDA) and dioleoyl iminodiaceticacid (DOIDA) are two IDA-functionalized lipids that have been used for phase targeting of histidine-tagged proteins. DPIDA has been demonstrated to partition into dipalmitoyl phosphocholine (DPPC)-rich Lo phase, while DOIDA partitions into dioleoyl phosphocholine (DOPC)-rich Ld phase when both phases are present in a bilayer.20 This partitioning is due to similarities in carbon tail structures, degree of unsaturation, and length. Phase-specific binding of histidine-tagged proteins to DPIDA and DOIDA in the presence of Cu(II)has been extensively examined by Sasaki and coworkers.18, 20-22 Histidine-tagged green fluorescent protein (GFP) was often used for studying targeted binding. When targeting DPIDA, GFP's fluorescence served as a visual indicator of binding to the Lo phase in Lo-Ld phase separated unilamellar vesicles (GUVs). GUVs exhibited significant changes in shape and morphology, such as membrane bending and tubule formation. This was attributed to protein binding localized to the Lo domains, which resulted in crowding in the headgroup region and induced local curvature. This was most often observed when diphytanoyl phosphocholine (DPhPC) was incorporated into GUVs.
Similarly, crowding-induced changes in Lo-Ld phase separation in GUVs containing DPPC, DOPC, and cholesterol as the main constituents was examined by Scheve et al.23 Targeting and binding of histidine-tagged Ubiquitin, GFP, and Transferrin to the Lo phase was achieved via incorporation of DPIDA. Rather than membrane bending and tubule formation the percentage of GUVs that were phase separated decreased. This behavior was attributed to the large steric pressure localized to the Lo domains by the Lo phase-targeted binding that lead to mixing of the Lo and Ld phase lipids. There was also an obvious trend linking protein size to membrane mixing capacity as measured by the percentage of mixed GUVs. Phase separated lipid bilayers have an inherent free energy of mixing (ΔGmix),24 thus Scheve et al. developed an empirical thermodynamic model to compare enthalpy of mixing to steric pressure exerted by bound proteins. Our previous work expanded upon the work of Scheve et al. to develop and experimentally test a first principles thermodynamic model that more universally describes mixing behavior and is capable of being used for a wide variety of lipid compositions.25 The model consisted of a Boltzmann distribution that was applied to mixing within GUV populations (i.e. percentage of mixed and unmixed GUVs). It also incorporated the steric-pressure contribution to free energy via the Carnahan-Starling equation of state. Values for ΔGmix were determined for various lipid compositions; its value decreased as a critical/mixing composition was approached, thus validating the thermodynamic model. Similarly to Scheve et al., we reported an increase in mixing efficacy as the size of the particle binding to the Lo phase of the GUV increased. We also qualitatively investigated Ld phase targeting in GUVs via DOIDA incorporation and Lo phase targeting in supported lipid multibilayers (MBLs) via DPIDA incorporation. In both instances mixing was observed at elevated IDA lipid concentration. Though the initial phase separated and final mixed states were analyzed, we made only a preliminary qualitative attempt to observe the kinetics and dynamics of the crowding-induced mixing process in one MBL sample.
