Engineered molecular sensors for quantifying cell surface crowding

Significance Cells interact with each other and the extracellular environment through a crowded assembly of polymers on their plasma membranes. The high density of these surface polymers can generate physical crowding that impacts cell function. However, tools to quantify the extent and effect of surface crowding on live cell membranes are lacking. In this work, we design macromolecular sensors that act as reporters of cell surface crowding. We combine experiments on reconstituted and live cell surfaces with molecular dynamics simulations to provide a mechanistic understanding of how cell surface crowding reduces binding of soluble molecules, and we show that crowding varies significantly with cell type and is affected by oncogene expression.


Chapter I. Dynamics of macromolecular binding on crowded surfaces
The goal of this chapter is to develop a theory of macromolecular adsorption to identify a quantitative metric of surface crowding. We aim to obtain a direct relationship between surface binding of soluble macromolecules and the crowding state of the surface, including the effects of variable glycoprotein length, polydispersity, stiffness, density, charge, and all other interactions. We propose that the osmotic pressure is a universal metric that acts as a quantitative reporter of cell surface crowding, as opposed to other proxy metrics like protein molecular weight or number density.

Momentum balance on crowded cell membrane surfaces
The Cauchy momentum balance in a control volume above the cell surface is given by where D/Dt is a material derivative, is the suspension average velocity, is the total stress of the suspension, and is an external force. Incompressibility further requires that ∇ ⋅ = 0 . The total suspension stress, which include both the fluid and the surface polymers, is given by = − + 2 0 (1 + 5 /2) + ( ) , (1.2) where is the fluid pressure, 0 is the viscosity of the continuous Newtonian solvent, E is the rate-of-strain tensor, is the volume fraction of particles (= 4πa 3 n/3 for spheres), n is the number density, 5 /2 is the Einstein shear viscosity correction that is present for all suspensions, and the particle contribution to the stress ( ) = −nk B T I + σ P , where = − 〈 〉 is the virial stress contribution from interparticle interactions. The force includes all interparticle interactions between the particles. At low Reynolds numbers and in the absence of external forces, the momentum balance of the suspension (solvent plus any particles and polymers) at equilibrium is (1. 3) It is important to note that an aqueous polymer brush surface is at minimum a 2-component system: the fluid plus the particles (polymers). Therefore, the total suspension stress includes contributions from both the solvent and the particles (polymers), = − + ( ) . Therefore, at every continuum point in the suspension, the overall pressure is a sum of the local fluid pressure, , and the osmotic pressure from interactions among the particles within the suspension, including polymers, free ions, and other interacting particles, Π = −tr ( ) /3 (see Fig. S1.1). If there are free ions in solution, then those electrolytes would generate an additional osmotic pressure that is included within Π via the stresslet 〈 〉. Assuming that there are no fluid velocities and that the system is translationally invariant (i.e., independent of in-plane coordinates x and y), Eq. (1.3) becomes ∂σ zz /∂z = 0. This reveals that the total suspension stress is constant everywhere along the z-direction (normal to the membrane surface).
Using Fig. S1.1, we shall conduct a momentum balance to clarify the relationship between the osmotic pressure and swelling of the polymer brush. Suppose that we perform a macroscopic momentum balance on the two regions indicated: bulk solution far away from the brush, and at a point within the brush. At equilibrium, the fluid pressure in the bulk and inside the brush must be equal; otherwise, we would get net flux of solvent to rush from one side to the other. Therefore, bulk = brush . Since the region inside the polymer brush also contains interactions among the polymer beads, these interactions generate an osmotic pressure, Π. This osmotic pressure increases the chemical potential of the solvent in the solution so that it equals that of the excess solvent surrounding the swollen polymer brush. The elastic swelling reaction of the network structure may be interpreted as a pressure acting on the solution, or swollen gel. The chain stretching and network swelling exactly balances the osmotic pressure generated by their interactions, in such a way that the overall momentum balance is satisfied. Therefore, polymer brush swelling and osmotic pressures are equivalent descriptions of the equilibrium structure of the polymer brush. Once we have a constitutive relation for the polymer, we can directly equate the osmotic pressure with the network swelling to determine the shape and size of the polymer gel. For example, the swelling of a gel is given by Eq. (3.75) in Doi (Soft Matter Physics, 2013) (1): where is the volume fraction of polymers in the gel (i.e., metric of gel swelling), 0 is the volume fraction in the reference state, and 0 is the shear modulus of the gel in the reference state. Paraphrasing Doi's text, the left hand side of Eq. (1.4) represents the force that drives polymers to expand and mix with the solvent, while the right-hand side represents the elastic restoring force of the polymer network which resists expansion. The equilibrium volume of the gel is determined by the balance of these two forces. Once again, this demonstrates that the polymer brush height and osmotic pressures are equivalent descriptions of the equilibrium structure of the polymer brush.
Figure S1.1: Cartoon illustrating the overall suspension pressure, which is composed of both a fluid pressure and the particle (polymer) osmotic pressure. Network swelling and osmotic pressures are equivalent descriptions of the equilibrium structure of the polymer brush.
In the x-and y-directions (tangent to membrane surface), the particle stress can take on any value, ( ) ≠ 0 and ( ) ≠ 0 . We therefore have an anisotropic particle stress tensor, ( ) = ( ) , with ( ) = 0. The mechanical (osmotic) pressure is defined as Π = −tr /3, and we define the in-plane pressure of cell surfaces as This is the in-plane pressure that we report in this document for both experiments and simulations.

