Phase Transition in a Heterogeneous Membrane: Atomically Detailed Picture
Membranes serve diverse functions in biological systems. Variations in their molecular compositions impact their physical properties and lead to rich phase behavior such as switching from gel to fluid phase and/or separation to micro and macrodomains with different molecular compositions. We present a combined computational and experimental study of the phase behavior of a mixed membrane of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) molecules. This heterogeneous membrane changes from gel to fluid and shows separate domains as a function of temperature. Atomically detailed simulations provide microscopic information about these molecular assemblies. However, these systems are challenging for computations since approaching equilibrium necessitates exceptionally long molecular dynamics trajectories. We use the simulation method of MDAS (Molecular Dynamics with Alchemical Steps) to generate adequate statistics. Isotope-edited IR spectroscopy of the lipids was used to benchmark the simulations. Together, simulations and experiments provide insight into the structural and dynamical features of the phase diagram.
<p>Multicomponent phospholipid membranes have recently attracted considerable attention as models for biological systems. Membrane reorganization and phase separation are critical to biological function.1 Phenomena such as microdomain and raft formation result from the diverse compositions of biological membranes, and their studies has attracted of considerable interest.2, 3 For example, lipid diversity has a significant impact on the selective permeation into cellular compartments and on cell sigaling.4–6</p><p>Atomically detailed computer simulations may help correlate microscopic details with macroscopic behavior. However, heterogeneity remains a significant challenge to simulations as relevant time scales are frequently inaccessible to conventional simulations (e.g. hours for lipid flips between leaflets).7 Therefore, most computational investigations of domains in phospholipid membranes were conducted with coarse grained models, such as the Martini force field.8–10 However, removing atomic information by coarse graining may miss critical thermodynamic coupling between different degrees of freedom, such as solvent, ions, and polar head groups.</p><p>Atomically-detailed studies of heterogeneous membranes are challenging due to the slow diffusion of the phospholipid molecules in the membrane plane compared to the typical time scales of computer simulations, making conventional MD simulations prohibitively expensive.11, 12 Several studies were conducted in the grand canonical ensemble using a combination of Monte Carlo (MC) and Molecular Dynamics (MD) simulations.13, 14 However, here we explore a multi-phase diagram as a function of temperature in a joint computational and experimental study.</p><p>We consider a heterogeneous membrane containing two phospholipid species: a 1:1 mixture of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC). The two phospholipids of interest, DPPC and DLPC, contain the same head group but their tails differ by four hydrocarbon units in length (Figure 1).</p><p>We use the algorithm of Molecular Dynamics with Alchemical Steps (MDAS15) to probe in atomic details the phase diagram of DLPC and DPPC. Infrared spectroscopy (IR) on the pure and mixed-lipid membranes is used to measure the phase transition temperature of the lipids, as a benchmark to the simulation results.</p><p>Computationally, we simulate pure DLPC and DPPC membranes and a 1:1 mixture at several temperatures. Recently we simulated a mixture of the phospholipids, DOPC and DPPC.15 However, DOPC/DPPC is a single homogeneous fluid phase which is well mixed. As we illustrate below, the phase diagram of DLPC/DPPC is considerably richer and shows multiple phases as a function of temperature and the formation of "islands" where each individual component is highly enriched.</p><p>The simulations were conducted for 100 phospholipid molecules on each leaflet using the NAMD program,16 the NPT ensemble, and the CHARMM36 force field in all types of trajectories.17 The water model is TIP3P and the aqueous solution is 0.15M NaCl, and the simulation box contains approximately 40,000 atoms. More details are in the Supporting Information (SI, section 1).</p><p>The MDAS algorithm was used to speed up the rate of convergence to equilibrium.15 The MDAS algorithm is formally the same as the algorithm of "candidate Monte Carlo move" which was introduced by Stern18, formalized by Nilmeier et al.19, and further developed by Chen and Roux20. In MDAS, we run a conventional MD trajectory of the system and attempt a double mutation move, (DLPC → DPPC) and (DPPC → DLPC), at random spatial positions every ~500 picoseconds. The mutations are conducted simultaneously along a single alchemical trajectory.19 The acceptance probability of the double mutation is computed with a gradual "alchemical" change. The Hamiltonian of the mutation is H (λ) where λ = 0 and λ = 1 correspond to the reactant (say, the pair AB) and the product (the pair BA), respectively, and λ is an interpolation parameter. The work, w, of a mutation trajectory of length t is w(t)=∫0t∂H/∂λ⋅λ˙(t')dt'. A Metropolis criterion accepts or rejects the mutation: Paccept = min[1, exp(−βw)] where w replaces the usual potential energy difference of MC. The work along the λ displacement is computed during a trajectory of several nanoseconds. This is to be contrasted with a conventional MC move in which the mutation is conducted instantaneously. The gradual mutation generates moves with higher acceptance probabilities, since the immediate neighborhood of the mutation has time to adjust to the mutation and relax to equilibrium. Following the mutation attempt we run a conventional MD trajectory.</p><p>First we consider the single component systems (Table 1) and examine the diffusion constants of DLPC and DPPC in their pure phases. The diffusion constant increases monotonically as a function of temperature for DLPC. This is the expected behavior for a fluid phase in which the diffusion coefficient is estimated as D = kBT/γ where kB is the Boltzmann constant, T the absolute temperature and γ the friction coefficient. In contrast, the diffusion coefficient of DPPC is almost temperature independent below 30°C. A linear increases with temperature is observed with a slope similar to DLPC at temperature higher than 30°C (fluid phase). The significant slowdown at the low temperatures suggests a gel phase with a transition to a fluid phase near 30°C.