In this present work, we utilize fluorescence microscopy to quantitatively examine the time-dependent crowding-induced mixing of Lo-Ld phase separated lipid bilayers. The process was observed on supported lipid multibilayers consisting of DOPC/DPPC/cholesterol and DPIDA for Lo targeting or DOIDA for Ld targeting. Bilayers in a lipid multibilayer remain associated with a flat surface throughout the process of exchange of buffers yet distanced enough to be decoupled from strong interaction with the substrate, making it easy to follow the dynamics of individual domains over relatively long periods of time. We varied the steric pressure by varying the size and molecular weight of the histidine-tagged crowding agent and the surface density of the target lipid, DPIDA. A schematic of crowding-induced mixing in a phase-separated lipid bilayer, and its reversibility, is depicted in Fig. 1. Histidine-tagged Ubiquitin (2.5 nm diameter, 10 kDa) and GFP (3.6 nm diameter, 28 kDa) were used. In addition to this, two different sized populations of histidine-tagged nanolipoprotein particles (NLPs) were used. NLPs are self-assembled particles consisting of phospholipids and proteins. Specifically, they are composed of a lipid bilayer patch (~100-200 lipids) with two parallel, amphiphilic membrane scaffold proteins (MSPs) belted around the outer periphery, shielding the exposed carbon lipid tails (Fig. 1). NLPs are discoidal in shape with a thickness of 5 nm (i.e. the thickness of a lipid bilayer), and a diameter that can vary on the order of 10-20 nm.26 The diameter of an NLP population is controlled by the length of the MSP.26-27 Histidine-tagged MSPs of various lengths are commercially available.28-29 MSP1 (25 kDa) and MSP3 (33 kDa) were used to synthesize NLP1 (9 nm diameter, 140 kDa) and NLP3 (14 nm diameter, 240 kDa), respectively. Histidine-tagged NLPs are particularly useful for this work because of their large size scale and size tunability through our choice of the scaffold protein. Our previous work validated the use of NLPs as model crowding agents.25 Here we show that particle size and target phase not only influences the efficacy of steric-pressure induced mixing, but the rate and controlling mechanism at which it occurs. We develop a mass transfer-based diffusional model that, along with visual observations and activation energy calculations, provides insight to crowding-induced mixing mechanisms.
Lyophilized, N-terminal histidine-tagged Ubiquitin was purchased from Sigma-Aldrich, Inc. Green fluorescent protein (GFP) also containing an N-terminal histidine-tag was purchased from Thermo Fisher Scientific. Lyophilized Membrane Scaffold Proteins (MSPs), which were used in the synthesis of NLPs, contained single N-terminal histidine tags and were purchased from Cube Biotech, Inc. The two types of MSP used were MSP1 (sold as MSP1D1-his, 217 amino acids, 25.3 kDa) and MSP3 (sold as MSP1E3D1-his, 277 amino acids, 32.6 kDa). Copper (II) chloride (≥ 99%), sodium cholate (≥ 99%), sodium chloride (≥ 99%), imidazole (≥ 99%), and methanol (≥ 99%) were purchased from Sigma-Aldrich, Inc. Chloroform was purchased from Fisher Scientific International, Inc. DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine), DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), and cholesterol were purchased from Avanti Polar Lipids, Inc. Texas Red® DHPE (Texas Red® 1,2,-dihexadecanoyl-sn-glycero-3-phosphoethanolamine) and Oregon Green® 488 DHPE (Oregon Green® 488 1,2,-dihexadecanoyl-sn-glycero-3-phosphoethanolamine) were purchased in lyophilized states from Thermo Fisher Scientific. DPIDA20 (1,2-dipalmitoyl-sn-glycero-triethyleneoxy-iminodiacetic acid) and DOIDA30 (1,2-dioleoyl-sn-glycero-3-triethylenoxy-iminodiacetic acid) were synthesized according to previously reported protocols. Tris(hydroxymethyl)aminomethane [Tris] (MB Grade) and hydrochloric acid (12.1 N) were purchased from USB Corporation and Fisher Scientific International, Inc., respectively. Ni-NTA agarose was purchased from 5 PRIME, Inc. All water used in the work described was purified using a Barnstead Nanopure System (Barnstead Thermolyne, Dubuque, IA) with a minimum resistivity of 17.9 MΩ•cm.
