Article pubs.acs.org/Langmuir
Tunable Nucleation Time of Functional Sphingomyelinase−Lipid Features Studied by Membrane Array Statistic Tool Charng-Yu Lin and Ling Chao* Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan S Supporting Information *
ABSTRACT: Aggregation or assembly of lipids and proteins could significantly change the proteins’ function. A peripheral membrane enzyme, sphingomyelinase (SMase), has been reported to be able to assemble to a functional feature with its lipid substrate, sphingomyelin (SM), and its lipid product, ceramide (Cer). SMase seems to processes its substrate more effectively in this feature. Here, we report that the functional feature has a tunable formation time. The peculiar behavior is that the feature formation has a time lag depending on the membrane composition. We hypothesized that the time lag is due to the significant nucleation energy barrier when the feature phase forms in its metastable parent phase in the 2-D lipid membrane. To study the stochastic nucleation of the feature, we built a corralled lipid membrane platform with numerous isolated membrane systems in parallel to capture the nucleation statistics. Using the high-throughput approach and the appropriate experimental design to circumvent the interplay of the complicated phase segregation in membranes induced by SMase, we found that the nucleation rate of the feature can be tuned by the supersaturation of the enzyme, the lipid substrate, and the lipid product, in the fluid phase of the membrane. The correlation between the supersaturation and the nucleation rate can be well described by the classical nucleation theory equation, suggesting that the feature formation follows the nucleation process with a certain component ratio specified in the equation. The certain relative component ratio suggests that the feature may have certain organization instead of being random aggregation. In addition, our finding suggests that nucleation could serve as a time lag control mechanism in this enzymatic system, and ways to reduce nucleation energy barrier could be used to shorten the aggregation time lag and vice versa.
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INTRODUCTION
We have previously reported that an enzyme sphingomyelinase (SMase) can form a 3-D feature with its lipid substrate and lipid product.10,11 This enzyme has been found to have an important role in various fundamental cellular processes,12−17 including differentiation and apoptosis. The substrate of this enzyme is called sphingomyelin (SM), and the products are ceramide (Cer) and phosphocholine. In our previous model membrane study,10 the formation of the 3-D SMase-rich feature is a key event triggering membrane morphology change. The feature is hypothesized as a slowly nucleating SMase-rich phase, where SMase can process its substrate, SM, more effectively. We found that the SMase enzymatic reaction has stages in model membrane systems. After the SMase was added to the membrane, the SM concentration in the fluid phase reached a steady level, and the SM concentration can further drop only after the SMase−lipid feature formed. In addition, after the SMase−lipid feature formed, we observed a depletion of SM concentration toward the feature. It seems that the SMase at the feature can process its substrate at a concentration lower
The occurrence of phase transitions of biomolecules is important for many biological functions.1 Some proteins and lipids can significantly change their functions after forming or joining a new phase. For example, phase segregation of lipids and proteins in the lipid membrane has been suggested to initiate many cellular processes, such as apoptosis (programmed cell death) and immune response, by including or excluding cell signaling membrane proteins into the new formed phase.1−3 Aggregation of proteins or assembly of lipids and proteins is also a type of phase change. In some cases, lipids can form complexes with proteins and cause the allosteric effects of the proteins.4,5 Apolipoproteins and lipids can assemble together to form high-density lipoprotein particles (HDL), which can help inhibit inflammation and platelet aggregation.6 Aggregation of proteins, such as amyloid fiber formation7,8 and prion aggregates,9 plays important roles in neurogenerative diseases. Developing tools and theories to study new phase formation in biology is important for obtaining underlying mechanism of many cellular processes and may also provide us insights into developing new biomimetic materials. © 2013 American Chemical Society
Received: May 14, 2013 Revised: August 25, 2013 Published: September 23, 2013 13008
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than what a SMase can do when it is dispersed at the fluid phase membrane. The change of the enzyme behavior results in different ceramide generation situation before and after the SMase−lipid feature forms. The different ceramide generation situation may be required for different functionality at different times in the cellular processes.18−20 Study about what physical or chemical factors can contribute to the timing of the SMase− lipid feature nucleation might reveal the control mechanisms of the feature, which could provide insights into novel therapeutic opportunities.21−23 Many studies have started to use nucleation theories to study the formation kinetics of protein aggregations or protein−lipid assemblies.24,25 The fundamental of the nucleation theories is to describe kinetic processes of how materials in a metastable state assemble to form nuclei (seeds) of the new phase.26 If a phase transition is thermodynamically favored, the materials assembled in the new phase state have lower chemical potential than they are in the parent metastable phase.27−29 However, the nucleation barrier arises from the energy penalty for creating an interface between the new formed phase and the parent phase.31,36 The largest nucleation energy barrier corresponds to a critical size, at which the assembled cluster is called a nucleus. As clusters grow beyond the critical size, the further growth is favorable. The net number of clusters passing this critical size per unit time is the nucleation rate.26,30 We have previously reported that SMase−lipid features contain significant amount of SMase, Cer, and SM10 but did not know if the features are in the form of random aggregation or are clusters with certain relative component ratios. Being able to well describe the feature formation kinetics by the classical nucleation theory may suggest that the growth of the feature follows the cluster growth process with certain component ratio specified in the classical nucleation equation. However, one of the largest challenges to study the nucleation event is that the significant energy barrier of nucleation can result in stochastic appearance of nuclei.26,29,30 In our previous study, we have observed that the nucleation time of SMase−lipid feature varies from system to system, and the nuclei appearance time may have a wide distribution. The stochastic nature of the nucleation makes it difficult to obtain enough information from a small number of samples. A method needs to be developed to accurately quantify and compare the nucleation time influenced by the factors to test. In this study, in order to statistically study the nucleation of the functional SMase−lipid feature, we constructed a platform where numerous isolated membrane systems can be observed in a single set of experiments. Observing the numerous corralled membrane systems with the same condition allowed us to capture the overall distribution of nucleation time, which cannot be captured by observing only a few systems. We developed a model based on classical nucleation theory to analyze the nucleation time distributions and demonstrated how the appearing time of this functional feature could be tuned by the supersaturation of the materials composing the feature in the 2-D lipid membrane. The result of fitting the feature formation rate to the classical nucleation theory equation suggests that the feature may have certain relative component ratios, and the feature could be viewed as a complex instead of random aggregation.
