SUPPLEMENTARY INFORMATION for

Cytosolic can exploit membrane localization to trigger functional assembly

Osman. N. Yogurtcu and Margaret. E. Johnson*

Department of Biophysics, The Johns Hopkins University, Baltimore, MD 21218, USA.

*Corresponding Author: [email protected]

SUPPLEMENTARY TEXT: 1. Model Definition 1A. Definitions of ordinary differential equations (ODEs) for the pair model

We provide here the system of ODEs that describes the time evolution of all 9 species where two proteins P1 and P2 bind each other and the membrane M. �! , �! , � , ��! , �!� , �!�! , ��!�! , �!�!� , �!�! , [��!�!�], where γ1=V/(2Aσ1), and σ1 is for PP binding and σ2 is for PM binding. We set them equal in simulations, and note that only σ1 !""# appears in Eq. 3 of the main text; σ2 only appears in the definition of [�]!" (see below). These equations were solved numerically using Mathematica.

Eq. ![!!] = −�!! � � + �!! � � − �!!! � � + �!!! �� − �!! � � � + !" !" ! ! !"" ! ! !" ! !"" ! !! ! ! S1.1 !! �!"" �!�!� Eq. ![!!] = −�!! � � + �!! � � − �!!! � � + �!!! � � − �!! � �� + !" !" ! ! !"" ! ! !" ! !"" ! !" ! ! S1.2 !! �!"" ��!�!

Eq. � � S1.3 �� !!! !!! !!! !!! = −�!" �! � + �!"" ��! − �!" �! � + �!"" �!� !!! !!! !!! !!! !!! − �!�!" �!�!� � −�!�!" ��!�! � +�!"" ��!�!� +�!"" ��!�!� −�!" �!�! � !!! !!! !!! −�!" �!�! � + �!"" ��!�! + �!"" �!�!� Eq. ![!"!] = !" S1.4 !!! !!! !! !! +�!" �! � − �!"" ��! + �!!! ��!�!� −�!�!" ��!][�!� − !! !! �!" ��! �! +�!"" ��!�!

Eq. �[� �] ! = +�!!! � � − �!!! � � + �!! �� � � −� �!! �� ][� � S1.5 �� !" ! !"" ! !"" ! ! ! !" ! ! !! !! − �!" �!� �! +�!"" �!�!� Eq. �[�� � ] ! ! = +�!!! � � � − �!!! �� � + �!!! �� � � −� �!!! �� � ][� S1.6 �� !" ! ! !"" ! ! !"" ! ! ! !" ! ! !! !! + �!" ��! �! −�!"" ��!�! Eq. �[� � �] ! ! = +�!!! � � � − �!!! � � � + �!!! �� � � −� �!!! � � �][� S1.7 �� !" ! ! !"" ! ! !"" ! ! ! !" ! ! !! !! + �!" �! �!� −�!"" �!�!� Eq. �[� � ] ! ! = +�!! � � − �!! � � + �!!! � � � + �!!! �� � − �!!! � � � S1.8 �� !" ! ! !"" ! ! !"" ! ! !"" ! ! !" ! ! !!! − �!" �!�! � Eq. �[��!�!�] S1.9 �� !!! = −�!"" ��!�!� !!! !!! !!! !! !! − �!"" ��!�!� +�!�!" �!�!�][� +�!�!" ��!�!][� +�!�!" ��! �!� −�!"" ��!�!�

1B. Protein pairs with self In the Methods and part 1A above, we define the system for two protein partners that are distinct (P1 and P2). For a homo-dimer forming protein, P1=P2, and the system reduces to only 6 species, �! , �!�! , � , �!� , �!�!� , ��!�!� , with the following individual equilibria.

!! S2.1. P1 + P1 ⇋ P1P1 (�! ) !! S2.2. P1M + P1 ⇋ P1P1M (2�! ) !" S2.3. P1 + M ⇋ P1M (�! ) !" S2.4. P1P1 + M ⇋ P1P1M (2�! ) !" !! !" S2.5 P1P1M + M ⇋ MP1P1M ( /(2� )) ! !! !! S2.6. P1M + P1M ⇋ MP1P1M (�! /(2� ))

Reactions 5 and 6 are in 2D. Reactions in 2D list the 2D Ka values and thus require species be in units of A-1. To solve all species in consistent units (i.e. solution concentrations: V-1), the listed 2D eff Ka values must be multiplied by V/A. The main result, our equation for Ka (Eq. 3), is identical for the self-pairs and the distinct pairs.

1C. Scaffold-mediated interactions: Individual binding equilibria Each scaffold protein S has two binding sites, one each for peripheral membrane proteins P3 and P4. S does not bind to the membrane directly and P3 and P4 do not bind one another. Thus, the only way to exploit localization in 2D is by bridging P3 and P4 via S. There are 14 total species possible: �! , � , �! , � , ��! , ��! , ��!� , ��!� , �!� , �!� , �!��! , ��!��! , ��!��! , ��!��!� The individual equilibria are given by:

!!! S3.1. P3 + S ⇋ P3S (�! ) !!! S3.2. P4 + S ⇋ P4S (�! ) !!! S3.3. P3S + P4 ⇋ P3SP4 (�! ) !!! S3.4. P4S + P3 ⇋ P3SP4 (�! ) !!! S3.5. MP3 + S ⇋ MP3S (�! ) !!! S3.6. MP4 + S ⇋ MP4S (�! ) !!! S3.7. P3 + M ⇋ MP3 (�! ) !!! S3.8. P4 + M ⇋ MP4 (�! ) !!! S3.9. P3S + M ⇋ MP3S (�! ) !!! S3.10. P4S + M ⇋ MP4S (�! ) !!! S3.11. P3SP4 + M ⇋ MP3SP4 (�! ) !!! S3.12. P3SP4 + M ⇋ MP4SP3 (�! ) !!! S3.13. MP3 + P4S ⇋ MP3SP4 (�! ) !!! S3.14. MP4 + P3S ⇋ MP4SP3 (�! ) !!! S3.15. MP3S + P4 ⇋ MP3SP4 (�! ) !!! S3.16. MP4S + P3 ⇋ MP4SP3 (�! ) !!! !!! S3.17. MP3S + MP4 ⇋ MP3SP4M (�! /(2� )) !!! !!! S3.18. MP4S + MP3 ⇋ MP3SP4M (�! /(2� )) !!! !!! S3.19. MP3SP4 + M ⇋ MP3SP4M (�! /(2� )) !!! !!! S3.20. MP4SP3 + M ⇋ MP3SP4M (�! /(2� ))

Here, reactions 17, 18, 19 and 20 are all in 2D and thus report the 2D Ka values.

