Figures and data
Schematics of the bulk-membrane coupled system.
a Schematic representation of scaffold proteins binding to the receptors anchored on a lipid bilayer. Each receptor (magenta) is tagged to a lipid (orange) in the supported lipid bilayers (SLBs). Scaffold proteins P (green) can bind to receptors R, forming a protein-receptor complex P R. We introduce two more effective components in the membrane: the lipids with a receptor without any protein bound but a water layer on top, and a lipid patch without a receptor but with the water layer on top. These components are termed “effective” because they also include water molecules that form a molecular layer adjacent to the membrane. For clarity, we do not depict these water molecules in the schematics, thereby providing a clearer view of the surface binding structure. We note that the height of the effective binding layer is denoted as h, which is also the height of protein-receptor complex units. In addition, hR represents the height of free receptors. Most importantly, the effective components are confined to the membrane and can only move diffusely parallel to it, or unbind and dissolve in the bulk. b shows the mathematical notations in our theoretical model. The volume fraction of proteins in the bulk is ϕ; ϕP R, ϕR are the area fraction of membrane-bound complexes and free receptors. Moreover, ϕ|z=0 is the volume fraction of protein at the membrane surface, which is denoted as S. So indicates the boundary surface of the bulk region V opposite to the membrane surface S. The boundary surfaces of the bulk region V , excluding S and So, are denoted by ∂V ; The membrane surface’s boundary is represented by ∂S.
Non-dilute surface binding behaviors with varying surface and bulk compositions.
(a) Binding fraction curves 
Surface behavior with varying binding affinity and membrane-bound interaction strength.
(a) Schematic illustrating bulk-membrane coupled system with surface condensates formed in the membrane S without and with bulk phase separation, respectively. (b) Phase diagram without bulk phase separation, indicating that strong binding affinity and (ωP R) interaction strength (χP R-L) among membrane-bound complexes promote surface phase separation. (c) If protein interaction in the bulk is strong and thus bulk phase separation occurs. With bulk condensates partially/completely wet on top of the membrane, the surface phase separation occurs in a much larger parameter regime. This illustrates that bulk protein properties, like interaction strength, also regulate the surface phase behavior. The basic parameter values we set in this study are: 
Illustration of tight junction initiation and in vitro reconstitution system.
(a) Schematic representation of tight junction initiation during cell-cell contact. Upon contact between Cell 1 and Cell 2, receptors (magenta) on the plasma membrane (PM) interact with scaffold proteins such as ZO1 (green) to form condensates that contribute to tight junction formation Beutel et al. (2019). (b) In vitro reconstitution system showing the binding dynamics of ZO1 proteins (green) with receptors (magenta) on a supported lipid bilayer. The His(10)-tagged receptors are anchored to DGS-NTA (Ni) lipid via His-Ni interaction and can bind and unbind with the ZO1 proteins in the bulk.
Model parameter value and their dimensionless values taken from the experimental data.
We note that the molecule sizes vP R, vR are values for 14-mer receptor. All other parameter values are shared in all the studies.
Surface stays homogeneous with 1-mer receptor anchored on the membrane.
(a) Fluorescence images of ZO1 and 1-mer at 1-mer receptor titrations, ranging from 19386 to 102689 μm−2. (b) Fluorescence images of ZO1 and 1-mer showing the effect of ZO1 titration (0 to 800 nM) on 1-mer binding. Scalar bars in the bottom panels represent 2 μm. (c) The linear relationship between membrane-bound ZO1 density and receptor density on the membrane. This is because, in this study, the binding is saturated for all the receptor densities. In this figure, the dots with error bars represent the experimental data (quantified from figure (a)), and the solid line depicts the theoretical prediction. (d) Curve of membrane-bound ZO1 density as a function of ZO1 bulk density compared between experimental data (points) and theoretical prediction (line). The plateau is obtained from the binding fraction limit for 1-mer, c = 0.014. See Appendix 7 for details. The data is a fit to the membrane-bound ZO1 density observed in panel (b). (e) Phase diagram illustrating the homogeneous surface state across a physiological range of receptor and ZO1 densities.