Equation of state (EOS) of crowded membrane surfaces
Modeling the cell surface proteins and glycans as coarse-grained polymers, we can obtain an equation of state relating the osmotic pressure of the cell surface suspension as a function of its material properties, including density, contour length, persistence length, and electrostatic charge. The equation of state for hard-sphere colloidal suspensions, including the Carnahan-Starling EOS, is used commonly to model macromolecular crowding on the membrane surface and inside the cytoplasm (2)(3)(4)(5). Here, we use our data from molecular dynamics (MD) simulations to determine the equation of state for cell surfaces (see Chap. II for details of MD simulations). The EOS may be represented as a virial expansion (6): where V p = πσ 3 /6 is the volume of a monomer, N R = L/σ is the degree of polymerization, B 2 and B 3 are the second and third virial coefficients and describe two-body and three-body interactions, respectively. For Weeks-Chandler-Andersen (WCA) potentials between all particles, B 2 > 0 and B 3 > 0, and the pressure increases beyond the ideal-gas value. As shown in Fig. S1.2, we find that truncation at the three-body level gives a proficient agreement over the concentrations that we tested in MD. For charge-neutral polymer surfaces, B 2 = 0.40, B 3 = 7.93. For charged polymers with Debye length κ −1 = 1σ, we obtain B 2 = 2.22, B 3 = 10.81; for κ −1 = 2σ, we obtain B 2 = 2.68, B 3 = 29.67. Figure S1.2: Coarse-grained molecular dynamics (MD) simulations were used to compute the osmotic pressure generated by polymers tethered to a membrane surface. The osmotic pressure is defined by Eqs. 1.5 and 1.6, and the ideal-gas pressure has been subtracted in this plot, Π ig = /( ), where is the volume of a monomer and = / is the degree of polymerization. The symbols are simulation data, and the solid curves are Eq. 1.6.

Analytical theory for brush inclusion penalty
Halerpin et al. (7)(8)(9) have conducted theoretical analyses of soluble protein adsorption onto chemically grafted polymer brush surfaces. They distinguish between an insertion versus compressive mechanism of protein adsorption, depending on the size of the protein compared to the mesh size of the polymer brush.
One key difference between chemically grafted polymer brushes and the cell surface glycoprotein brush is that a significant fraction of transmembrane proteins is mobile and can translate in 2D along the lipid bilayer surface. Therefore, a large macromolecule may adsorb onto the membrane via the insertion mechanism because it is energetically more favorable to exclude polymers from the interface as opposed to compressing the brush.
To obtain the free energy of inserting a large macromolecule into the cell surface glycocalyx, we follow the theory by Louis et al (10). The inclusion energy of a colloid in a polymer suspension is given by where Π( ) is the osmotic pressure, γ( ) is the interfacial tension, V s is the volume of the macromolecule (= 4πR 3 /3 for spheres), and A s is the surface area of the macromolecule (= 4πR 2 for spheres). The first term in Eq. 1.7 is the reversible work required to create a cavity of volume V s within the polymer brush. The second term is the energy penalty associated with creation of a depletion layer around the colloid surface. The osmotic pressure term has been discussed earlier and is given by Eq. 1.6. The interfacial tension for a planar interface is given by where the relative adsorption Γ( ) captures the effect of changes in local polymer density due to the creation of an interface. The adsorption is defined as where r is the distance from the colloid surface. The leading order expression of the adsorption is approximated by Γ ≈ −2 /√ ≈ − . This assumes that the adsorption is independent of local density and behaves as an ideal polymer. With this approximation, the surface tension is described solely by the entropic free energy penalty of creating an additional cavity of volume ΓA s ≈ A s , in addition to the volume of the sensor V s . Using this approximation, the surface tension term can be incorporated into a bulk osmotic pressure term in the insertion free energy as where the effective volume of the cavity due to macromolecular insertion is V eff = 4πR 3 /3+4πR 2 for a spherical polymer blob of size and macromolecule of size R (see Fig. S1.3). For our system with R ≈ , the effective volume is well-approximated as V eff = 4π(R + ) 3 /3. Figure S1.3: Schematic of the depletion layer and cavity related to the inclusion free energy of a colloid inside a polymer brush suspension. The size R is the radius of the macromolecule and is the radius of gyration of the glycoprotein.
We use coarse-grained MD simulations to validate our theory. As shown in Fig. S1.4(A), when the insertion energy is plotted as a function of the surface density of polymers, there is no collapse of the data across different sensor sizes and lengths of the polymer brush. This indicates that the surface density is not an accurate, quantitative metric of crowding. Other proxy metrics like molecular weight and number density are inadequate to characterize crowding, because they do not include effects of variable glycoprotein length, polydispersity, stiffness, density, charge, and other interactions.
However, when the energy is plotted as a function of the osmotic pressure, the data collapse onto a master curve, as shown in Fig. S1.4(B). It is important to note that there is no adjustable fitting parameters here. These results confirm our hypothesis that the surface osmotic pressure is the unique quantity that provides a direct, quantitative metric of crowding. When quantifying crowding effects on cell surfaces, one should use the osmotic pressure instead of other proxy metrics like molecular weight, size, and surface density of the surface proteins.