Lyophilized Ubiquitin was dissolved in Tris Buffer (20 mM Tris, 100 mM NaCl, pH 7.4) at a concentration of 1 mg/mL then purified using Ni-NTA resin as described previously with other histidine-tagged proteins.31-32 Protein yield was measured using UV-Vis absorption at 280 nm, then aliquoted and stored at -20°C. GFP was dissolved in water at a concentration of 0.1 mg/mL, aliquoted, and frozen at -20°C. Ubiquitin and GFP aliquots were thawed prior to binding experiments. NLPs containing DOPC and either MSP1 or MSP3 were synthesized exactly as previously described.25 NLPs used for DPIDA binding experiments were doped with 0.1 mol% Oregon Green-DHPE, while NLPs used for DOIDA binding experiments were not. This was due to potential electrostatic repulsion between the Oregon Green-DHPE in NLPs and Texas-Red DHPE in the Ld region of MBLs.25
Planar lipid multibilayers (MBLs) were prepared by a standard spin-coating technique as previously described.25 Briefly, appropriate amounts of DOPC, DPPC, Cholesterol, DPIDA or DOIDA, and Texas Red-DHPE were combined, dried under nitrogen gas, and dissolved in a Hexane/Methanol solution (93 %v/v Hexane) at a concentration of 1.1 mg/mL total lipid. Samples were then spin-coated onto a 1 cm2 mica substrate at 3000 RPM for 40 seconds and dried under vacuum for at least 2 hours. Samples were enclosed within open-top wells consisting of 3D printed polylactic acid (PLA) squares adhered to polystyrene Petri dishes with vacuum grease. PLA squares had dimensions of 1.5 cm × 1.5 cm with a depth of 0.4 cm. Each well was hydrated in Tris Buffer (20 mM Tris, 100 mM NaCl, pH 7.4), heated to 55°C on a heating plate, and held there for at least 5 minutes before being removed and allowed to cool to room temperature. After cooling, excess buffer around the outer periphery of the PLA well was removed. Prior to imaging, each well contained supported MBLs on mica hydrated with 900 μL of Tris buffer. To each well, 6.8 μL of 16 mM CuCl2 was then added. Afterward, concentrated stocks of Ubiquitin, GFP, NLP1, or NLP3 were added to their respective sample such that the final concentration was 0.2 μM. After mixing behavior was observed, 3.6 μL of 0.5 M EDTA was added to remove proteins and observe domain reformation.
Imaging was performed using a 60× water immersion lens on a Nikon TE400 fluorescence microscope. The microscope contained FITC and Texas Red filters (Chroma Technology, Bellows Falls, VT). For visualization of GFP and Oregon Green-DHPE-containing NLPs, the FITC filter was used, while Texas Red Filters were used to visualize MBLs containing Texas Red-DHPE. Since Ubiquitin is non-fluorescent, it could not be visualized directly. With the concentrations of dye and protein used, no visual overlap was observed between the two filters (i.e. lipid domains could not be seen in the FITC filter and GFP/NLPs could not be seen in the Texas-Red Filter).
Microscope images of MBLs used in quantitative analysis for examining diffusion behavior were processed by converting 16-bit images to black/white binary pixelated images with ImageJ as shown in Fig. S3. The area fractions of the converted images were then determined using the “Analyze Particles” tool. Standard deviations of 4 quadrants within the microscope field of view were used to determine the error in Area Fraction for data points that were regressed. Processed images were regressed with Least Squares using the Runge-Kutta 4th order method for numerical integration. The program for finding numerical solutions was written and performed in MATLAB. Errors in regressed parameters were determined by regressing parameters to the upper and lower ends of error bars from experimental data.
We incubated histidine-tagged Ubiquitin (~10 kDa), GFP (~28 kDa), NLP1 (~140 kDa), or NLP3 (~240 kDa) with supported lipid multibilayers (MBLs) that contained two different concentrations of DPIDA, 12 mol% or 9 mol% in a 3:2 molar ratio of DOPC:(DPPC+DPIDA), 18 mol% cholesterol, and 0.1 mol% Texas Red-DHPE. These compositions display liquid ordered (Lo) - liquid disordered (Ld) phase coexistence.23 The DPIDA lipid partitions to the Lo phase and the histidine tags of proteins bind to the IDA headgroup in the presence of Cu(II), thus targeting binding to the Lo phase.20, 23 Texas Red-DHPE partitions strongly to the Ld phase such that the Lo phase domains appear dark by fluorescence microscopy as shown in Fig. 2A. Cohen-Simonsen and coworkers have shown that the Lo phase domains proximal to the substrate are sub-microscopic while those in subsequent bilayers coarsen quickly to form microscopic domains, as seen in Fig 2A.33 The domains observed here are in the second, and only other, bilayer distal to the substrate indicated by the lack of observation of any overlapping domains.