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and cholesterol (Chol) were purchased from Avanti Polar Lipids (Alabaster, AL). Texas Red 1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine, triethylammonium salt (Texas Red DHPE), and Alexa Fluor 488 goat antimouse IgM (μ chain) were purchased from Life Technologies (Grand Island, NY). Sphingomyelinase from Bacillus cereus (SMase), monoclonal anticeramide antibody produced in mouse, and all other reagents, unless otherwise specified, were purchased from Sigma-Aldrich (St. Louis, MO). Preparation of Large Unilamellar Vesicles. Large unilamellar vesicles (LUVs) were prepared by the extrusion technique for formation of supported lipid bilayers (SLBs) by vesicle deposition. Lipids were mixed in chloroform and dried with nitrogen and then kept in vacuum for 5 h for further removal of chloroform. Dried lipids were reconstituted in a Ca−HEPES buffer (10 mM HEPES, 2 mM CaCl2, and 100 mM NaCl, pH = 7.4) at a concentration of 2 mg/mL. LUVs were formed by passing lipid solutions through an 50 nm polycarbonate filter in an Avanti Mini-Extruder (Alabaster, AL). The extrusion was performed above the transition temperature of the used lipid mixture. Formation of Corralled Supported Lipid Bilayers in a Microfluidic Device. We used the protein microcontact printing method developed by Kung et al.31 to construct bovine serum albumin (BSA) protein corrals. A polydimethylsiloxane (PDMS) stamp with a 50 μm × 50 μm corral configuration was used to perform microcontact printing. The stamp was activated by oxygen plasma for 30 s and then immersed in a BSA aqueous solution (250 μg/mL). The BSA on the stamp was then transferred to a coverslip cleaned by argon plasma for 10 min. The PDMS microchannel slab was treated with oxygen plasma for 18 s and then sealed with the coverslip patterned with BSA. LUV solutions were flowed into microchannels and incubated for 10 min to allow vesicle deposition to occur on the clean glass surface where there is no BSA. Later, water was flowed into channels for 10 min to wash excessive lipid vesicles. Formation of Sphingomyelinase−Lipid Features. The corralled membranes in an assembled microchannel (50 μm × 500 μm × 1.5 cm) was heated to 37 °C and kept at this temperature during the entire experiment by a homemade microscope heating stage. Some Mg−HEPES buffer (10 mM HEPES, 2 mM MgCl2, and 100 mM NaCl, pH = 7.4) was flowed into the channel to precondition the environment of membranes before the addition of SMase. A 30 cm tygon tubing with 2 in. inner diameter was used to connect the solution reservoir to the inlet of the microchannel. SMase solutions with desired concentrations were flowed into channels at a flow rate of 30 μL/min for 4 min and incubated for 1 min after the flow stopped. Later, 0.2 mL of the Mg-HEPES buffer was flowed into channels at a flow rate of 30 μL/min to wash away excessive SMase bulk solutions in the microchannel. All of the solutions were preheated to ensure that the solution temperature can be around 37 °C when they reached the membranes in the microchannel. Characterization of Ceramide by Immunostaining. To stain ceramide produced after SMase enzymatic hydrolysis, monoclonal anticeramide antibody produced in mouse and Alexa Fluor 488 goat antimouse IgM (μ chain) were used. The entire process was performed in the microchannel (100 μm × 500 μm × 1.5 cm), where the corralled membranes were made and the enzymatic reaction was performed. A 30 cm tygon tubing with 2 in. inner diameter was used to connect the solution reservoir to the inlet of the microchannel. 0.25 mL of anticeramide antibody at a concentration of 4 μg/mL in PBS buffer (0.01 M phosphate buffered saline, 138 mM NaCl and 27 mM KCl, pH = 7.4) was flowed into channels after PBS wash and incubated with the membranes for 25 min following a 0.3 mL PBS wash. After the wash, 0.25 mL of Alexa Fluor 488 goat antimouse IgM at concentration 10 μg/mL in PBS buffer was flowed into the systems and incubated with lipid membranes for 25 min followed by a 0.2 mL PBS wash. The entire immunostaining was performed at room temperature and protected from light. Fluorescence Microscopy Images. Images were captured by an Olympus CKX41 inverted microscope with an XM10 monochrome camera. Images of immunostaining were observed using an Olympus
METHODS
Materials. 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC), porcine brain sphingomyelin (SM), porcine brain ceramide (Cer), 13009
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Figure 1. Large number of membrane systems allow us to obtain nucleation statistics and to observe the variation of ceramide generation among the systems. The green color is from Alexa Fluor 488-labeled anticeramide, indicating where ceramide locates. The red color is from the fluorescently labeled phospholipid (Texas-Red DHPE). The SMase−lipid features are the round yellow bright features, containing both red-labeled phospholipid and green anticeramide antibody. The 40/40/20 DOPC/SM/Chol membranes were treated with 0.2 unit/mL SMase and (a−c) are the individual membrane platforms which were started to be washed with no-Mg2+ buffer at 5, 40, and 180 min after the SMase solutions were exposed to the membranes. The immunostaining procedures were followed after the wash.