</p><p>From local dynamics we continue to probe domain formation and mixing. We use the MDAS algorithm to generate configurations for the 1:1 mixture. Using the experimental phase diagram for the same mixtures as a guide,21 we conducted the simulations at the temperatures of 10°C, 30°C, 50°C, and 70°C. At the lowest temperature of 10°C two phases co-exist, the temperature 30°C is near the phase transition from gel and fluid phase to a fluid phase, and at 50°C and 70°C we have a single fluid phase. Figure 2 shows snapshots of the relaxation towards equilibrium as a function of MDAS steps.</p><p>The average acceptance probabilities for mutation steps in MDAS were 0.11, 0.21, 0.34 and 0.27 at the temperatures of 10°C, 30°C, 50°C, and 70°C, respectively. Thermal fluctuations are more significant at the highest temperatures which reduces the acceptance probability. The mutation trajectories lengths were for 4–14 ns, and the conventional MD trajectory between the mutation attempts is of 1.6 ns. The simulations are short and insufficient for equilibration with conventional MD. However, as we illustrate in reference15 MDAS can be more efficient than straightforward MD by a factor of about 1,000 if an appropriate mutation path is found. Recent conventional MD simulations suggest that microseconds may be sufficient for the simulation of fluid membrane systems.11,12 Therefore following the arguments of reference15 it is not surprising that MDAS simulation are equilibrated in tens of nanoseconds. Perhaps the clearer indication of the slow convergence of conventional MD simulations for the current system is Figure 2E. A DPPC cluster in Figure 2E is not assemble even in a microsecond simulation. We illustrate the evolution of the system in the MDAS simulation by following the relaxation of the number of neighbors to a lipid (SI, Figure S3).</p><p>The internal symmetry of crystals or clusters of the same molecule may differ appreciably.22 Of course, as the size of a cluster approaches macroscopic sizes the geometries converge to the crystal values. An example is the evolving packing symmetry of rare gas clusters.22 We observe a similar phenomenon for the packing of DPPC. A different (approximate) translation symmetry is detected for the pure form of DPPC, which is significantly tilted and the packing of DPPC in a "cluster", an island embedded in DLPC fluid. The DPPC in the island is significantly less tilted (Figure 3).</p><p>The island packing is considerably looser and allows for the individual DPPC molecules to straighten up. This is also illustrated by a quantitative measure of the acyl chain order parameter SCD:SCD=(12)<3cos2(θ)−1> where θ is the angle between C-H bonds and the normal to the membrane (SI, Figure S4).</p><p>Experimentally, we consider the same lipid membranes: a 1:1 molar mixture of DPPC and DLPC with isotope-labelled DPPC (13C=O). Isotope labels red-shift the C=O vibrational frequency by ~35 cm−1 enabling us to isolate the contributions from the individual lipids without perturbing their structure, environment, or dynamics. We also consider pure DPPC and DLPC membranes as references. Vibrational modes are sensitive to packing geometries, and therefore frequency shifts can be used to measure phase transition temperatures. Temperature-dependent spectra in the ester carbonyls and the CH2 stretching regions were recorded to measure the phase transitions of the lipids. The ester carbonyl absorption band in the fluid phase is slightly shifted towards lower frequencies compared to the gel phase. The spectroscopy of the CH2 groups confirms the phase transition temperatures from the study of the carbonyls and is reported in SI Section 4.</p><p>Figure 4 shows temperature-dependent FTIR spectra of ester carbonyls for pure DPPC and DLPC membranes together with the temperature dependence of the peak shift. The spectrum for DPPC shows a substantial shift near 40°C while DLPC shift is much smaller, in agreement with calorimetry.21 The high temperature transition of pure DPPC was previously assigned to a gel-to-fluid transition while DLPC remains in the fluid phase in the entire temperature range.</p><p>In the calculations, the temperature for the transition between the gel and fluid phases in pure DPPC is between 30°C and 50°C. The results are in good agreement.</p><p>Figure 5 shows corresponding spectra of the binary mixtures. The DLPC band in the mixed membrane undergoes a monotonic decrease as a function of temperature. In contrast, the DPPC band exhibits sigmoidal-like behavior, changing rapidly between 25–30°C. The abrupt modification of the peak location correlates with a phase transition in this temperature range. The temperature-composition phase diagram of21 suggests the co-existence of fluid and gel phases respectively at a 1:1 mixture and ~20°C.</p><p>In conclusion, we illustrated the combination of MDAS computations and experiments to capture the microdomain formation in a membrane composed of two lipid species. The simulations of aggregate formation and disassembly were made possible by the use of the MDAS algorithm even when the diffusion time is exceptionally slow for all-atom MD simulations. We generate candidate Monte Carlo moves19 by mutation pathways for the lipid chains computed with trajectories of hundreds of picoseconds length. The acceptance probability of these moves is more than ten percent is most of our simulations. We illustrate that the local structural properties of DPPC are different in the pure and mixed gel phases. In the mixed membrane DPPC is less tightly packed and as a result the phospholipid molecule is more in line with the membrane normal and having higher order parameter. We believe that this is reflected in the sharper lineshape changes of DPPC in the pure form compared to the mixed form.</p><p>Finally, we comment that the success of the MDAS approach is critically dependent on finding an efficient mutation pathway. Future applications in simulating and equilibrating mixed lipid systems will require identifying such pathways.</p>