Membrane prewetting by condensates promotes tight-junction belt formation

Biomolecular condensates enable cell compartmentalization by acting as membraneless organelles1. How cells control the interactions of condensates with other cellular structures such as membranes to drive morphological transitions remains poorly understood. We discovered that formation of a tight-junction belt, which is essential for sealing epithelial tissues, is driven by a wetting phenomenon that promotes the growth of a condensed ZO-1 layer2 around the apical membrane interface. Using temporal proximity proteomics in combination with imaging and thermodynamic theory, we found that the polarity protein PATJ mediates a transition of ZO-1 into a condensed surface layer that elongates around the apical interface. In line with the experimental observations, our theory of condensate growth shows that the speed of elongation depends on the binding affinity of ZO-1 to the apical interface and is constant. Here, using PATJ mutations, we show that ZO-1 interface binding is necessary and sufficient for tight-junction belt formation. Our results demonstrate how cells exploit the collective biophysical properties of protein condensates at membrane interfaces to shape mesoscale structures.


Binding, wetting, prewetting and their possible relation to ZO-1 surface condensates growth
Here we compare different plausible physical mechanisms that could drive the experimentally observed linear growth of ZO-1 surface condensates around the apical interface.First, we consider the scenario in which simple binding would give rise to the enrichment of ZO-1 at the apical interface.In this scenario, ZO-1 proteins would bind with a high affinity to a substrate that is located at the apical interface, presumably PATJ.Simple binding would lead to a homogenous enrichment of ZO-1 at the apical interface instead of something reflecting growth starting from a condensed phase.This scenario does not reflect the experimentally observed linear growth of ZO-1 condensates, pointing to a different physical mechanism of growth.As a second possible scenario we consider condensate wetting dynamics, which are characterized by the motion of the triple line.In this case, pre-formed 3D ZO-1 droplets would wet the apical interface and spread via capillary forces.This scenario predicts that condensates extension slows down over time with ()~ 1/10 in the case of a 3D bulk condensate, or with ()~ 1/7 in the case of a surface condensate (2D) 1,2 .In cells the extension of ZO-1 condensates varies linearly with time implying that junctional condensates grow with constant speed (Fig. 4b).Furthermore, condensate growth in cells is associated with the addition of material that is recruited from the bulk (Fig. 4c), in contrast to 3D condensates spreading on a surface where material stays constant.We could therefore rule out spreading via triple line dynamics or capillary motion 2,3 .In addition, a classical wetting scenario would require that the cytosolic concentration of ZO-1 is above its saturation concentration for bulk phase separation, which is not the case.Instead, ZO-1 concentration in the cytoplasm is around 700 nM, which is far below the saturation concentration for 3D phase separation in cells (around 12 μM) 4 .Thus, the system is in a sub-saturated regime, which suggests the possibility of a prewetting transition 5 .A prewetting transition is a type of surface phase transition below the saturation concentration for 3D phase separation, which leads to the formation of a condensed layer on the surface (Fig. 4f, Extended Data Fig. 5d (up).As we show below the scaling of surface condensate growth in a prewetting scenario reproduces the observed linear growth ()~.In addition, structural and dynamical evidence suggests that junctional ZO-1 condensates are indeed organized as a condensed surface layer 6 and FRAP measurements (Extended Data Fig 6 c-e) show exchange of condensate material with two distinct kinetics, suggesting a more tightly bound first layer and more loosely bound additional layers 4,7 .Below we discuss a minimal model that recapitulates the experimental observations and provide a thermodynamic basis for the formation of the tight junctional belt.Below we describe the thermodynamics of tight junction belt formation as a two-step process: First condensate nucleation at adhesion sites, second condensate growth around the apical interface.Both nucleation and growth can only happen at the membrane surface, because the system is in a prewetting regime.Nucleation is promoted by membrane binding of ZO-1 to adhesion receptors.The initial size of the nucleated surface condensate is limited to the adhesion sites.Condensate growth around the apical membrane perimeter is then promoted by ZO-1 condensate interactions with apical PATJ.The condensates grow along the apical interface by recruiting additional molecules from the bulk via a prewetting transition.