Analytical theory for effective brush potential
In our coarse-grained MD simulations, the Weeks-Chandler-Andersen (WCA) repulsive potential (11) was implemented between the polymer-polymer, polymer-sensor, polymer-substrate, and sensor-substrate. For the sensor-substrate interactions, we also add an attractive Morse potential to model affinity of the sensor to the membrane, which effectively approximates a short-range, attractive harmonic potential, k(z−r 0 ) 2 /2, with stiffness k. These two potentials are sufficient to predict the free-energy landscape for the bare membrane simulations.
where the repulsive WCA potential is given by and the attractive potential to the membrane surface is given by Obtaining the Δ contribution to the overall free energy is non-trivial, since we only include WCA potentials for sensor-polymer interactions and no explicit potential of the brush into the sensor's equation of motion. We do not apriori know what the effective potential posed by the polymer brush will be. Figure S1.5: Local monomer volume fraction as a function of distance from the membrane, for a surface density of 8000 chains/µm 2 . The symbols are simulation data, and the solid curve is Eq. 1.16.
From MD simulation data, the monomer volume fraction of the polymers as a function of height from the membrane surface is modeled by (1. 16) We verified that this model for the polymer brush agrees with data from MD simulations, as shown in Fig.  S1.5. The parabolic form inside the brackets is well known from polymer theory (12); we observe a steeper decay of density, likely due to the fact that the chains are not grafted and instead free to diffuse in 2D. The free energy of a sensor binding to a crowded polymer surface is given by Substituting Eq. 1.16 into the virial pressure equation of state, Eq. 1.6, gives the local osmotic pressure as a function of distance from the membrane surface. The crowding energy as a function of distance, Δ ( ), is obtained by using Eq. 1.10. The resulting crowding energy is used in Eqs. 1.17 -1.20 to obtain the total energy as a function of distance, ( ). As shown in Fig. S1.6, the data from our MD simulations (black symbols) demonstrate excellent agreement with our theory (red curve). Chapter II. Coarse-grained molecular dynamics (MD) simulations