ceramide generation. 0.5 mol % of fluorescently red labeled phospholipid (Texas-Red DHPE) was incorporated into our lipid membrane systems in order to show where each corralled membrane locates. The green color is from Alexa-Fluor 488 labeled anticeramide antibody, indicating where ceramide locates. The SMase−lipid feature contains both Texas-Red DHPE and ceramide and therefore is shown in yellow in Figure 1. Images a−c qualitatively demonstrate that more and more systems had features with time. More importantly, a high amount of green color can be only observed in the system that already contained a SMase−lipid feature, supporting that significant ceramide generation occurs after the appearance of the feature. Note that we demonstrate the feature formation and the ceramide generation in the membrane with 40/40/20 molar ratio of DOPC/porcine brain SM/Chol, since it is a conventional model raft membrane composition10 and has been used to demonstrate a series of membrane morphology changes induced by SMase (top illustration in Supporting Information Figure 1). In addition to this membrane composition, we have observed that the feature can form in membranes with various molar ratios of phospholipid to sphingomyelin and with lipids from different species (Supporting Information Figure 2). Moreover, the feature can appear in the membrane systems with or without cholesterol (Supporting Information Figure 1). These observations indicate that the SMase−lipid feature can form in a wide range of membrane compositions; however, their sizes and appearing times are observed to be influenced by the membrane composition. Overall Nucleation Time Distribution by Counting the Number of the Corralled Membranes Having Features with Time. In order to obtain the nucleation time distribution of the SMase−lipid feature among the numerous corralled membranes, we recorded the morphology evolution revealed by the 0.5 mol % Texas-Red DHPE incorporated in the membrane. By counting the number of corralled membranes which already had the features with time, we can obtain the overall statistical distribution of the nucleation time. Figure 2 demonstrates an example of how the nucleation time distribution could be influenced by SMase concentrations in membranes with 40/40/20 molar ratio of DOPC/SM/Chol at 37 °C. Each line in Figure 2 is from nine sets of 78-corral experiment with the same condition. The three lines represent the cases when three different SMase concentrations (0.2, 0.1,
IX81 inverted microscope with a Hamamatsu ORCA-R2 digital CCD camera.
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RESULTS Significant Ceramide Generation Only Occurred after a SMase−Lipid Feature Formed in a Membrane System. We have previously reported that SMase can form a functional feature, where SMase is hypothesized to process its substrate, sphingomyelin, more effectively. However, it is difficult to study the formation and the function of this feature due to its slow nucleation rate and a large variation of its appearing time. Therefore, a large set of experimental data is required for studying the nucleation conditions of the SMase−lipid feature. To construct proper membrane systems for observing the stochastic nucleation, we used a sacrificial protein to corral supported lipid bilayers to numerous membrane systems with a size of 50 μm × 50 μm, mimicking the size of a piece of plasma membrane in a cell. The SLBs in each corral can be viewed as an individual isolated system, since the lipids in each membrane system cannot go across the corral to another membrane system. The composition change in each corral does not influence the one in another corral even if they are in the same platform. Therefore, we are able to observe many individual systems at the same time and obtain enough data for studying the stochastic nucleation event. In our previous study,10 comparing the SMase induced membrane morphology evolution revealed by Texas-Red DHPE and the anticeramide antibody characterization results at different time points suggests that a significant amount of ceramide-rich domain is observed after the formation of the SMase−lipid feature in individual systems. Here, to observe the ensemble behavior and the variation among membrane systems, we applied the same antibody characterization method to the numerous membrane systems in a single platform. Panels a−c of Figure 1 are the fluorescently labeled images of 40/40/20 DOPC/SM/Chol membranes obtained after we tried to stop the enzymatic reaction by excessive wash with no-Mg2+ PBS buffer (Mg2+ is necessary for the reaction of the SMase we used) and stained the ceramide using the procedure shown in the Methods section. Figure 1 is to qualitatively demonstrate the variation of the feature formation time among the numerous corralled membrane systems and whether there is a correlation between the SMase−lipid feature formation event and the large amount 13010
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Figure 2. How the number of corrals having SMase−lipid features changes with time in a set of experiment with 78 corrals. Each line is from nine sets of 78-corral experiments treated with the same SMase concentration. The three lines represent the cases when the 40/40/20 DOPC/SM/Chol membranes were treated with three different SMase concentrations (0.2, 0.1, and 0.001 U/mL) at 37 °C.