Thermodynamics of ZO-1 condensation on a membrane
We describe a membrane that is polarized into a lateral and apical domain (Fig. 4d) and is in contact with a bulk solution containing ZO-1 protein with bulk chemical potential   (Fig. 4f and Extended Data Figure 5d).ZO-1 proteins can bind to the membrane, where they can form condensates.The surface density of proteins is denoted ( ⃗), where  ⃗ is the position on the membrane.We also introduce a dimensionless composition variable ( ⃗), describing surface condensation, where  = ( −  0 ).Here  is a calibration factor and  0 a reference surface density.The thermodynamics of ZO-1 condensation on the membrane is described by the free energy where the integral is over the membrane surface and the free energy density is given by here,  and  are parameters that control the double well shape of the free energy, and  is the surface area occupied by a single ZO-1 protein molecule on the membrane.The two wells represent dilute and condensed phases of ZO-1 (Fig. 4e).The parameter  describes a free energy contribution related to interfacial tension and the integration is carried over the membrane surface area.Finally, ( ⃗), is the binding affinity of ZO-1 molecules to the membrane, which depends on position  ⃗ on the membrane.ZO-1 molecules bind preferentially to the apical interface where PATJ is enriched.We denote the binding strength at this interface by   and binding strength to the membrane far from this interface by  0 .The interface width is denoted .To initiate condensates, we introduce nucleation sites at positions  ⃗  , where  = 1, … , , where  is the number of sites.The binding affinity to nucleation sites is   and their width is denoted   .We therefore write Here  is the position coordinate along the apical-lateral axis and denotes the position of the apical interface on the membrane.
The chemical potential of proteins on the membrane,  = /, reads For simplicity, we use the same parameter values and binding affinity at the apical and lateral domains.Below we discuss the dynamics of nucleation and elongation of ZO-1 protein condensates described by this model.

Elongation dynamics of ZO-1 condensates
In order to describe the protein dynamics on the membrane driven by recruitment of proteins from the bulk, we consider the Allen-Cahn equation 8 for the composition variable : where  is a kinetic coefficient.The composition variable increases when proteins are recruited from solution and   > .It decreases when   < .At steady state  =   .The steady state condition is satisfied both for the condensed phase with  =   , as well as for the dilute phase with  =   .At the edge of a growing condensate where material is recruited, we have   >  (Extended Data Fig. 5 d, e, j, k).
We solve Eq. 5 numerically and find that once condensates are nucleated at the predetermined nucleation sites   ���⃗, they subsequently elongate along the apical interface at constant velocity  if the binding affinity   is sufficiently strong.Varying this binding affinity, we find that the elongation velocity  increases for increasing binding affinity (Fig. 4g, h).Furthermore, condensate elongation only happens for   larger than a threshold value   , or in terms of the relative binding affinity, Δ =  +   , for Δ > Δ  .Below this threshold, condensates nucleate and grow to a limited size but do not elongate along the apical interface (Extended Data Fig. 5 e, d (lower panel).
When multiple condensates are nucleated at the same time on the apical interface, the process to form a condensate covering the whole apical interface is faster, while the elongation speed of individual condensates is unchanged.In such a process the elongation of condensates jumps discontinuously when condensates fuse (Extended Data Fig. 5g-i).In all numerical calculations we vary the binding affinity to the interface,   , and keep the other parameters fixed (see Extended Data figure 5 l)

Elongation speed in a one-dimensional system
We can calculate the elongation speed of condensates in an infinite one-dimensional system 9,10 To this end, we write the dynamic equation for the composition variable along the centerline  =   of the apical interface, where  =   : here we defined Δ =   +   .An elongating condensate can be described by a front profile that connects the condensed to the dilute phase.We seek solutions of fronts  = ( − ) moving at constant velocity .In order to determine this profile as well as the velocity , we express Eq. 6 in the reference frame that is comoving with the front.In this reference frame, the variable  =  −  measures the distance to the front.Eq. 6 then becomes In order to solve this equation, we write the cubic polynomial in terms of its roots   ,   and  * .We then have  3 −  + Δ = ( −   )( −   )(− * ) .( 8) The roots can be expressed explicitly as These roots are stationary values of the composition  of the dynamic equation, Eq. 6.The values   and   are the steady state solutions corresponding to a condensed phase and to a dilute phase, respectively.The value  * is an unstable steady state.
In order to determine the velocity , we use the ansatz where  is a constant to be determined.Here () has a vanishing derivative for  =   or  =   , representing a front profile that connects a condensed and a dilute phase.Using this ansatz in Eq. 7, leads to This profile transitions from the condensed phase for  < 0 to the dilute phase  > 0 over the width of the front,  = √(  −   )/(2√2).
Using the expressions Eq. ( 9) and ( 13) we show that the elongation velocity  as a function of relative binding affinity Δ is an increasing function (Extended Data Fig. 5e,f).In this case the velocity can be both negative and positive, depending on the sign of Δ, corresponding to elongating and shrinking condensates, respectively.This can be compared to the elongation velocity in the case of pre-nucleated condensates in 2D, which is always positive but requires a binding affinity relative to the chemical potential of the bulk above a threshold value (Extended Data Fig. 5f).