Basic construction of the model
To construct a molecular model of macromolecular transport across cell surface proteins and glycocalyx, we performed coarse-grained Molecular Dynamics (MD) simulations of colloidal transport within semiflexible polymers diffusing on 2D surfaces. This is a modified extension of our protein polymer surface model presented previously (13).  (14), individual beads of diameter σ are connected by a finitely extensible nonlinear elastic (FENE) potential and a bending stiffness is invoked by a 3-particle angular potential, U B . The bottom bead is confined to remain along a 2D surface but can diffuse laterally along the surface. Sensor particles of size R are added to the bulk above the polymer brush. The sensors have a short-ranged binding affinity to the substrate.
We modeled surface protein chains using a Kremer-Grest bead-spring model (14), with each bead representing a structured protein domain or a coarse-grained unit of an intrinsically disordered domain. A bead at one end of the chain is confined between two parallel walls separated by one bead diameter, allowing it to diffuse freely in 2D but cannot escape out of plane. All other beads on the chain are free to move in 3D, except through a bottom wall that acts as a solid substrate, thereby modeling protein diffusion along a membrane that is in-plane fluid. Because the size of each protein domain is large compared to the surrounding solvent molecules, the solvent is coarse grained and its dynamics are not explicitly evolved. In other words, the protein chain experiences a hydrodynamic drag and Brownian motion from the continuous solvent. In this work, the membrane does not deform nor fluctuate out of plane, although these effects may be included.
Simulations were performed using a GPU-enabled HOOMD-blue molecular dynamics package (15,16), and all simulations contained at least 2000 protein chains and 10000 sensor particles. The dynamics of particle i is evolved in time following the overdamped Langevin equation where is the hydrodynamic drag factor, is the velocity, = �2 2 is the translational Brownian force, D i is the Stokes-Einstein-Sutherland translational diffusivity of a single monomer, and is the interparticle force. The left-hand side is zero since inertia is negligible for coarse-grained proteins embedded in a viscous solvent. The translational diffusivity is modeled with the usual white noise statistics, is a delta function and I is the identity tensor. The drag coefficient ζ i of particle i is linearly scaled with the particle size σ i . The interparticle force (described below) includes contributions from sensor-polymer chain interactions, intrachain polymer potential, interchain bead-bead pair interactions, and bead-wall interactions.
All interactions between the particles and walls are modeled with a Weeks-Chandler-Andersen (WCA) potential (11), in which a Lennard-Jones (LJ) potential is shifted upwards, truncated at the potential minimum of 2 1/6 σ i (such that the potential is purely repulsive), and assigned a well depth of = (where k B T is the thermal energy). All lengths are expressed in units of the LJ diameter σ and is set to unity. We connect the polymer chains with a finitely extensible nonlinear elastic (FENE) potential, using a spring constant of k 0 = 30 and a bond length of R 0 = 1.5 (expressed in terms of reduced LJ units, = = 1). To model semi-flexible polymers, we implemented a bending potential between 3 neighboring particles to capture chain stiffness, = �1 − cos( ijk − 0 )�, where is the bending energy, ijk is the bond angle between neighboring particles (i,j,k), and θ 0 = π is the resting angle. The persistence length of the chains was measured by calculating the bond angle correlation, 〈 1 ⋅ 〉 = exp(− /ℓ ), where e i is the unit vector connecting the center of mass positions of particles i and i + 1, and s i is the path length along the polymer to particle i. To implement the persistence length ℓ as an input to the simulations, the bending energy is set to /( ) = ℓ / to achieve the desired polymer stiffness. We have set ℓ = 3 for all of our protein-based simulations based on previous work, and have verified the angular correlation for unbound polymers in 3D as a validation of proper implementation (13).
Sensor particles of different sizes were added to the bulk of the simulation box to model the dynamics of sensor transport and binding to the cell surface. The diameters of the Chol-0.5k PEG, 10k dextran, and 40k dextran sensors were modeled with spheres of diameter 3, 5, and 10 nm, respectively (17). The sensor particles have an attractive potential to the membrane via a Morse potential with the HOOMD parameters (D 0 = 3 × 10 9 , α = 10 −4 , r 0 = σ/2, and r cut = σ/2 + R), which effectively approximates a short-range, attractive harmonic potential U att = k(z − r 0 ) 2 /2 with stiffness k = 2D 0 α 2 = 60. All other particle pairs experience a short-ranged repulsive WCA potential, as described earlier. The dynamics of sensor particle i is evolved in time following the Langevin equation where F i wall = F i att +F i WCA is the short-ranged potential that the sensor particle experiences with the surface, F i att = −∇U att is the attractive linear force, and F i WCA = −∇U WCA is the WCA potential with the surface (see Eqs. 1.14 and 1.15 for definitions of the potentials). In summary, each sensor particle experiences the potentials in Eqs. 1.11 -1.13 as a function of height z, in addition to the pair-wise WCA potentials with the protein polymers. It is straightforward to add flexibility and non-spherical shape effects into our sensor model.
Unlike our previous work (13) where a large concentration of passive PEG depletants were added to the bulk to compress the cell surface proteins, in this work we focus on dilute concentrations in which the osmotic compression is negligible. Furthermore, we did not observe any depletion flocculation nor any large-scale protein clustering. Simulations with dilute concentrations of sensors are very time consuming because acquiring sufficient statistics requires many time steps at equilibrium. Therefore, we accelerated our simulations by using a larger concentration of sensor particles that interact only with the protein polymer and the surface, but not with each other. The sensors act as "ideal-gas" particles to each other but interact with WCA potentials with the surface proteins. However, sensor concentrations that are too large can interact with each other indirectly via correlated motion of the protein polymers. A sensor volume fraction less than 1% was used in this work. We used a system box size of V = L 2 L z , where L was adjusted to achieve the specified area density and number of polymer chains, and L z was chosen to be sufficiently large to maintain a uniform bath concentration of sensors in the bulk. Dilute surface densities were conducted with ∼ 200 chains/µm 2 , and the dense surfaces contained ∼ 20,000 chains/µm 2 . We imposed periodic boundary conditions in the x and y directions, and no-flux hard walls at z = 0 and z = L z to prevent any particles from passing through. Initial configurations were generated by placing the particles in lattice locations, and sufficient time steps were run to reach a steady-state. Time steps were varied from ∆t = 10 −6 − 10 −4 and verified to be sufficiently small to capture relevant dynamics.
A snapshot of the simulations is shown in Fig. S2.2. Simulations were conducted for long enough time steps to sample equilibrium properties. Figure S2.3 shows the concentration of sensors on the membrane surface as a function of time, and we can see that sufficient configurations are sampled after equilibrium is achieved.