For the case where P3=P4, S then has two identical and independent sites to bind P3. As a result, from the individual equilibria listed above, every other equation is removed, leaving 10 total equilibria for 9 distinct species. Similar to section 1B above, several reactions then acquire a factor of two due to the symmetry of binding or unbinding two identical species. Specifically, Eqs. 1, 5, and 11 gain a factor of 2 multiplying Ka, and Eqs. 3, 17, and 19 gain a factor of ½ multiplying their Ka.

sol, SP eff, SP 1D. Scaffold-mediated interactions: Ka and Ka . For the scaffold-mediated interactions, we now are tracking complex formation between three, not two proteins. To measure enhancement in complex formation from solution to solution with membrane localization, we define a complex as requiring all three proteins present. The definitions we supply are eff, SP sol, SP again not true equilibrium constants, either with or without membrane present (Ka and Ka , eff respectively). This is distinct from the case for pairs, where the limits of Ka produced true equilibrium constants. However, they are consistently defined with and without membrane present, such that as eff, SP sol, SP membrane binding reduces to zero, we have that Ka ⟶Ka . Thus this formulation provides a similar measure of enhancement that is measured for the pair protein system. In particular,

!"# !"! !"",!" !!!! !" ! !!!! !" �! = !"# !"! !"# !"! Eq. S4 !! !" ! !! !" !! !" ! !! !"

Now the only way to have a P3P4 complex is with an S sandwiched in between, requiring three proteins. The unbound components of the denominator thus include all the remaining species sol mem except these full three protein complexes. To be explicit, [P3P4] = [P3SP4]; [P3P4] = [MP3SP4] + sol mem sol [MP4SP3] + [MP3SP4M]; [P3] = [P3]+ [P3S]; [P3] = [MP3] + [MP3S]; [P4] = [P4] + [P4S]; and mem sol,SP [P4] = [MP4] + [MP4S]. For pure solution binding, the Ka is given by:

!"# !"#,!" !!!! !" �! = !"# !"# Eq. S5 !! !" !! !"

using these same definitions. We emphasize that this equation is also not a true equilibrium constant, as the definitions of unbound states contain multiple species that combine in more than one way to form the bound state.

2. Theoretical Derivations eff 2A. Derivation of solution and membrane species from Ka

All theory derivations correspond to the pair protein model of binding (Figure 1, Eq. 5 (Methods)). eff From Ka , one can directly calculate the concentrations of bound proteins, !"! !"# [Complexes]eq= �!�! !" + �!�! !" , and unbound proteins at equilibrium by solving the eff quadratic equation Ka =[Complexes]eq /(([P1]0-[Complexes]eq)([P2]0-[Complexes]eq)). The unbound protein is then simply [Pn]0-[Complexes]eq. However, these bound and unbound protein concentrations include both solution and lipid bound copies. To quantify the fraction of bound complexes on the membrane, we can use the exact equilibrium expressions

!"! !! �!�! !" = �! � �!� �!� + �!� �! + �! �!� Eq. S6 !"# !! !!! ��� �� and �!�! !" = [�!][�!]�! . Taking the ratio and using �! = we then find: � �� �� ��

!"! !!! !!! ! !!! !!! ! ! !! ! ( ! !") ! ! !" ! !! ! ! !" = ! ! ! ! Eq. S7. ! ! !"!! ! ! !"# !!! !!! ! !!! !!! ! ! !" ! ! !" !!!!! !! ( ! !") ! ! !" !! !!! which is plotted in Fig S1. The fraction of unbound proteins (P1 or P2) on the membrane is similarly derived giving for P1, for example:

! ! ! !"! ! ! ! ! !" = ! !" Eq. S8. ! !"!! ! !"# !!! ! !" ! !" !!!! ! !"

Using these relations as well as Eq. 4 for [M]eq and the pairwise equilibrium equations (Eq. 5) from the methods, all equilibrium species can be calculated.

PM 2B. Derivation of critical membrane concentration, [M]c and critical value of Ka [M]eq

eff From our equation for Ka , we can also determine the critical lipid concentration [M]c needed to pull all proteins to the membrane and obtain close to the maximum number of complexes (Fig S3), !"" !! which occurs when �! = ��! . [M]c must be at the very least >[P1]0+[P2]0, and in general will be PM much larger than this given finite values of Ka . To get within ε of the maximum, we insert Eq. 3 into the following:

!"" !! �! = 1 − ε ��! , Eq. S9

!!! !!! to get [M]eq. From [�]! = [�]!" + [�!]! + [�!]! we find (assuming �! = �! for simplicity)

!!!!!!!!"! !!!!!!!!!!!!! [�]! = !" + [�!]! + [�!]! Eq. S10. !!" !!

This gives the expected trend that with stronger affinity of proteins for the , a lower concentration of lipids is needed to achieve maximum enhancement. This same approach gives us the critical value of the membrane stickiness via

! ! �!"[�] = !!!!!!!!"! !!!!!!! !!! ! Eq. S11 ! !" !!" showing how it varies as a function of the dimensionless geometry constant γ (Fig 3C).