We observed crowding-induced dissolution of the Lo domains of MBLs containing 12% DPIDA when incubated with histidine-tagged GFP, NLP1, and NLP3, as demonstrated by a decrease in domain size as time progressed in Fig. 2A-D. We characterize the dynamics of this crowding-induced mixing mechanism by plotting the relative Lo domain Area Fractions (AF), i.e. AF/AF0, vs. time, which decays exponentially to zero (apparently complete dissolution) as shown in Fig. 3A. The Lo domains bound by the smallest species, Ubiquitin, exhibited partial dissolution with a final relative AF of 0.87±0.08, but no clear exponential decay (Fig. 3A). The Lo domains bound by GFP, NLP1, and NLP3, in order of smallest to largest, exhibited a final relative AF of zero within 9, 6, and 2 minutes, respectively. Immediately afterward, 2 mM EDTA was used to remove these bound proteins, resulting in the reappearance and growth of Lo domains as demonstrated in Fig 2D-F. In Fig. 3B, it can be seen that the relative AF returned to 80% of the original value for GFP and 90% for NLP1 and NLP3 within 1 minute after EDTA is added, indicating that the dissolution that we observe here is a reversible mixing transition. During all domain dissolution and domain growth, the vicinity close to the domains tended to have a granular appearance as shown clearly in Fig. 2B (inset).
For MBLs containing 9 mol% DPIDA, complete dissolution of the Lo domains was observed when incubated with NLP3, the largest species of the four (Fig. 3C). Incubation with NLP1 resulted in significant dissolution, with a residual relative AF of 0.06±0.01 after completion. This final value did not change significantly over the final 5 minutes as seen with the data points in Fig. 3C. After addition of 2 mM EDTA, the relative AF for these two cases returned to 85-90% of their original value within a 1 minute time period, as shown in Fig. 3D. No significant change in relative AF was observed when incubating in the smaller species, Ubiquitin or GFP, over an 8-9 minute period as shown in Fig. 3C.
Dissolution of Lo phase domains began immediately after NLP1 and NLP3 were added to phase-separated MBLs containing 12 mol% DPIDA and when the larger of the two NLPs, NLP3, was added to phase-separated MBLS containing 9 mol% DPIDA. However, for other samples, immediately after protein was added, smaller Lo domains were ejected from larger Lo domains, keeping the relative AF constant over the course of about 1 minute as demonstrated in Fig. 4A-B. These ejected domains were seen to grow by coalescence or Ostwald ripening as demonstrated in Fig. 4B-C. Imaging of bound GFP showed that the bound species were primarily located in the Lo phase (small and large green domains in Fig. 4C) during this initial period. After this initial period of domain break up, domains proceeded to dissolve for GFP binding (demonstrated in Figs. 4D-F in Texas Red channel and Fig. S4 for representative GFP channel images) or Ubiquitin binding to 12 mol% DPIDA MBLs and NLP1 binding to 9 mol% DPIDA MBLs. In the case of Ubiquitin binding to 12 mol% DPIDA MBLs, domain dissolution took place so slowly that coalescence and Ostwald ripening were still observable phenomena during dissolution (see Fig. S5). Only the domain break-up was observed when GFP was incubated with 9 mol% DPIDA MBLs. The small protein Ubiquitin imparted no observable change in relative AF or domain size to the 9 mol% DPIDA MBLs.
The dissolution of liquid ordered domains was modeled using the time-dependent diffusion equation, as shown in equation 1, where D corresponds to the diffusivity of the lipids (μm2/s). The idealized system is illustrated in Fig. 5A, where Lo domains are shown starting with an initial radius of Ro that decreases in size over time. The region of mass transfer (r) corresponds to the annulus between the outer periphery of a domain (R(t)) and the average midpoint to neighboring domains (Rb). Ro corresponds to the average initial domain radius. The initial and boundary conditions for equation 1 are listed in equations 1a-c. At initial time, there is a concentration of Lo domain lipids in the annulus (C1). The Lo domains are assumed to have constant, uniform concentrations of Co throughout the dissolution process. Since domain lipids diffuse outwardly towards the boundaries, the net flux across boundaries midway between domains is equal to zero.