Surface condensates form with 14-mer Receptor on the membrane
(a) Fluorescence images showing the distribution of 14-mer receptors and ZO1 across a range of receptor titrations, from 7 to 2744 μm−2. Surface phase separation occurs at intermediate receptor densities. Too few or too many receptors result in a homogeneous membrane phase: a dilute phase at low receptor densities and a dense phase at high receptor densities. (b) Fluorescence images of 14-mer receptors and ZO1 as a function of increasing ZO1 bulk concentration, from 4 to 14000 nM, demonstrating the emergence of phase-separated domains. Since receptor density remains constant during this titration, the area of surface condensates does not change with increasing ZO1 bulk concentration. Once the ZO1 bulk concentration exceeds the saturation level, bulk condensates form in the presence of surface condensates (refer to Fig. 3a for illustration). Scalar bars in the bottom panels represent 2 μm. (c) Membrane-bound ZO1 density as a function of receptor density on the membrane, showing how receptor density influences surface phase behavior. In this figure, the dots with error bars represent the experimental data (quantified from figure (a)), and the solid line depicts the theoretical prediction. (d) Membrane-bound ZO1 density dependence on ZO1 bulk concentration, comparing experimental data with theoretical predictions. The data is a fit to the membrane-bound ZO1 density observed in figure (b), revealing a transition from a homogeneous surface phase to a two-phase coexisting state (protein-poor and protein-rich phases). (e) Phase diagram with respect to the receptor density on the membrane and Bulk ZO1 density, indicating that 14-mer receptor promotes surface phase separation.
Snapshots of ZO1 surface condensates from simulation (top) and experiments (bottom) when titrating the 14-mer receptor and ZO1 bulk concentration.
(a) Schematic of the system in our theoretical model, with 3D bulk volume V and membrane surface S, where surface condensates formed via surface phase separation. (b) Snapshots of ZO1 from simulation (top row) and experimental observations (bottom) under varying receptor titration levels, from 25 to 3800 μm−2, at 15 mins. (c) Snapshots of ZO1 from simulation (top row) and experimental observations under varying ZO1 concentration levels, from 4 to 100 nM, at 15 min. The experimental results match well with the theoretical predictions from perspectives of both condensate pattern and condensate size. Scale bars in the bottom panels represent 2 μm. we set the diffusivity coefficient value as Di = 0.01 μm2s−1, i = P , P R, R. The gradient coefficients κ = κP R = κR = 2 × 10−5μm−1.
(a) Illustration of the mask for receptor intensity to determine the surface concentrations inside and outside of the surface condensates in the membrane. The blue area represents the dilute phase and the yellow area the dense phase. Mean absolute error (MAE) color maps with respect to interaction parameters χP R-L and internal free energy ωP R for 1-mer receptor and 14-mer receptor are shown in (b) and (c), respectively. For the considered parameter range, MAE is minimized for 14-mer at χP R-L = 1.09 and ωP R = −1.37, and for 1-mer at χ = −0.4 and ωP R = 1.1. We note that though there is a minimum of the MSE corresponding to at χP R-L = −0.4, the color map in figure (c) suggests that the χP R-L value for the 1-mer cannot be determined as there is a “valley” of similar MAE value along χP R-L.
(a) Time-resolved snapshots illustrating the emergence and growth of ZO1-rich condensates on a model membrane surface (top row: theoretical simulation; bottom row: experimental observation). Initially uniform at t = 0, the membrane surface progressively develops well-defined droplet patterns by 15 minutes. The system includes 100 nM ZO1 in the bulk and 800 μm−2 14-mer Receptor in the membrane. The scale bar in the experimental images represents 2 μm. (b) Temporal evolution of the total membrane-bound ZO1 fraction, comparing the theoretical prediction (blue line) and experimental measurement (black line). Both approaches show an increase over time, and they closely agree on the final coverage levels. (c) Average droplet area as a function of time, demonstrating the consistency between theory (blue line) and experiment (black line) in capturing the size growth and stabilization of condensates. (d) Time-dependent count of individual droplets, showing that both the model (blue line) and the experimental data (black line) reproduce the overall trend in droplet formation and coalescence. we set the diffusivity coefficient value as Di = 0.01 μm2s−1, i = P , P R, R. The gradient coefficients κ = κP R = κR = 2 × 10−5μm−1.