���� 2C. Derivation of equation for [�]��

We provide here the solution to the problem where a protein with two lipid binding sites (1,2) is in !""# equilibrium with lipid recruiters, thus defining the [�]!" used in the equation for [M]eq (Eq. 4). We first consider the case where both sites target the same lipid M. This case is analytically solvable, and the solution is almost certainly available elsewhere as well. In the second case, we consider each site targeting a distinct lipid. For this second case, we introduce an approximation to produce an analytical solution to this otherwise non-analytic problem. For the first case, we have four pairwise equilibria, where the order of M in the complex indicates which site is bound, 1 or 2. We list all equilibrium constants here in volume units, enforcing all species are in volume units as well. !!! Eq. S12.1 P1,2+M⇋MP1,2, (�! ) !!! Eq. S12.2 P1,2+M⇋P1,2M (�! ) !!! Eq. S12.3 MP1,2+M⇋P1,2M (��! in Volume units) !!! Eq. S12.4 P1,2M+M⇋MP1,2M (��! in Volume units).

PM !""# where γ=V/(2Aσ ). The solution for [M]eq in this problem, which we define as [�]!" , is the root of a cubic equation. We note that [P1,2]0, the initial concentration of proteins with two lipid binding sites, is defined based on the full system (Fig 1) as [P1,2]0=min([P1]0, [P2]0). The cubic equation in one form is

!""# ! ! ! ! ! ! ! ! !""# [! ] ! (! ! !! ! !!!! ! ! ! ! ) !""# !,! ! !" ! ! ! ! !" Eq. S13. [�]! = [�]!" + !!! !!! !""# !!! !!! !""# ! !!(!! !!! )[!]!" !!!! !! ([!]!" )

For comparison, if the protein has only one lipid binding site, the equation is quadratic, [�]! = [�]!" + !" !! [!]!"[!]! !", , and as expected, is independent of the geometry constant γ. The solution to the cubic !!!! [!]!" !""# !""# ! !""# ! !""# equation for [�]!" is the real root (of three possible) of: a([�]!" ) + �([�]!" ) + �[�]!" + !!! !!! !!! !!! !!! !!! !!! !!! � = 0, where � = −��! �! , � = − �! + �! − 2�[�!,!]!�! �! + �[�]!�! �! , !!! !!! !!! !!! � = − �! + �! [�!,!]! + (�! + �! )[�]! − 1, and � = [�]!.

Finally, we have the solution:

!""# !! !!!!! /! [�]!" = !! ! Eq. S14

! ! ! ! !/! ∆ ! ∆ !!!(∆ )! where ∆!= � − 3��, ∆!= 2� − 9��� + 27� �, and � = ! ! ! ! . While this solution is cumbersome, we note firstly that just solving for [M]eq without this correction (Eq. PP 4 setting λ=0) is quite accurate in most regimes; the error increases with low recruiters and strong Ka . Secondly, the full solution is still a matter of just plugging in known values, and requires no simulations or numerical methods. Hence it can be easily calculated via an Excel file or a Matlab script, as we provide here. We note that if each protein targets a distinct lipid, then Eq. S13 becomes more complicated, and we have !!! !!! !!! [!!,!]! !! !! !"!!!! !! !! !" !! !" [�!]! = [�!]!" + !!! !!! !!! !!! Eq. S15 !!!! !! !"!!! !! !"!!!! !! !! !" !! !" and !!! !!! !!! [!!,!]! !! !! !"!!!! !! !! !" !! !" [�!]! = [�!]!" + !!! !!! !!! !!! Eq. S16 !!!! !! !"!!! !! !"!!!! !! !! !" !! !"

Solving these simultaneously requires numerical methods. To produce a cubic root, we define an approximate relationship between M1 and M2. We can assume the bound states of each site, without cooperativity, is in the same proportion as the bound states of each site with cooperativity. That gives us,

!"! !" [�!]!" = [�!]! − �! ! − �! !" Eq. S17 !"! !" where ! [�� ] = ! [� ] + [� ] + ! − � + � + ! − 4 � � . Eq. S18 ! !" ! ! ! !,! ! !!! ! ! !,! ! !!! !,! ! ! ! !! !!

This transforms Eq. S16 (or Eq. S15) into a cubic equation for [�!]!", that can then be solved in the same manner as the above.

eff 2D. Approximation to Ka that lacks cooperativity

eff We use one other theoretical approach to predict Ka that simply splits the proteins into two pools based MP on their lipid binding strengths, Ka . From the initial state with all proteins unbound in solution we (1) PM update protein-lipid bound states assuming simple equilibrium controlled by Ka . We then (2) evaluate complexes formed in the solution pool and the (3) membrane bound pool. Thus, this approximation does not capture the cooperative effect and is therefore useful in highlighting its significance. This method requires us to solve a sequence of three quadratic equations to get equilibrium concentrations first for the proteins on the membrane, and then based on the separation of proteins between solution and membrane, solving for the protein complexes in each isolated subsystem. It has an analytical formula so the input parameters can be plugged directly into this. However, unlike Eq. 3, the resulting equations are not easy to interpret, as the results of each quadratic root must be fed into the next quadratic formula. This approach works well when the cooperative effect is less pronounced, including for weak binding proteins or when the lipid recruiter concentrations are low (Fig 2).

3. Further Simulation details 3A. Simulation parameters for ODEs of Figures 2 and 3.

For the simulations of Fig 2, V=50μm3 and V/A=0.76μm. Initial protein concentrations were 4 -2 3 -2 PM 6 -1 [P1]0=[P2]0=2μM. For 2a, [M]0=2.5x10 μm . For Fig 2b [M]0=1x10 μm , Ka =1x10 M , and -1 3 -2 koff=0.1s . For Fig 2c1, [M]0=1x10 μm , and for Fig 2c2, protein concentrations were increased to !!! 10μM. Fig 2d is the same as Fig 2a1, except only P1 can actually bind to lipids (�! = 0). In Fig 3, 4 -2 PP 6 -1 default values for all simulations were [P1]0=[P2]0=1μM and [M]0=2.5x10 μm , Ka =1x10 M , PM 6 -1 Ka =1x10 M , and the other parameters were varied as noted. Because the lipid concentration is fixed in μm-2 units, as V/A changes, the copy numbers of lipids changes at a different rate than the copy numbers of proteins. Therefore, in Fig 3 a maximum enhancement is reached at finite V/A. PM 4 -1 3 For Fig 3c, we used Ka =1x10 M and [P1]0=0.1μM, V=50μm and V/A=0.76. For Fig 3d, we used 4 -2 [M]0=1.7x10 μm and otherwise default values. For the RD simulations, we used the same V/A ratios, but the value of V was smaller (0.16μm3) as these simulations are significantly slower to run.