Calculation of mechanical stress (and pressure) of cell surface proteins
The pressure of cell surface proteins is given by the negative trace of the virial stress tensor, where = 2 〈ℎ〉 is the volume of the polymer brush, is the length of the simulation box, 〈ℎ〉 is the average height of the polymer surface, is the interparticle distance, and is the pair-wise interparticle force between all particles, including individual monomers within a single polymer. The first term in Eq. 2.3 is the ideal-gas stress and the number density is defined as n = N/V where N is the total number of particles. The second term is the Irving-Kirkwood virial stress tensor that measures the contribution from interparticle interactions. For polymers, it is important to note that the ideal-gas pressure is Π ig = n c k B T and not nk B T, where n c is the number density of chains, n c = N c /V (N c is the total number of chains). Particles lose their translational degree of freedom when constrained as a polymer, so the ideal-gas pressure decreases with increasing degree of polymerization. Returning to our virial EOS in Eq. 1.6, we can rewrite the idealgas expression as Π ig = (k B T/V p ) /N R , where the degree of polymerization N R = N/N c . For very large molecular weight polymers (N R → ∞), the ideal-gas contribution is zero and the first term contributing to the osmotic pressure is two-body interactions (i.e., second virial coefficient).
In calculating the osmotic pressure using Eq. 2.3, it would seem like we are overestimating the pressure based on the first term, which assumes that all N particles are independent. However, the virial stress term will cancel the "excess" stress contribution from the nk B T term. That is, the FENE potential applied to the constitutive particles on the polymers (which represent elasticity) has the opposite sign and subtracts the independent degrees of freedom. The net result is that we correctly recover the ideal-gas pressure of a polymer, Π ig = (k B T/V p )φ/N R .

Calculation of free energy potentials
The free energy experienced by the sensor particle as a function of the distance from the membrane surface is given by U = −k B T ln P(z), where P(z) is the normalized probability distribution of the sensors. We calculate P(z) by binning the simulation into thin slabs and ensemble averaging over all particles and time. From these distributions, we calculate the effective binding energy and the insertion penalty at equilibrium, as shown in Fig. S2.4. The offset at the energy minimum gives the glycocalyx contribution U g and the inplane osmotic pressure of the cell surface. As shown in Fig. S2.4, our analytical theory in Eqs. 1.17-1.20 agrees very well with the direct energy calculations from MD simulations. Once the sensor-substrate affinity is determined in the theory by fitting to the bare-membrane simulations (black symbols and curve), there are no fitting parameters for the crowded surface simulations and theory (red symbols and curve).

Incorporation of charges on protein polymers
Charge effects were analyzed in MD simulations by adding a screened coulomb (Yukawa) pair potential between the constituent monomers of the polymer. The energy scale was set to = B , and the Debye length was varied from κ −1 = σ to κ −1 = 2σ. Electrostatic interactions were not included for sensor-polymer or sensor-sensor interactions.

