Experimental observations of dynamic critical phenomena in a lipid membrane

Near a critical point, the time scale of thermally-induced fluctuations diverges in a manner determined by the dynamic universality class. Experiments have verified predicted 3D dynamic critical exponents in many systems, but similar experiments in 2D have been lacking for the case of conserved order parameter. Here we analyze time-dependent correlation functions of a quasi-2D lipid bilayer in water to show that its critical dynamics agree with a recently predicted universality class. In particular, the effective dynamic exponent $z_{\text{eff}}$ crosses over from $\sim 2$ to $\sim 3$ as the correlation length of fluctuations exceeds a hydrodynamic length set by the membrane and bulk viscosities.

💡 Research Summary

In this paper the authors present the first systematic experimental investigation of dynamic critical phenomena in a quasi‑two‑dimensional lipid bilayer suspended in water. Lipid membranes composed of a ternary mixture (DiPhyPC, DPPC, cholesterol) exhibit a liquid‑liquid miscibility transition that belongs to the 2D Ising universality class for static critical exponents (ν≈1, β≈1/8). By recording fluorescence movies of giant unilamellar vesicles (diameter ≈200 µm) at several frame rates and temperatures near the critical temperature Tc, the authors extract a time‑dependent order‑parameter field m(r,t) from pixel intensities. They compute the spatial‑temporal correlation function C(r,τ) and its Fourier transform, the dynamic structure factor S(k,τ).

The key methodological step is a scaling collapse of the normalized structure factor S(k,τ)/S(k,0) plotted against k^z_eff τ for many wave numbers k. For each temperature (and thus each correlation length ξ) they search for a single exponent z_eff that best collapses all curves onto a universal master curve. Near Tc the correlation length grows and eventually exceeds a hydrodynamic length L_h defined as the ratio of the membrane’s two‑dimensional viscosity η_2D to the bulk water viscosity η_3D. The authors find that when ξ ≪ L_h the effective exponent is close to 2, while for ξ ≫ L_h it rises to about 3. The crossover occurs around ξ≈13 µm, and the optimal exponent across the whole dataset is z_eff ≈ 2.8 ± 0.2.

These observations are compared with several theoretical dynamic universality classes. Model B (conserved order parameter only) predicts z≈4‑2β≈3.75, which is far larger than the measured values for small ξ. Model H in two dimensions (conserved order parameter plus collective hydrodynamics confined to the membrane) predicts z≈2, which matches the data only when ξ ≪ L_h. The recently proposed Model HC incorporates (i) a conserved order parameter, (ii) collective hydrodynamics, and (iii) hydrodynamic coupling between the membrane and the surrounding 3D fluid. Model HC predicts a crossover of the dynamic exponent from ≈2 to ≈3 as ξ passes L_h, exactly as observed.

To validate the analysis pipeline, the authors perform Monte‑Carlo simulations of Model B dynamics (Kawasaki exchange) on a 400 × 400 lattice, then artificially blur the simulated movies to mimic the experimental exposure time and frame rate. Applying the same scaling collapse yields z≈3.6 ± 0.2, confirming that the methodology correctly recovers the known exponent.

By fitting the full time‑dependent structure factor predicted by Model HC to the experimental data, the authors extract a hydrodynamic length L_h = 6.0 ± 1.5 µm, corresponding to a membrane 2D viscosity η_2D ≈ (6 µm) × η_3D. This value agrees with independent measurements of domain diffusion in similar membranes (2‑4 µm) and demonstrates that the membrane’s intrinsic viscosity is essential for describing its critical dynamics. Setting η_2D = 0 (i.e., ignoring membrane viscosity) underestimates decay times by a factor of 5‑10, further supporting the necessity of the full Model HC.

The paper also discusses experimental complexities, such as the use of ternary mixtures that pass through a plait critical point rather than a true critical point, and the potential small corrections to scaling due to fixed composition versus fixed chemical potential. Nevertheless, the static exponents remain those of the 2D Ising class, and the dynamic measurements are robust against these subtleties.

In summary, the study provides compelling experimental evidence that the dynamic critical exponent in a 2D lipid membrane is not fixed but crosses over from the 2D Model H value (z≈2) to the Model HC value (z≈3) as the correlation length exceeds the hydrodynamic coupling length. This work bridges a long‑standing gap between theory and experiment for conserved‑order‑parameter dynamics in two dimensions, establishes lipid bilayers as a powerful platform for studying critical dynamics, and highlights the crucial role of membrane‑bulk hydrodynamic coupling in determining universal dynamic behavior.