3B. RD simulation treatment of recruitment from solution to the surface

For proteins that interact when one is bound to a lipid and the other is in solution, the interaction is still a 3D search and uses solution (3D) rates. The same on-rates are therefore applied: 3D,recruit 3D kon =kon . This is also needed to preserve detailed balance and reach an equilibrium steady- state. However, in the RD simulations, using the same intrinsic rate for this reaction produces a 3D macroscopic rate that is ½ that of the expected kon because the proteins can only approach one another from above once one is stuck to the membrane. To preserve the equilibrium solution, the !"#!$%& !! !"#!$%& 3D RDs must therefore be solved with �! ≠ �! , but rather with �! defined using kon 3D,recruit multiplied by 2 first, and then extracting ka from Eq. 8, thus reproducing the correct kon value at steady state.

4. Theoretical Background 4A. Smoluchowski model and reactivity of binding association in 2D and 3D

2D 3D Here we provide some additional justification for the use of Eq. 13: ka =ka /(2σ). In the well- established Smoluchowski model for binding association in all dimensions, two species diffuse and can react when they collide with one another at distance σ, which formulated mathematically results in the !"(!,!) boundary condition(39) �!"! = ��(�, �). The distribution p(r,t) defines the probability of !" !!! finding the particles at separation r at time t. The reactivity of the surface at collision is quantified by κ in units of length/time, regardless of the dimensionality, and Dtot is the sum of the species’ diffusion constants. We choose to preserve the reactivity κ of the reaction from 3D to 2D, as it is independent of any changes in diffusion that accompany surface restriction. Given that for a reactive sphere of radius σ 3D 2 2D in 3D, κ=ka /(4πσ ) and in 2D κ=ka /(2πσ), we set both κ definitions equal and this produces Eq. 13: 2D 3D ka =ka /(2σ).

4B. Calculation of time-scales of complex formation from simulation

To compare the time-dependence of our simulations with and without membrane recruitment, we use a mean-first passage time (MFPT) between the starting state with all proteins unbound in solution, and the final state with all proteins at equilibrium. C(t) is the number of complexes present at time t, C(0)=0, and Ceq is the equilibrium complexes formed. C(t)/Ceq is therefore the cumulative fraction of complexes formed by time t and its derivative, ! !"(!) , is the probability !!" !" density function describing the probability of complex formation at time t. The MFPT is then (40) ! ! !"(!) �! = � �� Eq. S19. ! !!" !"

4C. Theory estimates for time-scale bounds

For reversible binding reactions, there is no general analytical solution for the time-dependence or characteristic time-scales even when binding is purely in solution. For irreversible association, however, there are well-known solutions to the kinetics of A+B→C and A+A→C (see e.g. (19, 20)). We use these solutions for complexes as a function of time, Cirr(t), where Cirr(t)=0 and a kon is defined in either 3D or 2D. To then estimate the time-scales for reversible association, we use the equilibrium PP concentration of complexes formed, Ceq, defined from Ka , and then using the irreversible formula for Cirr(t), solve for t1/2:

Cirr(t1/2)=Ceq/2 Eq. S20

These t1/2 values when multiplied by two give a good estimate of the mean first passage times calculated -1 from simulation in either 3D or 2D when the off rates are not too fast (i.e. koff=1s works). While these formulas do not describe time-scales for the full system (Fig 1), they provide approximate bounds for pure solution (3D) or pure membrane bound (2D) time-scales, showing that pure 2D binding is generally significantly faster, even when kon accounts for the slower diffusion on membranes (Fig S4f).

5. Biological proteins 5A. BAR protein membrane localization

Several of the proteins included in our interactions sets contain BAR domains, of either the F-BAR (FCHo1, FCHo2, Syp1) or N-BAR (Amphiphysin, SH3GL2/Endophilin) variety. While affinities of these domain types for membranes has been measured (47), the binding is dependent on the multi-composite nature of the membranes targeted, with each protein stabilized most likely through multiple, rather than 1:1 lipid contacts. These proteins target only negatively charged membranes containing phosphatidylserine (PS) present at some percentage via their F-BAR (16, 18, 48, 49) or N-BAR domain (11, 17, 47). The addition of PI(4,5)P2 to these membranes tends to increase affinity for the membrane particularly for FCHo1 and 2, (49) and less so for other BAR domains (16, 47). Sphingolipids also play a role for the yeast N-BAR RVS proteins (11). The affinity of several BAR domains for membranes also varies with membrane curvature(17, 50), and since most of these proteins have been shown to curve and tubulate membranes in vitro (11, 18, 49), this creates a positive feedback influencing subsequent protein targeting to the membrane. Although this type of feedback is not present in our model, meaning our predictions are a lower bound on localization to the membrane, we note that estimating affinities of BAR domains for membranes is quite possible, although dependent on the particular membrane studied. As noted in the main text, the ratio of proteins bound to the membrane versus in solution for an in vitro PM experiment is equivalent to our membrane stickiness quantity, Ka [M]eq. This means it is possible to extract these values even for more complex protein-membrane interactions from in vitro experiments.