Binding isotherms for dextran sensors
In the main text, we obtained the relative difference between the crowded and bare surfaces by taking the ratio of the slopes of the bound sensors at small bulk sensor concentrations. This provides a direct measurement of the relative difference, / 0 (or / proK for RBCs), assuming that the bound saturation concentration, max , is equal on the crowded and bare surfaces. As a control, we performed a measurement of the effective dissociation constant of the dextran sensors by obtaining the full isotherm across a larger range of bulk concentrations. The maximum saturating concentrations of the sensors, max , were obtained by incubating the beads and RBCs with 0.5 M bulk sensor concentration. The bound sensor concentrations at each bulk sensor concentrations were normalized by the maximum concentration at saturation to obtain the fractional surface coverage, = / max . The slope at small bulk concentrations were used to obtain the dissociation constant. A representative dataset containing the full isotherm on RBCs for the dextran 40k sensor is shown in Fig. S3.1. The relative ratios of the binding affinities were / proK = 1.5 and 2.6 for sialidase-treated and untreated RBCs, respectively, which agree with the results in the main text obtained using a ratio of the slopes at small bulk concentrations.

Effective dissociation constants of multivalent binding species
As shown by Cremer et al. (18,19), interpretation of the effective dissociation constant of multivalent binding species requires some care. For bivalent-binding antibodies, there are two dissociation constants, is a number that varies between 0.5 and 1.0, and the effective dissociation constant is given by Therefore, the binding isotherm still takes on the classic Langmuir form, except the interpretation of the effective is slightly different. At small bulk antibody concentrations, [ ] ≪ 1, we are still fitting a line with the slope that gives the effective dissociation constant. The main potential issue is that the effective dissociation constant is now a function of the ligand concentration, [ ] . This is not an issue for our dextranbased sensors because the "ligand" concentration is simply the total available surface area on the beads and cells, which is fixed constant in each respective experiment.
However, this is a potential issue for our antibody-based measurement because our biotin-DNA cholesterol sensors incorporate into cell membranes with different affinities. Therefore, the ligand concentration [ ] could be changing drastically as a function of cell type, over-expression, etc. As shown in the expressions above, varying [ ] will change the effective dissociation constants, which is an unwanted problem. In fact, we did indeed see this effect when we used a very large concentration of the biotin-based cholesterol sensors. This issue has been addressed previously by Yang et al (19), in which they observed a 10x decrease in effective of monoclonal antibodies on SLB-coated beads when the ligand surface density was increased from 1400/ 2 to 40,000/ 2 . Fortunately, they found that the effective increased only from 13 to 18 when increasing the ligand surface density from 1400/ 2 to 4200/ 2 (small ligand concentrations). We therefore hypothesized that staying at small surface ligand concentrations would reduce or eliminate this potential uncertainty of determining the effective .
To these ends, we performed control experiments with varying amounts of biotin-based cholesterol sensors on beads, RBCs, and mammalian cells. We found that the effective dissociation constant was insensitive to changes in [ ] when [ ] ≪ 1. In other words, the parameters and above were not a function of [ ] at the low ligand concentrations used in our measurements.
The rationale for this result in the context of the equations above is that lim In other words, we are measuring essentially the monomeric binding affinity of the antibody because the surface ligand concentration is so low, and the second binding constant 2 drops out of the problem. Therefore, our approach to obtain the effective dissociation constant from the Langmuir isotherm form is an appropriate way to obtain the binding affinities and energies, and our results are insensitive to the absolute surface concentrations of the ligand sensors.

Sensors have no non-specific adsorption onto membranes
Our dextran sensors have a strong affinity to insert into the lipid bilayer via cholesterol tags bound to the dextran molecules. To rule out the possibility of other, non-specific interactions of the dextran sensors onto membranes, we conjugated the dextran molecules to Alexa Fluor dyes only, without cholesterol tags. Upon incubating these dextran-dye sensors with lipid-coated beads and red blood cells (RBCs), we did not detect enrichment on the membrane, validating that the main adsorption mechanism of our sensors is via the cholesterol tags. A representative microscopy image is shown in Fig. S3.2. We conclude that there is a negligibly small adsorption and non-specific interaction of our dextran macromolecules with the membrane. For our other probe based on anti-biotin binding, an antibody-only control was performed on cholesterol anchors containing no biotin tag (a cholesterol-FITC construct), and we observed no nonspecific anti-biotin binding on the membrane.

Figure S3.2.
There is no non-specific adsorption of our sensors onto membranes. Dextran-dye sensors in the absence of cholesterol does not incorporate into lipid coated beads or RBC membranes.