Figure 3. How the steady state nucleation time changes with the SMase concentration ranging from 0.001 to 0.2 U/mL. Each point is from nine sets of experiments, and each set of experiment contains 78 corralled membranes. The membrane composition is 40/40/20 DOPC/SM/Chol, and the hydrolysis is at 37 °C.
and 0.001 U/mL) were applied to the membranes. Observation started at 10 min after SMase was flowed into microchannels, and images were taken every 5 min in the first 30 min and every 10 min from 30 to 180 min. The number of SMase−lipid features in an image was counted by using Matlab image processing toolbox. As shown in Figure 2, the nucleation time of the features has a wide distribution. The appearing time difference of the nucleus in the first corralled membrane and the one in the last corralled membrane can be a couple of hours (for the 0.2 or 0.1 U/mL case) or about 1 day (for the 0.001 U/mL case). Figure 2 shows that the feature formation rate is higher when we treated the set of corralled membranes with higher SMase concentration. However, due to the wide distribution of feature formation time, some of the corralled membranes in the set with a lower SMase concentration may have nuclei at an earlier time than some of the corralled membranes in the set treated with a higher SMase concentration. This situation indicates the need to obtain the nucleation time distribution from numerous systems instead of the nucleation time from only a few samples, in order to accurately compare the influence by SMase concentrations. Steady State Nucleation Rate Increases with SMase Concentration. In order to more quantitatively compare the nucleation time distribution curves like those shown in Figure 2, we used a quantity called steady state nucleation rate. In a conventional nucleation kinetics curve, a steady state nucleation is supposed to be observed soon after the nucleation starts.26 The steady state can last until the species to nucleate start to deplete in the parent phase and the curve becomes flatter. In this study, the steady state nucleation rate was obtained from the slope of the kinetic data during the steady state time interval determined from the Chow statistical test (details in the Supporting Information). Figure 3 shows how the steady state nucleation time changes with the SMase concentration (0.2, 0.15, 0.1, 0.04, 0.02, and 0.001 U/mL) in the 40/40/20 DOPC/SM/Chol membranes at 37 °C. We found that the nucleation rate increases with the SMase concentration but is not directly proportional to the concentration in the range we provided. We will further discuss their correlation in a later section. In all of our experiments, we removed SMase from the bulk solution after the membrane was exposed to the SMase solution for 5 min. The procedure is probably more physiologically
relevant than immersing the membrane system under a SMase solution over the entire process, since SMase is translocated to the plasma membrane only upon stimulations in nature.13 In this procedure, the supply of SMase to form a SMase−lipid feature can be only from the SMase binding to the membrane during this 5 min period and remaining after the washing step. Although we do not know the exact amount of SMase binding to the membrane with this experimental procedure, previous studies have shown that the dissociation of SMase from membranes is very low32 and the remaining concentrations on the membrane after wash are high and proportional to the original bulk concentrations.33 It is noteworthy to mention that the sizes of the feature are similar when we applied different SMase concentrations to fixed size and fixed composition model membranes (Supporting Information Figure 6) although the higher SMase concentration can kinetically cause faster steady state nucleation rate. The consistent size in every corral despite the varying SMase concentration suggests that the applied SMase concentrations are excessive, and the feature size is limited by the amounts of the lipids confined in a corral. The limitation of size by the amounts of lipids suggests that the features could form with certain relative ratio of SMase to the lipids from the lipid membrane. Substrate/Product Ratio in the Fluid DOPC-Rich Phase Significantly Influences the Nucleation Time. Our previous work suggests that the SMase−lipid feature may nucleate in the fluid DOPC-rich phase (details shown in the Supporting Information Figure 3 and the related text), probably because the high fluidity is required for the multicomponents to organize themselves to form the feature with certain component ratio or structure. We hypothesized that the SM and Cer concentrations in the fluid DOPC-rich phase can directly influence the nucleation of the feature and intended to examine how the substrate/product ratio can influence the nucleation time. However, being able to control the SM and Cer concentrations in the fluid phase is not straightforward. The two major challenges are the complicated phase behavior of DOPC/SM/Cer membrane systems and the membrane composition change during the enzymatic hydrolysis. Castro et al.34 have shown that the membrane system with sphingomyelin, ceramide, and unsaturated phospholipid has a 13011
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on the SMase enzymatic reaction path, illustrated in the phase diagram scheme in Figure 4, to vary the relative SM to Cer concentration ratio in the system. The enzymatic reaction path is based on the 1:1 stoichiometry of the reaction (one SM to one Cer). The steady state nucleation rates in the membranes with 85/15/0, 85/13.5/1.5, 85/12/3, 85/10/15, 85/9/6, and 85/0/15 molar ratio of DOPC/SM/Cer were obtained from the slopes of the SMase−lipid feature number growth curve in the time region determined by the Chow statistical and are plotted in Figure 4. As shown in Figure 4, the feature nucleation rate increases when a small amount of Cer is incorporated into the membrane, but the rate decreases when the Cer amount further increases. The curve supports that both Cer and SM are important for the feature formation. We hypothesized that the SMase feature is formed by a certain number ratio of SM and Cer. In order to obtain the possible ratio, we used the membrane compositions with the same total amount of SM and Cer, so that the concentrations of SM and Cer in each system are correlated. This correlation allows a system to have the maximum formation rate when the system’s SM/Cer concentration ratio is equal to SM/Cer reaction order ratio to form a unit cluster. Figure 4 shows that the fastest rate occurs in the membrane with concentration ratio of SM:Cer ∼ 13.5:1.5, indicating that the reaction order ratio of SM: Cer to form a cluster is close to 13.5:1.5. More details will be introduced in the Discussion section.
complicated phase diagram, including phase coexistent regions of fluid phase, SM-rich phase, and Cer-rich phase. If we prepare a membrane composition that is in the phase-coexistent region or enters into the phase-coexistent region after slight enzymatic hydrolysis, the SM and Cer concentrations in the fluid phase are not easily controlled and significantly influenced by thermodynamic phase equilibrium. Therefore, in order to directly control the SM and Cer concentrations in the fluid phase and to examine the influence of SM and Cer to the feature formation, we prepared several 85/15 DOPC/(SM + Cer) membranes compositions with varying ratios of SM to Cer. The reason is that we found there is no phase separation occurs in this set of compositions before the feature nucleates and all of these compositions are in the one homogeneous fluid phase region (as illustrated in the top right scheme in Figure 4).