SUPPLEMENTARY FIGURES: abe 1 Tot 1 Tot 0 #(P) #(P) 0 = 0.004 0 = 1.84 0.8 #(M)0 0.8 #(M)0 /[P]

eq 0.6 0.6 0.4 0.4 0.2 0.2 [Complex] 0 0 101 103 105 107 109 101 103 105 107 109 KPP (M-1) KPP (M-1) c a d a

all eq #(P)Tot 1 1 0 = 1.84 #(M)0 0.8 0.8

/[Com.] 0.6 0.6

mem eq 0.4 0.4 #(P)Tot 0.2 0 = 0.004 0.2 #(M)0

[Com.] 0 0 1 3 5 7 9 10 10 10 10 10 101 103 105 107 109 KPP (M-1) KPP (M-1) a a

Figure S1: The simple theory developed here quantifies bound protein complexes for all eff systems with great accuracy. a,b) From Eq. 3 Ka , we can directly calculate the concentration of eff bound protein-protein complexes, as Ka =[Complex]eq/(([P1]0-[Complex]eq)([P2]0-[Complex]eq)). PM 4 -1 Simulation (red) vs theory (black). a) V/A=0.76, Ka =10 M , [P1]0=[P2]0= 0.1 �� , 4 !! 3 !! [M]0=2.510 �� . (b) Same as (a) except [P1]0=[P2]0=2 �� and [M]0= 10 �� c,d) The fraction of these complexes that are specifically on the membrane (Eq. S7). e) Network of reactions between all states. States with black outline all contain protein-protein complexes. Reactions in 2D are in green text.

a

b 102 Cystosol to Plasma Membrane Organelle, interior 3T3 EE 101 Organelle, exterior S. Cerevisiae EE 3T3 LYS V/A=R/3 S. Cerevisiae VAC OM m) Rat Hepatocyte Nuc IM µ 0 3T3 Mouse Fibroblast 10 Euglena Human Erythrocyte Rabbit Chondrocyte S. Cerevisiae 3T3 MIT OM Human Neutrophil 3T3 MVB IV 3T3 Golgi

V/A ( Human Lymphocyte S. Cerevisiae MVB IM S. Cerevisiae MIT OM Lamprey Motor Neuron -1 S. Cerevisiae VAC IM S. Cerevisiae Golgi 3T3 ER 10 E. Coli

3T3 MIT IM S. Cerevisiae ER V/A=2σ S. Cerevisiae MIT IM 10-2 100 101 102 103 104 Volume (µm3) Figure S2: Membrane localization of proteins in a variety of cell types will produce increased protein binding interactions. a) Proteins in the cytosol can localize to membranes by binding specific lipids (yellow). Peripheral membrane proteins that do not bind directly can be bridged by a scaffold protein (green/gray) b) We collected the solution volumes (V) and membrane surface areas (A) for both plasma and organellar membranes in a variety of cell types (Table S3). Only when the V/A ratio drops below 2σ, where here σ is set to 10nm, does the membrane reduce binding relative to solution (bottom black line). The only case found here is for proteins inside the yeast Mitochondria, which has a small volume but a large surface area due to the highly invaginated structure of the membrane. The V/A ratio for a sphere (V/A=R/3) is shown for reference in the diagonal black line. ab 200 109 ) Init. [P1]=[P2]:1 M

PP a Init. [P1]=[P2]:10 M

/K Init. [P1]=[P2]:100 M 7 150 ) 10 eff. a -2 m 5 100 ( 10 c P 2 -1 PM 4 -1

K :10 M , K :10 M M a a KP:102M-1, KPM:108M-1 3 50 a a 10 KP:109M-1, KPM:104M-1 a a KP:109M-1, KPM:108M-1 a a Enhancement: (K Enhancement: 0 101 1 3 5 7 9 100 103 106 109 10 10 10 10 10 [M] ( m-2) KPP M (M-1) cd0 a 6 ) 10 [P] : 0.1 M KPP: 104 M-1 0 PP a a [P] : 1 M /K 4 KPP: 106 M-1 0 10 a eff. a [P] : 10 M 0 KPP: 108 M-1 a 102

1

Enhancement: (K Enhancement: 10-2 10-4 10-2 1 102 104 10-4 10-2 1 102 104 V/A ( m) V/A ( m) ef6

) 10 100 [M] :2.5 104 m-2 : 0.05 nm 0 PP a : 1 nm

[M] :0 /K 75 0 104 : 20 nm eff. a

50 102 25 1 % Complexation % 0

Enhancement: (K Enhancement: -2 101 103 105 107 109 10 10-4 10-2 1 102 104 KPP (M-1) a V/A ( m) ghPM K 2 d :0.08 M 10 ) 700

PP a PM K :0.25 /K d PM K d :0.33 M

eff. a PM

eff a 1 K 690 d :0.44 /K

eff* a [M] :103 m-2

K -2 PM 10 0 K 680 d :0.93 [M] :2.5 104 m-2 WT Epsin:AP2 0 5 -2 H73A Epsin:AP2 PM [M] :6.3 10 m K -4 0 WT AP180:AP2 d :1.20

10 (K Enhancement: -6 -4 -2 2 4 670 10 10 10 1 10 10 7.2 7.4 7.6 7.8 8 8.2 KPM*/KPM pH a a PP Figure S3: Role of protein concentration, Ka , mutations, and lipid concentration in enhancement and complex formation. a) Once the enhancement due to membrane localization is near to the maximum value, the addition of more lipids changes the binding equilibrium imperceptibly. Even a relatively low concentration of lipids is needed to trigger the maximum PM binding interactions, particularly with strong Ka . b) This critical lipid concentration, [M]c, beyond which no further changes are observed in binding is derived in SI Text (simulation results eff PP are points, theory is lines). We define maximum binding as within ε of Ka =γKa , with results here shown for ε=0.01. c) Protein interactions between proteins with weak solution binding (low PP Ka ) or d) low protein concentrations benefit more widely from recruitment. This is because PP -1 these systems will form minimal complexes in solution (with (Ka ) >[P]0/2, fewer than half of proteins are in complex). Increased concentrations on the membrane can then substantially increase complex formation. e) Similar to Fig 3d, membrane localization can act as a switch to turn PP PM 4 -1 on assembly from <50% to >50% (shaded areas) depending on Ka . Here we used Ka =10 M and [P]0=1μM. f) Enhancement increases with smaller � as is clear from Eq. 3. In g) We show how PM 6 -1 PM* mutations that would alter Ka (initially set here to 10 M ) to a new value, Ka , would result in eff eff* PP 6 -1 a change from Ka to Ka . Here we set Ka =10 M and [P]0=1μM. For systems with higher [M]0 , only significant (>factor of 50) decreases in affinity due to mutation affect the enhancement. h) For Epsin and AP180, the effect of pH and mutations on lipid binding affinity have been measured experimentally(26). We illustrate here that because these proteins target PI(4,5)P2 at 4 -2 [M]0=2.5x10 μm , these up to 10-fold changes in affinity have relatively minor impact on enhancement.