Control experiments of dextran sensors with different chemistries.
In the previous section, we showed that the intrinsic dextran macromolecules (without cholesterol) do not exhibit non-specific adsorption onto the membrane. However, the Alexa Fluor dyes conjugated to the cholesterol-dextran macromolecules are negatively charged and may interact electrostatically with the charged cell surface. As a control, we conjugated our cholesterol-dextran sensors with BODIPY, a chargeneutral dye. As shown in the main text, RBCs have highly charged cell surfaces that we can modulate using neuraminidase (NA) treatment; RBCs are a good model system to examine the interactions between the cell surface and the sensor dye charges. We conducted two tests on RBCs to assess the impact of the dye charges. First, to test whether the binding kinetics are equivalent between the Alexa Fluor and BODIPY conjugated cholesterol-dextran sensors, we took a time series of sensor binding on untreated and neuraminidase (NA) treated RBCs. As shown in Fig. S3.3, the binding kinetics of both dye types are essentially identical across the RBC surfaces. Note that the important feature from Fig. S3.3 is the time constant towards equilibrium, not the final saturation value. The final equilibrium value is irrelevant because the intensity units from the flow cytometer is different across the two different laser channels, and because the two sensor types may contain a slightly different labeling ratio of cholesterol. The dashed and solid curves in Fig. S3.3 are a fit to a firstorder kinetic rate law, C/C ∞ = 1 -exp(-t/τ). The characteristic decay time towards equilibrium is = 7.53 min (WT) and = 7.05 min (NA) for the Alexa Fluor 647 conjugated dextran sensors and = 7.38 min (WT) and = 7.51 min (NA) for the BODIPY conjugated dextran sensors. All of these values are similar to each other, which validates that the binding kinetics between the charged Alexa Fluor dyes and neutral BODIPY dyes have no difference. Within the same dye, the fact that the binding kinetics are the same between the WT cells (fully charged) and NA-treated cells (reduced charge) is another indication that the kinetics are unaffected by cell surface charges. Next, we tested whether the effective dissociation constant D is different between the Alexa Fluor and BODIPY conjugated cholesterol-dextran sensors. As described in the main text, we performed an equilibrium measurement of sensor binding on untreated and NA-treated RBCs using both types of sensors. The binding measurement at large bulk concentrations provide the saturating binding concentration, max , and the fractional coverage may be obtained using small bulk concentrations, = / max . As presented in the main text, our key metric of comparison is the relative difference between the binding affinities of WT and NA-treated cells, not the absolute value of D . As shown in Fig. S3 We believe that the negative charges on the dextran sensors play a small role for our particular system in part because the bound sensor concentrations are very dilute on the RBC surface. The average separation distance between the dextran sensors on the RBC surface over the range of interest is ≈ 100 nm at 100/ 2 surface density, and the average distance between the dextran sensors and the GYPA proteins is ≈ 10 nm at 2000/ 2 GYPA surface density. Both of these distances are more than an order of magnitude larger than the small 0.7 nm Debye length in physiological buffers, so we expect that the majority of the charge interactions are screened. Interestingly, the absolute magnitudes (not the ratio) of D for the BODIPY sensors are larger than the Alexa Fluor sensors, which is the opposite of what one may expect based on electrostatic repulsion between the dye and the charged cell surface. One may naively expect that the negative charge repulsion between the Alexa Fluor and the RBC surface would cause less binding and a larger D for the Alexa Fluor sensors. At very large sensor concentrations, the surface is saturated with a dense packing of sensors. Here, we believe that the average separation distance between neighboring sensors may be similar to the Debye length, and the negative charge repulsion among the neighboring sensors' Alexa Fluor dyes may lead to smaller packing and a smaller max than the BODIPY conjugated dextran sensors. A smaller saturating concentration would normalize the fractional coverage to a larger value, leading to smaller absolute magnitude of D for the Alex Fluor conjugated dextran sensors. In summary, the effects of negative charges on the dye do not impact the normalized ratio of the binding affinities at the dilute concentrations that form the basis of our crowding measurements; however, they are an important consideration in general when the absolute magnitudes of D are desired or one would like to use these sensors at much larger concentrations.
Once again, the absolute magnitudes of D are unimportant for our work because we are only interested in relative ratios between the different cell treatments. The crowding free energies come from the ratio in the binding affinity on bare and crowded surfaces, Δ = ln ( / 0 ) , not the absolute magnitude. The absolute magnitudes for the dextran sensors depend on the intrinsic chemistries of the cholesterol interaction with the membrane, which is irrelevant for our crowding measurements.