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DISCUSSION Nucleation Theory To Describe Nucleation Time of SMase−Lipid Feature. We hypothesized that the formation kinetics of the SMase−lipid feature can be described by classical nucleation theory. Nucleation of a new phase from a metastable state is known to be a kinetic process, influenced by the organization of the new formed phase. The nucleation theory describes the kinetic process of how the components of a new phase form clusters with a size distribution and how the clusters grow to stable nuclei. During the process, the chemical potential decreases when the components cluster together, which is energy favorable; however, the generation of the interface during clustering is energy unfavorable. The combination results in an energy barrier during the nucleation process, and the energy needed to form a cluster with size r is shown in eq 1 and illustrated in Figure 5.
Figure 4. How the steady state nucleation time changes with the Cer and SM concentrations in 85/15 DOPC/(SM + Cer) membranes. Each point is from nine set of experiments, and each set of experiment contains 78 corralled membranes. The membranes were treated with 0.2 U/mL SMase at 37 °C. The used membrane compositions are shown in the top right conceptual phase diagram scheme. The phase diagram reported by Castro et al.34 is used as a guideline of the relative locations of the phase regions. The abbreviations correspond to F, fluid DOPC-rich phase; GSM, SM-rich phase; and GCer, Cer-rich phase.
That no phase separation occurs before the feature nucleates can allow us to more accurately control the SM and Cer concentrations in the fluid phase where the feature nucleates. We used the phase diagram reported by Castro et al.34 as a guideline to draw the phase regions in the scheme in Figure 4. Note that their phase diagram is based on the ternary mixture of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/ palmitoylsphingomyelin (PSM)/palmitoylceramide (PCer) in multilamellar vesicle (MLV) at 24 °C, while we used the ternary mixture with 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/porcine brain sphingomyelin (SM)/porcine brain ceramide (Cer) in supported lipid bilayers at 37 °C. Despite the difference, a previous study35 has suggested that the phase regions in the phase diagram should be qualitatively similar but the phase boundary would be shifted. We are not sure about the exact location of the phase boundaries in the phase diagram of our membrane system. However, we observed only one homogeneous phase appears in the 85/15 DOPC/(SM + Cer) membranes before the feature nucleates, indicating that phase boundary between the fluid phase region and the phase coexistent regions are in fact on the right of the 85/15 DOPC/ (SM + Cer) path in the top right scheme in Figure 4. We chose six different compositions (85/15/0, 85/13.5/1.5, 85/12/3, 85/10/15, 85/9/6, and 85/0/15 of DOPC/SM/Cer)
ΔG(r ) =
πr 2 Δμ + 2πrσ nA
(1)
where the first term on the right is the energy reward by the size increase of the new phase and the second term is the energy penalty by the interfacial energy. Δμ is the chemical potential of the species in the new formed phase minus the one in the metastable parent phase, which is a negative value. nA is the area size of a unit of cluster, r is the radius of the cluster, and σ is the interfacial energy per unit length. The size at the largest energy is the critical size for a stable nucleus to form, above which the cluster can grow faster than dissolve. Note that eq 1 is derived in a 2-D system and does not look the same as a conventional equation in 3-D classical nucleation theory. We observed that SMase−lipid features always attach to and grow from the 2-D lipid bilayer membrane plane. Therefore, we consider that the growth of clusters to the critical-size nucleus all occurs in the 2-D membrane plane. The 13012
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SMase, SM, Cer, and other type of lipid with the reaction order equal to a, b, c, and d, respectively. Examples of the other type of lipid include DOPC, cholesterol, and Texas-Red DHPE. If there is more than one type of the other lipid involved in the complex formation, we can add more terms in eq 5. aSMASE + bSM + cCer + d other lipid + ... → SMase−lipid complex
When the species concentrations are low in the parent phase, the difference in chemical potential between the species in the supersaturated state and in the phase equilibrium state can be expressed as a function with the supersaturated and saturated concentrations of the species in the parent phase.27 For the nucleation of SMase−lipid complex in a parent fluid phase with supersaturated SMase, SM, Cer, and other lipids, we may write the supersaturation, S, as27
Figure 5. How nucleation free energy changes with cluster radius. Illustrations along the nucleation free energy curve are potential cluster growth configurations of SMase−lipid features. r* is the critical radius size for a stable nucleus to form, above which the cluster can grow faster than dissolve. The cluster with radius r* has the largest free energy ΔG*. Note that we assume that the feature cluster grows in 2D before the cluster becomes a nucleus with radius r* and that the 3-D structure could form after the nucleus forms.
e−Δμ / kBT ≡ S [SMase]a [SM]b [Cer]c [other lipid]d ... = [SMase]eq a [SM]eq b [Cer]eq c [other lipid]eq d ...