c eps15/ede1 Yeast a 3 -2 b [M] : 10 m AP2(Human) Human(not AP2) 0 itsn1/sla1 Human

mem c 2 4 -2 [M] : 2.5 10 m AP2+cargo Yeast AP2:s:DAB2 10 0 SLA2:s:SYP1 /

0 c 5 -2 1 [M] : 6.3 10 m (FCHO2) ARH 0 10 HIP1R:HIP1R 1 FCHO1:2 (SYP1) AP2:s:FCHO1 HIP1:HIP1 (SLA2) AP180 ENT2:s:SYP1 (SH3GL2) AP2:s:FCHO1 10 (FCHO1) AP2:s:AP2 1 DAB2:FCHO2 FCHO1 PICALM EPN1 DAB2:FCHO1 FCHO2 ARH DAB2

PICALM:FCHO1 -1 AP2:s:EPN1 EPN1 10 AP180 AP2:s:AP2 FCHO1 2xEPN -1 DAB2 1 10 FCHO2

PICALM -2 -2

Speed Enhancement Speed 10 10 Relative Speed, Relative 10-1 -2 -1 1 2 3 10-1 1 101 102 103 -4 -2 2 4 10 10 1 10 10 10 10 10 1 10 10 PM K [M] KPM [M] V/A ( m) a 0 a 0 dePP 7 -1 PP 8 -1 PP 8 -1 MP P M K :10 M K :10 M K :3.2 10 M a a a f 1 1 2 1 KPP:106 M-1 0 MP P +P P M a M) 1 2 1 2 10 0.8 0 KPP:105 M-1 MP 0.8 a 1 -1 KPP:104 M-1 10 0.6 P M a 2 0.6 (s) -2 P P c 10 0.4 1 2 0.4 KPP:103 M-1 -3 a 10

0.2 [Complex]/[P] 0.2 KPP:102 M-1 Concentration ( Concentration a 10-4 0 0 0 2 4 6 8 10-4 10-3 10-2 10-1 100 10-4 10-3 10-2 10-1 100 101 10 10 10 10 10 KPP (M-1) Time (s.) Time (s.) a Figure S4: Average time to reach equilibrium is shifted by membrane localization. a) ODE simulations show how localization can produce relative speed-ups and slow-downs to reach equilibrium relative to pure solution binding. The dashed line is a theoretical maximum estimated from comparing time-scales of pure 2D binding to pure 3D binding (Methods and Supplementary Text). We started with V=50µm3 and A=65.63µm2, and then kept the volume constant and varied the PP 6 -1 PM 6 -1 area. Ka =10 M , Ka =10 M b) For the CME binding pairs, many binding reactions are ultimately slowed by membrane localization. For human proteins, V=1200µm3 and A=767µm2 and for yeast proteins, V=37.2µm3 and A=75.8µm2 (Table S3). c) The trend is even more evident for scaffold-mediated interactions. Same interactions as Fig. 4 (Datasets S3 and S4). d) Time- dependence of the simulations comparing ODES (black lines) with RD simulations (colors). Time- scales from ODEs are similar to RD methods despite lacking explicit diffusion because our PP 7 -1 -1 definitions of macroscopic rates implicitly account for diffusion (20). Ka =10 M koff=1s , PM 6 -1 Ka =10 M . e) We verify that the ODE (black lines) and RD simulations (colors) give the same equilibrium. Time-dependence is also similar to reach that equilibrium, although we note that a 3 -1 relatively small system size was used here. Spherical V=0.0096 μm [P1]0=[P2]0=17.36µM koff=1s -2 [M]0=17000µm , and for large systems the RD simulations will be slower to reach equilibrium due to the time needed to diffuse to the membrane. f) Pure 2D binding (green-RD or blue-ODE) is generally faster than 3D (red) despite slow-downs (factor of 100 here) in diffusion. Only for very strong (diffusion-limited) binding reactions does the impact of the diffusional search make a dominant impact on binding. V/A=0.762, and same copy numbers in 3D and 2D, [P1]0=[P2]0=1µM. Theory in black dashed (3D) and gray (2D). ab AP2(Human) Human(not AP2) 3 AP180 10 3 PICALM ARH AP2+cargo Yeast (HIP1R)(HIP1) EPN1 10 DAB2 ARH (FCHO1) AP180 (FCHO2) (SH3GL2) PICALM EPN1 PICALM FCHO1:2 (HIP1R) AP180 DAB2 (HIP1) (SLA2) 2 PICALM DAB2 2 FCHO1&2 DAB2 ARH EPN1 10 ARH 10 (SYP1) FCHO1&2 EPN1 AP180 FCHO1&2 (SH3GL2) FCHO1&2 (FCHO2) (SLA2) FCHO1:2(FCHO1) 1 (SYP1) 1 10 10 PICALM:FCHO1

PICALM:FCHO1DAB2:FCHO1

DAB2:FCHO2 DAB2:FCHO2 DAB2:FCHO1 1

Ratio of Enhancement of Ratio 1 -2 -1 1 1 2 3 10-210-1 1 101 102 103 10 10 10 10 10 PM KPM [M] K [M] a 0 a 0 cd 100 100