Verification that the stock sialidase is protease-free.
A sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) protein gel of bovine serum albumin (BSA), MW = 66 kDa, is shown in Fig. S3.5. BSA was treated with various concentrations of sialidase and Proteinase K at 37C for 5 hours. The protein was subsequently heat-denatured in 1x Laemmli Sample Buffer (Sigma Aldrich) in the presence of -mercaptoethanol. The sample was then loaded onto a NuPAGE Novex 4-12% gradient Bis-Tris gel (Fisher Scientific) and separated by electrophoresis. This gel confirms that our stock sialidase does not have protease activity. In addition to BSA, we collected the supernatant of RBCs treated with sialidase and found no detectable signal of proteins released from the RBC surface as a result of sialidase treatment. This verifies that soluble sialic acid-binding proteins are not embedded in the glycocalyx to hinder the binding of the sensors. We detected no protease activity in our stock sialidase. In our experiments, RBCs were treated with sialidase at 50 mUn/mL.

EDC conjugation to remove negative charges from cell surface
We used a carbodiimide crosslinker chemistry based on 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) to remove negative charges present on carboxylic acid groups on the red blood cell surface. Most surface negative charges come from the carboxylic acid on the sialic acids, but charged amino acids (e.g., aspartic acid and glutamic acid) may also be impacted by this reaction. We added EDC and hydrazidebiotin (a charge-neutral molecule) to a suspension of red blood cells, and the effectiveness of the reaction was assessed by imaging with AF555-labeled straptavidin. As shown in Fig. S3.6, the reaction was qualitatively very effective and we believe that most negative charges were neutralized on the cell surface. Figure S3.6. EDC chemistry was used to remove negative charges from the red blood cell surface. The reaction conjugated hydrazide-biotin to carboxylic acid sites, which enabled detection using AF555-labeled streptavidin to image the red blood cell surface. Scalebar is 10 m.

Sensor internalization in mammalian cells is minimal when performed on ice.
To prevent internalization of the macromolecules into the mammalian cell interior, the cells were incubated on ice throughout the measurement. We confirmed using confocal microscopy that the majority of the sensors are localized on the cell surface and appear to be bound homogeneously, as shown in Fig. S3.7. In Fig S3.7, the sensors were not added at the same concentration to test for robustness against internalization across a wide range of sensor concentrations. In all of our reported measurements, we did not observe significant internalization of neither the biotin anchor nor the antibody when performing the experiments on ice.

Bound antibody concentration normalized by the bound biotin-FITC-cholesterol concentration
is independent of heterogeneities in cell size. The advantage of using the DNA-based FITC-biotin-cholesterol sensor is that this construct acts as a proxy of cell size and cell membrane surface area. A plot of normalized bound antibody signal (i.e., antibody intensity divided by the FITC intensity) as a function of forward scattering (a metric of cell size) is shown in Fig. S3.8. We observe a constant normalized bound antibody across a 6x change in forward scattering, which indicates that the variations in cell membrane area is properly accounted for in our calculation of cell heterogeneities. By obtaining the fraction of bound antibodies by dividing against the FITC signal, we are normalizing for cell heterogeneities in shape and surface area. This normalization enables a measurement of population heterogeneities within a sample, which we cannot do using the dextran sensors. (A) The dissociation constant of a surface-binding macromolecule is given by its binding energy, , which is a sum of the intrinsic affinity, 0 , and the penalty due to crowding, Δ . The energy penalty posed by surface crowding is directly related to the change in normalized binding affinity, / 0 , and the osmotic pressure of the surface, Π.
(B) Coarse-grained molecular dynamics (MD) simulations were used to calculate the binding energy curves for spherical sensors of sizes = 0.25 (small), (medium), and 2 (large), where is the coarse-grained effective diameter of a glycocalyx polymer chain. The depth of the minimum gives the effective binding energy at equilibrium. The surface contains polymers with contour length 10 at a concentration of ∼ 10,000/ 2 .
(C) The energy penalty across various sensor sizes, surface polymer lengths, and surface polymer charges all collapse onto a unifying scaling line when the data are plotted against the osmotic pressure generated by the surface polymers, Π. The multi-domain proteins on the surface have varying lengths and are either charged (cyan and magenta circles) or neutral (all other symbols). Electrostatic interactions among the polymers are modeled by a Yukawa potential with different Debye lengths, −1 . The energy penalty Δ is normalized by the effective volume of the sensor immersed inside the crowded surface, , and Π is calculated via the Irving-Kirkwood virial stress tensor. Error bar indicates standard deviations of ensembles over all time and particles. The solid line is given by analytical theory and is not a fit.  We confirmed that our alternative measurement using antibodies provides a readout of crowding consistent with the dextran-40k sensor.