Equation 1 was solved analytically using separation of variables and a 1-dimensional Cartesian Laplacian (Fig. 5B), rather than cylindrical, because an analytical solution in cylindrical coordinates with the given boundary conditions is difficult to obtain. By looking at numerical solutions to both Cartesian and Cylindrical coordinates, it was found that this is a reasonable approximation in the region of the concentration profile close to the domain boundary (i.e. the region of interest for this analysis). The concentration profile is shown in equation 2, where the eigenvalues of the Sturm-Liouville problem are defined in equation 2a. (See Supporting Information for detailed derivation)
An interfacial mass balance was performed around the outer surface of a domain. The time-dependent rate of change of mass within a domain is equal to the flux of lipids out of the domain multiplied by the domain perimeter. The ordinary differential equation for this balance is shown in equation 3, with an initial condition of the radius equal to Ro (equation 3a).
By algebraically manipulating equation 3 and substituting in equation 2 for C, equation 4 for was obtained and solved numerically. The average relative area (R/Ro) of domains corresponds to the relative area fraction (AF/AF0) as shown in equation 5.
The data for AF/AF0 vs. time in Fig. 3A and Fig. 3C were regressed using equations 4 and 5 by the least squares method. The variable parameters for this regression were D and C1/Co. For modelling the reversed process (i.e. protein removal and domain reformation), equations 4 and 5 were used with a negative sign on the right hand sign of equation 4, as the diffusive flux is now into the domain rather than out of it. The value of AF0 from the mixing model was used for its corresponding reversal model.
As shown in Fig. 3, regression curves are in agreement with experimental data, for all samples. Meaningful regression curves could not be generated in the cases where there was no dissolution or where the change in relative AF was minor. Diffusion coefficients (D) obtained from dissolution data appear to be correlated to the size of the bound protein or NLP, as seen in Table 1. D increased from ~0.02 μm2/s to an at least an order of magnitude higher as particle size increased from 10 nm2 (GFP) to 153 nm2 (NLP3). It is also worth noting that bound NLP3 imparted a higher D value in 12 mol% DPIDA in comparison to 9 mol% DPIDA. Diffusion coefficients obtained by demixing data shown in Table 1 were of magnitude ~0.5 μm2/s, and relatively similar for all samples, as expected, since protein was no longer bound.
The range of diffusion coefficients obtained from the dissolution data could indicate a transition from a kinetically-limited process (slow dissolution) to a diffusion-limited process (fast dissolution). The activation energy (EA) associated with lipids transferring from a Lo domain to the surrounding Ld region was approximated using Arrhenius kinetics. Detailed calculations are provided in the Supporting Information. Briefly, relative rates of domain dissolution induced by GFP, NLP1, and NLP3 binding to 12 mol% DPIDA MBLs were compared. Using the Arrhenius equation (equation 6), an activation energy cannot be calculated directly since there are 3 equations (an Arrhenius equation for each particle binding) and 4 unknowns (an Activation Energy for each particle binding and the Arrhenius pre-exponential factor A).
By comparing regressed first-order reaction rate constants (k) between two samples, a change in activation energy ΔEA was determined. Dissolution time scales decreased as particle size increased (Fig. 3), indicating that EA also decreased as particle size increased (i.e. reaction rate increased). MBLs bound with NLP1 exhibited a 0.1kT decrease in EA relative to MBLs bound with GFP, whereas MBLs bound with NLP3 exhibited 1.8kT decrease in comparison to those bound with NLP1. Based on these values for ΔEA, we were able to infer that EA for a bilayer with no particles bound is on the order of 1-2kT (~ 4 to 8×10-21 Joules/lipid).
The Boltzmann distribution, shown in equation 7, relates the free energy to the partitioning of lipids between two states (mixed and unmixed) at equilibrium.34 For the system being examined, there are two contributions to the free energy; the inherent free energy of mixing (ΔGmix) and the free energy associated with steric pressure (ΔGp). The partition coefficient (K) is shown in equation 7 and defined in equation 8 as the ratio of unmixed lipids to mixed lipids at equilibrium. This result was obtained by performing a mass balance on a domain with initial and final equilibrium radii assuming a mixing zone exists. (See supporting information).