πnA σ 2 −Δμ
(3)
By using transition state theory, we can obtain the steady state nucleation rate, which describes how fast the clusters in a nucleating system can grow beyond the critical size. ⎡ πn σ 2 ⎤ A ⎥ I st = A exp⎢ ⎣ Δμ(kBT ) ⎦
(6)
where a, b, c, and d are the numbers of SMase, SM, Cer and other lipid components in a unit of the new phase cluster. [SMase], [SM], [Cer], and [other lipid] are the supersaturated concentrations of SMase, SM, Cer, and the other lipid in the provided parent phase. [SMase]eq, [SM]eq, [Cer]eq, and [other lipid]eq are the saturated concentrations of SMase, SM, Cer and other lipid in the situation when the parent phase is in equilibrium with the new formed phase. If there is more than one type of the other lipid involved in the complex formation, we can add more terms in both the numerator and the denominator of eq 6. Tunable Nucleation Time by Controlling Supersaturation of SMase, SM, and Cer. If the nucleation theory can be used to describe the formation kinetics of SMase−lipid features, we expect to observe a steady state nucleation rate at the early time after the nucleation process starts, and the rate could be controlled by the supersaturated concentrations of SMase, SM, and Cer in the fluid phase. We did two sets of experiments, one with varying SMase concentration and the other with varying SM/Cer concentration ratio, in order to examine whether the SMase−lipid feature formation time can be influenced by the supersaturation of the three components based on the nucleation theory. In the set of experiments with varying SMase concentration, eqs 4 and 6 can be rewritten as eq 7 with SMase concentration as the only variable. All of the terms except SMase concentration in the supersaturation can be viewed as constants in this set of experiments and are grouped to a new parameter C.
energy reward is from the chemical potential difference between the state of the components in a formed cluster and the state of the components dispersed in the parent fluid membrane phase. The energy penalty is from the interfacial energy at the 2-D interface between a formed cluster and the parent fluid phase. The cluster with critical size has the largest free energy, which occurs at the situation when the derivative of ΔG to r is equal to zero. Therefore, the critical size and the largest energy barrier can be expressed as eqs 2 and 3. nσ r* = A −Δμ (2)
ΔG* =
(5)
(4)
st
where I is the steady state nucleation rate, A is a dynamical prefactor, which is a function of the driving free energy, interfacial free energy, viscosity, and temperature, nA is the area of a clustered unit, σ is the interfacial energy per unit length, kB is Boltzmann’s constant, T is the temperature, and Δμ is the chemical potential of the clustered species in the new formed phase minus the one in the metastable parent phase, which is a negative value. We have observed that SMase, SM, and Cer are the necessary components for a SMase−lipid feature to form,10 while it is possible that the feature also contains some other lipids. We hypothesized that the SMase−lipid feature is a protein−lipid complex with a certain ratio of components arranging in a certain way, like high density lipoprotein complexes36 or photosystem protein−lipid complexes.37 Equation 5 shows the case when we assume that a unit of the complex is formed by
ln(I st) = ln A −
B ln[SMase] + C
(7)
where B=
C=
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πnA σ 2 a(kBT )2
⎛ ⎞ [SM]b [Cer]c [other lipid]d ... 1 ⎜ ⎟ ln⎜ a ⎝ [SMase]eq a [SM]eq b [Cer]eq c [other lipid]eq d ... ⎟⎠ dx.doi.org/10.1021/la401826b | Langmuir 2013, 29, 13008−13017
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We have shown in the Results section how the steady state nucleation rate of the SMase−lipid feature changes with the bulk SMase concentration ranging from 0.2 to 0.001 U/mL (Figure 3). Figure 6 shows that the measured steady state rate
C′ =
Note that A′ and B′ parameters in eq 8 can be different from the A and B parameters in eq 7 since the interfacial energy per unit length (σ), the area of a complex unit (nA), and the number of SMase in a unit of complex (a) could be all different in the membrane systems without cholesterol. Equation 8 correlates the steady state nucleation rate and the combinational effect of SM and Cer concentrations. Since the combinational expression originates from the supersaturation, the larger the combinational value, the larger the supersaturation. According to the physics of nucleation, the larger supersaturation should cause faster nucleation rate. Therefore, the values of b and c, the reaction orders of SM and Cer, need to allow the combinational value to increase with the experimentally measured nucleation rate. In order to obtain the possible values of b and c (or b/a and c/a) in the combination, we used the membrane compositions with the same total amount of SM and Cer, so that the concentrations of SM and Cer in each system have a reversed correlation. With this correlation, a system has the maximum nucleation rate when the used SM and Cer concentrations have the ratio equal to b:c (or b/a:c/a) (details shown in the Supporting Information). We observed that the membrane with SM:Cer = 13.5:1.5 has the largest nucleation rate among the compositions we tested (Figure 4). However, the maximum nucleation rate could occur in a membrane composition which we did not test. According to the trend observed in Figure 4, the maximum must occur at the composition close to SM:Cer = 13.5:1.5 and between SM:Cer = 15:0 and 12:3. In addition, slow hydrolysis could occur before the feature nucleates. To account for the small composition difference, we systematically examined several cases of b/a:c/a in the possible ratio range and found that the best fitted result indeed can be obtained when the SM:Cer is close to 13.5:1.5 (data analysis details in the Supporting Information), indicating that the reaction orders of SM and Cer to form a feature (b/a:c/a) is about 13.5:1.5 (or 9:1). Figure 7 shows the fitted result when we used the 13.5:1.5 as the reaction orders of SM and Cer. The steady state nucleation rate data are well fitted to the classical nucleation theory
Figure 6. Experimentally measured steady state nucleation rate from 40/40/20 DOPC/SM/Chol and the provided SMase concentration can be well fitted to eq 7 based on the classical nucleation theory.