80 80

60 60

40 40

20 20 %Complexation 0 0 ARH ARH DAB2 (HIP1) DAB2 EPN- (HIP1) EPN- AP180EPN- FCHO1FCHO2(SLA2)(SYP1) EPN- AP180 FCHO1FCHO2(SLA2)(SYP1) (HIP1R) PICALM (HIP1R) (FCHO2)(FCHO1) PICALM (SH3GL2)FCHO1:2(FCHO2)(FCHO1) (SH3GL2)FCHO1:2 DAB2:FCHO1DAB2:FCHO2 DAB2:FCHO1DAB2:FCHO2 PICALM:FCHO1 PICALM:FCHO1 Figure S5: CME interactions assuming weaker 2D binding or fewer lipids have lower but still significant enhancements. a) If we increase σ from 1nm to 10nm, the maximal enhancement decreases by a factor of 10. b) If we reduce the lipid concentration by a factor of 10 (with σ=1nm), enhancement again decreases relative to Fig 4. Now we are in the regime where lipids only slightly outnumber proteins. c) Complexation for pairs of (a) is still quite large, because of the overall high PM enhancement. d) Complexation for pairs in (b) is now much more sensitive to Ka . Notably, when PM AP-2 binds cargo (light green relative to dark green bars), Ka is 40 times higher. The PM consequence of this stronger Ka in (c) is marginal, but with limited lipids in (d), it drives significantly larger increases in complex formation. All results in Dataset S3. with AP2 with AP2 with DAB2 with PICALM with FCHO2 a K PP:1μM K PP:50μM K PP:3μM K PP:3μM K PP:2.5μM d d d d d 100

80

FCHO1 60

40

20

%Recruited 0 M M M M M M M M M M M M M M M

:10 :10 :10 :10 :0.1 :10 PM :100 :500 PM :100 :500 PM :100 :500 PM :100 :500 PM :100 PM PM PM PM PM PM PM PM PM PM K d K d K d K d K d K d K d K d K d K d K d K d K d K d K d b with AP2 with EPN1 100 + 80

60

40

%Recruited 20

0 + EPN1 EPN1 EPN1 AP2 AP2 AP2

Figure S6: Peripheral membrane proteins can be stabilized on the membrane via their protein-protein interactions. a) We compare FCHo1’s localization to the membrane by itself (gray bars) or with help from protein-protein interactions (colors). We consider a range of PM PP possible values for Ka and two different Ka for binding to AP-2 to show how the ability to bind other proteins will help stabilize the lipid binding FCHo1 on membranes, where we estimated [M]0 as 25000μm-2. b) The same effect is possible if the protein pairs can bind through multiple domains. Because AP-2 can use both its α and β appendages to bind epsin, it can form more complexes and stay tethered more strongly to the membrane. Results here used 10 times less PI(4,5)P2. Other model inputs are based on in vivo measurements and are collected in Dataset S3.

Figure S7: Model of scaffold-mediated interactions with membrane localization We show all the possible interactions for a system with three cytosolic proteins and a membrane lipid. The two peripheral membrane proteins P3 and P4 do not directly bind one another, but both can bind to a scaffold protein S. The scaffold protein thus has two binding sites, one for P3 and one for P4. Only P3 and P4 can bind the lipid, not S. a) Binding interactions occurring purely in solution (3D) are shown in this box. b) All the orange boxed interactions involve the localization of a protein or protein complex from solution to the membrane via lipid binding. Hence these are all 3D interactions. In panels c-f we show all the 2D interactions that can thus exploit membrane localization to enhance complex formation. a 6 b 10 104 100% 3 [S] : 0.5 µM PP a PP a 0 10 90% /K 102 No AP2 /K eff. a 1 100 [S] : 1 µM 10 4 0 K 100 AP2

eff. a 10 0.1 1 10 [S] : 2 µM [S] /[P] AP2+Cargo 0 0 0 75 102 50% 50 33% 1 25

Enhancement: K Enhancement: -2 0 10 Legs Bound % 0 1 2 3 10-4 10-2 1 102 104 10 10 10 10 V/A (µm) K ( M) d cd104 100 103 75 102

(s) 1

c 10 50 No PIP2 0 AP2 10 25 AP2+Cargo 10-1 -2 0 10 % AP2-with a Clathrin a AP2-with % 0 1 2 3 100 101 102 103 10 10 10 10 KCC ( M) KCC ( M-1) d d Figure S8: Scaffold-mediated interactions and clathrin polymerization also benefit from localization on surfaces. a) For scaffold-mediated interactions (Fig S7), the two peripheral membrane proteins do not directly bind one another. Thus, no shift in localization will occur unless a scaffold protein bridges them. Increasing concentration of the scaffold protein increases enhancements. Inset shows how the enhancement at a fixed V/A increases with increasing scaffold to peripheral protein. b) We simulated a system of clathrin and the adaptor AP-2 to mimic in vitro experiment (1) using rule-based Gillespie simulations (Methods). We extracted a V/A ratio of 9.46μm and a lipid concentration of 54,668 μm-2 from the study, and used clathrin and AP-2 -1 concentrations of 0.4μM each. Stronger Ka (=Kd ) values for the clathrin-clathrin (CC) interaction produce more polymerization, particularly with membrane localization included (green lines). Yellow pie is percent clathrin on the membrane for simulations with AP-2. The enhancement is not limited by the AP-2:PI(4,5)P2 interaction, but rather because the recruitment of clathrin to the membrane requires AP-2, which is only at 0.4μM (~25 times lower than lipid at this V/A=9.46μm). c) Clathrin binds moderately to AP-2 (22μM). However, because clathrin has three leg domains that can each bind AP-2, once on the membrane, it will quickly bind multiple AP-2s. d) Time-scales to reach equilibrium are slowed (relative to pure solution in red) due to the time needed to bind AP-2 to the membrane, and then clathrin. Simulation inputs in Dataset S4.