Previously, we demonstrated that the steric pressure contribution to free energy can be determined by integrating the Carnahan-Starling equation state over the change in fractional surface coverage (η) of the binding species before and after complete mixing.25 The initial surface coverage (ηi) and final surface coverage (ηf) were determined by knowing how much DPIDA is contained in the bilayer.23, 25 We did not include an additional term for electrostatic interactions because the Debye length is short (~0.5 nm) in the presence of electrolytes. Details of these calculations are provided in the Supporting Information. When this is applied to ΔGp in equation 7, equation 9 is obtained. NP and NL correspond to the number of proteins and lipids in a given area of bilayer, respectively.
Use of equation 9 requires a final relative AF that is neither 0 nor 1. Two samples yielded values that satisfy this criteria; NLP1 bound to 9 mol% DPIDA MBLs (0.06 ± 0.01) and Ubiquitin bound to 12 mol% DPIDA MBLs (0.87 ± 0.08). Based on these AF values, ΔGmix was determined to be (1.0±0.5) × 10-20 Joules/Lipid for the former, and (1.1±0.3) × 10-20 Joules/Lipid for the latter. These values are on the same order of magnitude as those previously determined for this lipid composition in giant unilamellar vesicles.25
Next, we incubated histidine-tagged NLP1 (~140 kDa) with lipid multibilayers (MBLs) of compositions that display liquid ordered (Lo) - liquid disordered (Ld) phase coexistence and contained 20 mol% DOIDA, 18 mol% cholesterol, 0.1 mol% Texas Red-DHPE, and a 3:2 molar ratio of DOPC:(DPPC+DPIDA). The DOIDA lipid partitions to the Ld phase, therefore histidine-tagged NLP1 binds primarily to the Ld domains rather than the Lo domains. As shown in Figs. 6A-C, binding of NLP1 to the Ld region resulted in a generally less circular appearance of the Lo domains, some of which appear to have coalesced. The relative AF of the domains had not perceptively changed. However, small, light Ld domains can be seen to appear inside the Lo domains after 1.5 minutes (Fig. 6C). This phenomenon is similar to the break-up of the Lo phase observed previously for example in Fig. 4A-C. The Ld region also appeared to darken as time progressed. After addition of 2 mM EDTA (Figs. 6D-F), the Ld region became brighter and numerous small vesicles appeared on the edges of the Lo domains, as indicated by the white dots, and the domains took on a leaf-like shape as seen in Fig. 6D. In addition, holes formed in the Ld portion of the bilayer as illustrated by the irregularly shaped dark red patches. Lo domains proceeded to become more round and coalesce while avoiding contact with bilayer holes, while entrapping some Ld “subdomains” within the Lo domains (Fig. 6D-E).
When we waited longer before adding the EDTA, the Ld domains inside of the Lo domains appear to increase in density and finally form vesicles (see Fig. S6) rather than mixing with the Lo phase via dissolution. Therefore, the quantitative dissolution model could not be applied to these binding experiments. Wide-spread removal of the MBL through a process reminiscent of surface folding was the next step (Data not shown). When EDTA was added no reversible effects were observed.
The elongated appearance and lack of change in size of the domains was initially thought to be indicative of a gradual mixing process, akin to reversal of spinodal decomposition. To investigate this hypothesis, domain formation during cooling at this same lipid composition was observed as shown in Fig. 7. The domain formation is clearly indicative of nucleation and growth with the lipid composition used, thus the observed behavior is likely not related to spinodal decomposition.
To further examine the possibility that the mechanism of the mixing process is coupled with the mechanism of domain formation (i.e. nucleation and growth vs. spinodal decomposition), we examined the targeted binding of NLP1 to Lo domains in MBLs with a composition consisting of a 1:1 DOPC:(DPPC+DPIDA) with 26 mol% Cholesterol and 0.1 mol% Texas Red-DHPE. The DPIDA concentration used was 14 mol%. In Fig. 8, it can be seen that this composition was in the spinodal region of the phase diagram indicated by the elongated interlaced domain shapes (Fig. 8B) during domain formation by cooling. After Lo domain formation and NLP1 addition to the system, domains were observed to undergo mixing via dissolution over the course of 3 minutes as illustrated in Figs. 9A-D. Upon removal of the NLP1 with EDTA (Figs. 9E-F), Lo domains reappeared and were elongated enough (Fig. 8C and Fig. 9E are comparable) to suggest recovery of growth in the spinodal region. These results indicate that during Lo targeted mixing of MBLs, the domains will undergo mixing via a dissolution mechanism rather than gradual spinodal-like mixing regardless of their compositional location on a phase diagram.