and the provided bulk SMase concentration can be fitted well in the range from 0.02 to 0.2 U/mL by eq 7 based on the classical nucleation theory. The R-squared value and the fitted parameters A, B, and C can be found in Figure 6. We did not include the 0.001 U/mL data into the fitting process, since eq 7 describes homogeneous nucleation and literature has suggested that heterogeneous nucleation might dominate in the systems with very low SMase concentrations38 (details in the Supporting Information). Note that we used the provided bulk SMase concentration instead of the SMase concentration at the membrane as the [SMase] in eq 7 during the fitting process. The substitution is valid since SMase concentration at the membrane is found to be proportional to the provided bulk SMase concentration,33 and the proportionality constant can be canceled out and not shown in the final form of eq 7. In order to study the influences from the other two major components, SM and Cer, we prepared several samples with different concentration ratios of SM and Cer in the fluid phase. A series of membrane systems with compositions of 85/15 DOPC/(SM + Cer) were used because the SM and Cer concentrations in the fluid phase can be directly controlled and not complicated by the phase separation (details shown in the Results section). In order to analyze the experimental data obtained by varying Cer and SM concentrations shown in Figure 4, we can rewrite eqs 4 and 6 to eq 8. Since only the concentrations of SM and Cer are the variables and the other concentrations are kept constant in this set of experiments, we can move all of the constants in the supersaturation to the fitted parameter, C′. ln(I st) = ln A′ −
B′ ln([SM]b / a [Cer]c / a ) + C′
(8)
where B′ =
⎛ ⎞ [SMase]a [other lipid]d ... 1 ⎜ ⎟ ln⎜ a ⎝ [SMase]eq a [SM]eq b [Cer]eq c [other lipid]eq d ... ⎟⎠
Figure 7. Experimentally measured steady state nucleation rate from 85/15 DOPC/(SM + Cer) and the provided combination of SM and Cer concentrations with reaction order ratio = 13.5:1.5 (or 9:1) can be well fitted to eq 8 with b/a:c/a = 13.5:1.5 (or 9:1).
πnA σ 2 a(kBT )2 13014
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equation in the form of eq 8, and the R-squared value and the fitted parameters A′, B′, and C′ are shown in Figure 7. The well-fitted result supports our hypothesis that the SMase−lipid feature is a SMase−lipid complex and the relative number ratio of SM to Cer is close to 13.5:1.5. Note that although we provided the same bulk SMase concentration, the amount of SMase bound to the membrane is possible to be influenced by the membrane composition. However, the fitting algorithm and the 13.5:1.5 (or 9:1) fitted ratio at the power order of [SM] and [Cer] should not be significantly influenced, as long as the SMase concentration at the membrane for the complex nucleation has a power-series correlation with SM and Cer concentrations. The real ratio of SM to Cer in a complex can be fixed later after we know how the SMase concentration at the membrane is correlated to the SM and Cer concentrations (Supporting Information). In addition, the differences in the fitted parameters of A and B from the 40/40/20 DOPC/SM/ Chol membranes and A′ and B′ from the 85/15 DOPC/(SM + Cer) membranes are probably due to the effect of cholesterol, which could influence the interfacial energy of membranes. Functional SMase−Lipid Complex. Our previous work has shown that SMase can form a SMase−lipid feature with SM and Cer. The feature is hypothesized as a slowly nucleating SMase-enriched phase, where SMase processes sphingomyelin more efficiently. In this work, we further suggest this 3-D SMase−lipid feature could be an enzyme−lipid complex because of the following three evidences. The first evidence is that the final sizes of the features are similar when we applied different excessive supersaturated SMase concentrations to fixed size and fixed composition model membranes, indicating that the feature contains certain relative ratio of SMase to some of the lipids from the membrane. Second, the 9:1 ratio of SM to Cer makes the feature have the fastest nucleation rate in the DOPC/SM/Cer membrane, suggesting that the feature contains certain ratio of SM to Cer. Third, being able to well fit the experimental data to the classical nucleation theory equation suggests that the growth of the feature follows the nucleation process with certain component ratio specified in the equation (the reaction orders of [SMase], [SM], and [Cer] in the equation). The certain relative component ratio suggests that the feature has certain organization instead of being random aggregation. Time Delay in Biology. Time delay in biology has been reported to play important roles in initiating appropriate responses in sequence and synchronizing physiological responses.39 We found that the formation of the SMase−lipid feature can cause a change of ceramide generation situation. The change of ceramide generation situation causes the changes of lipid membrane morphology, which could be important for cellular functions since different domain morphologies may assume different functional states. In fact, some physiological studies have reported that a large amount of ceramide is generated after a long time delay after this enzyme is translocated onto the plasma membrane. The time delay is thought to have its function since the membrane domain morphology induced by small amount of ceramide in early stage of apoptosis is required to help the signal initiation in cells of diverse origins.14,40−42 The later significant ceramide generation seems to be necessary in the late stage of apoptosis when the appearance of membrane bulges whose formation could be facilitated by the existence of Cer-rich membrane domains.16,17,43