Crowding-induced dissolution of Lo phase domains in Lo-Ld phase separated lipid bilayers could involve two sequential rate processes, the kinetic process of release of Lo phase clusters from the domains followed by diffusion of those clusters driven by a concentration gradient. Evidence includes the increase by almost 2 orders of magnitude in the diffusion coefficients calculated from the dissolution data as the steric pressure is increased by increasing the size of the bound protein or NLP. In comparison there is a relatively steady diffusion coefficient calculated from the time-dependent growth of domains after removal of the bound proteins or NLPs by EDTA. The variation in this apparent diffusion coefficient could represent a transition from a slow kinetically-limited dissolution process at low steric pressure, induced by a small bound protein such as GFP, to faster kinetics and thus a diffusion-limited process at high steric pressure, induced by a large bound particle such as NLP3. This could be explained by considering the mechanism of the kinetic process. The intermediate state is likely a thermal shape fluctuation of the domain boundary that results in pinching off of a small cluster of the target phase evidenced by the graininess, i.e. domains below ~0.5 μm in size, in the Ld regions surrounding domains as they dissolved. Such thermal fluctuations are normally of energy approximately kT.34 As the size of the bound particle increases, the free energy contribution from steric pressure is increased. This corresponds to higher energy in the initial, phase-separated state. This relative increase in initial energy would result in a decrease of the energy barrier for the mixing process. Using Arrhenius kinetics, this corresponds to a faster rate of reaction, i.e. pinching off clusters, as steric pressure is increased. Thus this kinetic process would no longer limit the dissolution rate. We calculated that the decrease in the activation energy would have to be at least 1.8 kT in agreement the energy scale of commonly occurring thermal shape fluctuations.
The plateau in diffusion coefficient values between 0.2 μm2/s and 0.8 μm2/s is additional evidence of dissolution (and regrowth) by lipid clusters vs individual lipids, as diffusivity generally varies inversely with cluster size. Typical diffusion coefficients for lipids diffusing in an Ld phase are on the order of 1-10 μm2/s.35-37 The Saffman–Delbrück model is an appropriate model for calculating diffusion coefficients of species within lipid bilayers.38 Using this model, it was calculated that lipid clusters consisting of 103-104 lipids result in an order of magnitude reduction of diffusion coefficient relative to that of a single lipid (see Supporting Information). Clusters of such small size would only appear as a change in image texture (graininess) of the region around the dissolving or regrowing domains – consistent with what is observed. Such nanoscopic clusters are capable of dissolving or appearing rapidly through thermal compositional fluctuations which we postulate happened in the final stage of mixing by the highest free energy contributions from steric pressure (NLP3 bound to 9 mol% and 12 mol% DPIDA domains and NLP1 bound to 12 mol% DPIDA domains) and first stage of regrowth by addition of EDTA.
We attempted to change the mechanism of crowding-induced mixing from dissolution (reversal of nucleation and growth) to gradual demixing (reversal of spinodal decomposition) by changing the membrane composition to one that is near a critical point. However, dissolution was still observed in the new composition when NLP1 bound to the Lo phase. This can be explained by considering that during domain formation, small composition fluctuations in the spinodal region of the phase diagram exhibit negative free energies, thus making them favorable.39 This allows for the gradual formation of interlaced domains that gradually change in composition, as typically seen in spinodal decomposition. However, when the process is reversed (i.e. steric pressure induced mixing), the composition fluctuations now exhibit positive free energies and are unfavorable. This eliminates the gradual mixing of the two phases as a process. It becomes more favorable to maintain the initial compositions of the Ld and Lo phases during mixing process as this minimizes composition fluctuations. The dissolution process occurring via lipid clusters rather than individual lipids is especially favorable, since they help to maintain domain composition. These can finally break up through large compositional fluctuations similar to reversal of nucleation.
When the magnitude of the free energy contribution from the crowding pressure (ΔGp, a negative number) is less than the free energy change from mixing (ΔGmix), the addition of ΔGp to ΔGmix gives a new apparent ΔG. This smaller ΔG will, in turn, be associated with a new equilibrium composition of each phase with more similar compositions closer to a critical point. A possible mechanism to achieve this new equilibrium was observed here in the break-up of the target phase by release of micron-scale domains from the target phase. The similarity in size of the ejected domains is suggestive of a Plateau-Raleigh line tension-driven instability which would be interesting to characterize using high-speed microscopy equipment in the future. The release of small domains of the target phase was followed by Ostwald ripening and coalescence as these may serve as mechanisms to move to a new equilibrium composition of each phase by slightly readjusting the composition of each phase without significantly changing the relative area fraction of each phase. In case the new equilibrium compositions nearly merge, i.e. near a critical point, the line tension is extremely low which may contribute to the stabilization of submicroscopic domains.40 This might be mistaken as complete mixing when in fact nanoscopic domains still exist. This might explain the apparent observation of complete dissolution of Lo domains in MBLs containing 12 mol% DPIDA when bound by GFP, as this was not expected. The calculated free energy contribution from steric pressure (ΔGp) for GFP binding to 12 mol% DPIDA MBLs was -5.5 × 10-21 Joules/Lipid, as determined from the integral term in equation 9. The magnitude of ΔGp is smaller than ΔGmix determined to be roughly (1.0 ± 0.5) × 10-20 Joules/Lipid.
When targeting the crowding agent, NLP1, to the Ld phase, membrane shape changes such as vesiculation and hole formation, played a major role in the drive toward equilibrium making it difficult to study mixing. Although we did find some evidence of lipid mixing, (i.e. the appearance of micron-scale Ld domains in the Lo phase domains), it is interesting that a similar experiment resulted in complete mixing of approximately 80% of the population of GUVs in our previous work.25 This could be accounted for by a difference in tension of the bilayers used in these two studies. MBLs are presumably free of any osmotic gradients that would create tension to smooth out membrane bending. The GUVs in our previous study were placed in a slightly hypotonic solution that creates enough tension to prevent excessive vesiculation.
We examined the lipid mixing and demixing dynamics in Lo-Ld phase separated supported lipid multibilayers induced by steric pressure from phase targeted binding of histidine-tagged proteins and molecular assemblies of various sizes. When targeting the Lo phase by inclusion of DPIDA, mixing by the process of Lo domain dissolution was suggestive of a two-step reaction-diffusion process, reaction-limited and slow when the steric pressure was low and diffusion-limited and fast when steric pressure was sufficiently high. Visual observation and the scale of the diffusion coefficients, determined through mass transfer analysis of the data, indicate that Lo domains appeared to break up and dissolve into the neighboring phase via ejection of sub-microscopic clusters and/or micron-scale domains rather than individual lipids. Therefore, the initial reaction consisted of release of lipid clusters from Lo domains via shape fluctuations of the domain perimeter that we determined were of energetic order kT. This was followed by diffusion of lipid clusters via a concentration gradient in the Ld region. Reversibility was exhibited in all instances where domains appeared to completely or nearly completely dissolve. These results were obtained by targeting Lo domains that formed in the nucleation and growth region of the phase diagram. For Lo domains formed in the spinodal region of the phase diagram, Lo domains mixed in a manner nearly identical to the dissolution observed in the nucleation and growth region as demanded by the curvature of the mixing energy with respect to composition. Moreover, using theory we previously derived, we were able to calculate values of ΔGmix for lipid multibilayers that are in agreement with our previously reported values for giant unilamellar vesicles using similar compositions. In addition to Lo domain targeting and dissolution, we qualitatively examined Ld region targeting in MBLs using DOIDA. We found that the overall mixing process induced by steric pressure from the Ld phase is inherently more complex and differs from what was observed with Lo targeting, as the Ld phase is more prone to deformation and shape fluctuations out of the two-dimensional MBL plane.
MLL, SHR, WFZ, and KEJ acknowledge partial support from the National Science Foundation under award number DMR-1500275. WFZ was partially supported by Grant Number T32-GM008799 from NIGMS-NIH. SHR also acknowledges partial support derived from his Blacutt-Underwood Endowed Chair funds. DYS was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.