It has been known that time delays in biology could arise by several ways, such as by diffusion or transport of substances through a distance, and by the reaction kinetics of a series of biochemical reactions. Diffusion of substances through a distance takes time and therefore the distance between the reactants can significantly influence reactants’ interaction rate. Many biological events are composed of a series of biochemical reactions, and it takes time for the intermediate reactants to transform to the intermediate products in each reaction step. Therefore, a series of reaction steps can cause significant time delay between the addition of initiating reactants and the observation of the interested products. In this study, we report that the time delay of this feature may be caused by the nucleation energy barrier. Small clusters could grow to form larger clusters or dissolve to form smaller clusters, before a stable nucleus forms. The entire nucleation event can be viewed as numerous steps of the association (addition) and dissociation (subtraction) of molecules. The association and dissociation constants of each step depend on the cluster size, resulting in a cluster population with a timevarying cluster size distribution. The nucleation rate usually indicates how many clusters can grow to a size above the critical size or how many nuclei can be observed per unit time. Because of the numerous clustering steps, there is always a time delay between the time when the system enters into a metastable situation and the time when a new phase nucleus can be observed. The size of the nucleation energy barrier is the most important factor influencing the nucleation rate. The energy barrier is due to the interfacial energy penalty when the cluster becomes larger. As shown in eq 4, the nucleation energy barrier can be increased by increasing interfacial energy or decreasing the supersaturation level. These suggest that the apparent time delay is majorly influenced by the nucleation barrier and that changing the supersaturation of the composing materials and interfacial energy could dramatically tune the appearing times of these features. Since the interfacial energy plays an important role in decreasing the interfacial energy penalty, the existence of heterogeneous nuclei in cells might dramatically influence the time delay. Correlating Individual Nucleation Events to Bulk Kinetic Assays. With the help of corralled membranes, we were able to observe that the ceramide generation becomes significant after the SMase−lipid feature nucleates and the nucleation time has a distribution. The ability to observe the SMase hydrolysis situations of each individual membrane system in a population could tell us more information than the ensemble hydrolysis rate measured from the sample with bulk lipid vesicles. The measured bulk hydrolysis rate is contributed from the hydrolysis occurring on each lipid vesicle. In our membrane platform with numerous corralled membranes, the lipid materials in one corral cannot go to other corrals. The isolation situation of the corralled membranes is similar to the situation that the membranes of different lipid vesicles in bulk are not connected. Therefore, the ensemble of the ceramide generation rate from the corralled membranes should be similar to the hydrolysis rate measured from the bulk kinetic assay.44−47 In fact, when we estimated the ensemble ceramide generation rate from our corralled membrane systems, we obtained a plot of hydrolysis amount vs time with a sigmoidal curve shape and a significant time lag, which are the two characteristics shown in bulk vesicle kinetic assay.44−47 Previous bulk assay or monolayer studies attributed these two character13015
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istics to complicated enzyme kinetic mechanisms determined by data fitting;46−50 however, the mechanism details were difficult to be proved. In this study, since we are able to observe the hydrolysis situation in each individual system among a population, we show that one of the major mechanism steps contributing to the sigmoidal shape curve and the time lag might be due to the nucleation kinetics of the SMase−lipid feature. The hydrolysis rate significantly influenced by the nucleation of SMase−lipid features could also explain why the hydrolysis rate is not positively correlated to the substrate amount.45 Many studies attribute this situation to the phase separation in membranes, since the enzyme may have higher activity at the phase boundaries (domain interfaces).51−54 However, the SMase activity in the gel-fluid phase coexisting membranes with phase boundaries is lower compared to the one in a homogeneous fluid phase. In addition, a recent study shows that SMase is located in the more fluid phase and not at the boundaries.55 The previous study showing that formation of ceramide at the phase boundary51 could be from the preferential adhesion of ceramide molecules to the pre-existing domain boundary. These evidence suggest that the phase boundary amount may not be the major factor governing hydrolysis rate or apparent SMase activity. What influence the overall hydrolysis rate could be the membrane compositions in the fluid phase, which can significantly influence the nucleation rate of the SMase−lipid feature.
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ABBREVIATIONS SMase, sphingomyelinase; SM, sphingomyelin from porcine brain; Cer, ceramide from porcine brain; Chol, cholesterol; DOPC, 1,2-dioleoyl-sn-glycero-3-phosphocholine.
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REFERENCES
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CONCLUSION Herein, we report that a functional sphingomyelinase (SMase)−lipid feature has a tunable formation time. In order to study the stochastic formation of the feature, we built a corralled lipid membrane platform with numerous isolated membrane systems in parallel to capture the formation kinetics. We found that the formation rate of the feature can be tuned by the supersaturation of SMase, its lipid substrate (SM), and its lipid product (Cer) in the fluid phase of the membrane. The correlation between the supersaturation and the measured formation rate can be well fitted to the equations derived from the classical nucleation theory. Comparing the experimental result with the theory further suggests an approximate 13.5:1.5 (or 9:1) molar ratio of SM and Cer in the SMase−lipid feature. In our previous study, the complex was known as a SMase-rich feature, where SMase processes sphingomyelin more effectively. In this work, we showed that the feature formation kinetics can be well fitted to the classical nucleation theory equations, suggesting that the formation follows the nucleation process with certain component ratios specified in the equation. The certain relative component ratio suggests that the feature may have certain organization instead of being random aggregation. ASSOCIATED CONTENT
S Supporting Information *
Supporting Figures 1−8 and data analyses. This material is available free of charge via the Internet at http://pubs.acs.org.
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ACKNOWLEDGMENTS
We thank the National Science Council in Taiwan for the funding support for this work (NSC100-2218-E-002-023MY2).
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AUTHOR INFORMATION
Corresponding Author
*E-mail
[email protected] (L.C.). Notes
The authors declare no competing financial interest. 13016
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