VPS17:VPS5 VPS17:SNX3 abVPS17:VPS5 VPS17:SNX3 100 100

80 80

60 60 40 40

20 20 %Complexation %Recruited VPS17 %Recruited 0 0 M M M M M M M M :100 :300 :100 :300 :100 :300 :100 :300 PM PM PM PM PM PM PM PM K d K d K d K d K d K d K d K d cd(SH3GL2) FCHO1:2 SH3GL2 FCHO1 FCHO2 100 100

80 80

60 60 40 40 %Recruited %Oligomerized 20 20

0 0 M M M M M M M M M M M M M M M

:10 :10 :10 :10 :10 :0.1 :0.1 :0.1 :100 :100 :100 :100 :100 :0.03 PM PM :0.03 PM PM PM PM PM PM d PM d PM d PM d PM d PM PM d d d K d K d PM K d K d K d d K K K K K d K K K K K Figure S9. Higher order assemblies studied via rule-based stochastic simulation. a) PP Retromer components VPS17 and VPS5 bind weakly to PI(3)P on endosomes. Ka values are not known for these interactions, so we estimate a range (0.1-100μM: error bars). Since the protein- lipid affinity is only known to be >100µM (26), we compare values of 100µM and weaker binding of 300µM. We compare dimerization without membrane (gray bars) and with (dark red). When assisted by an (putative) interaction between SNX3 and VPS17, more complexation occurs of the now 3-protein complexes (light red). Because SNX3 binds strongly to PI(3)P, it will drive more complexation even without VPS5 (right bars). b) VPS17 is more effectively recruited to the endosome when it also interacts with SNX3. Pink is VPS17 by itself, dark red is with dimer formation allowed, and light red is with the third protein added (SNX3 on left, VPS5 on right). Although this direct interaction between SNX3 and VPS17 is not physiological, SNX3 does bind the full 5-protein retromer complex (38). These results illustrate how the retromer complex could be more strongly recruited to endosomes with the help of SNX3. c) We simulated BAR (SH3GL2:SH3GL2) and F-BAR (FCHo1:FCHo2) domain proteins forming both dimers and higher- order oligomers (Methods). Both pairs are given a weak oligomer binding strength of 500µM. Binding strength of proteins to the membrane is either not known or is reported at widely varying values, so we consider a range of values (0.1-100µM). Oligomerization in solution is <0.01%, but with membrane (light blue) it is especially prominent for the homodimer forming endophilin (SH3GL2). This is because SH3GL2 forms large oligomers (>20 proteins per complex) feeding back into stabilization at the membrane. In contrast, FCHo1 has much lower concentration than FCHo2, so oligomer contacts are much less likely to form large filaments. d) Dimers (no oligomer allowed) in dark blue. Simulation inputs in Dataset S4.

PI(3)P PI(4)P PI(3,5)P2 PI(4,5)P2

OSH2:SWH1 (OSH2) (OSH2) (KES1) OSH2:SWH1 (SWH1) 3 VAM7:BEM1 (SWH1) (OSH2) 10 BOI2::CLA4 OSH2:SWH1 BOI1:BEM1 BOI2:BEM1 (SWH1) OSH2:SWH1(OSH2) (SWH1)(KES1) SLA2:CLA PP a CLA4:SKM1 CLA4:SKM1 2 BOI2:CLA4 BOI2:CLA4

/K 10 BEM1:CLA4

VPS5:VPS17

eff. a VPS17:SNX4 SNX4:SNX41 ATG20:SNX4 endosome assembly K 1 10 oxysterol binding morphogenesis polarization budding 1 10-1 1 101 102 103 KPM [M] a 0 Figure S10. Membrane localization can enhance binding for pairs of protein binding partners in diverse pathways targeting distinct organellar membranes. Yeast proteins that can also bind lipids including PI(4,5)P2, PI(3)P, PI(4)P, and PI(3,5)P2 at distinct organelles are reported in Table 1, with interactions collected in Table S1 and Dataset S2. These proteins are involved in oxysterol binding (yellow), membrane remodeling (mauve, purple and turquoise) and vesicle assembly on endosomes (green). Most of the proteins exhibit significant enhancements, except for the endosome assembly proteins (VPS5, VPS17, SNX4, SNX41, ATG20) due to their low affinity for PI(3)P on the endosomal membrane.

SUPPLEMENTARY TABLES Table S1. Pairwise protein-protein interactions (PPIs) and affinities PP b PPI Speci Kd Literature Refs (distinct e (μM) pairs)a 1 FCHO1:AP-2 (2) Human Used 1, 50 PPI: PMID:25303365. Affinity not known. 2 EPN1:AP-2 (5) Human 1 (α) & 35 (β) PPIs and affinities: PMID:15496985&16903783. 3 PICALM:AP-2 Human 50 PPI: PMID:17713526. Affinity, homology (PICALM<-AP180), PMID:15496985. (2) 4 PICALM:FCHO1 Human 3 PPI: PMID:22484487. Affinity, homology (PICALM<-EPS15), PMID:27237791. 5 DAB2:AP-2 (2) Human 10 PPI: PMID:12234931. Affinity, homology (DAB2<-AP180), PMID:15496985. 6 DAB2:FCHO2 Human 3 PPI: PMID:22484487. Affinity, homology (DAB2<-EPS15), PMID:27237791. 7 DAB2:FCHO1 Human 3 PPI: PMID:22484487. Affinity, homology (DAB2<-EPS15), PMID:27237791. 8 AP180:AP-2 (2) Human 10 PPIs and affinities: PMID:15496985. 9 ARH:AP-2 (2) Human 2.4 PPI: PMID:12234931. Affinity, homology (ARH<-βArrestin), PMID:16516836. 10 HIP1:HIP1 Human 0.001 PPIs and affinities: PMID:18790740 Affinity estimate for stable dimers. 11 HIP1R:HIP1R Human 0.001 PPIs and affinities: PMID:18790740. Affinity estimate for stable dimers 12 AMPH:AMPH Human 10 PPI: PMID:22888025. Affinity, homology (AMPH<-SH3GL2), PMID:16763559. 13 SH3GL2:SH3GL2 Human 10 PPIs and affinities: PMID:16763559. 14 FCHO1:FCHO1 Human 2.5 PPI: PMID:20448150. Affinity, homology (FCHO1<-FCHO2), PMID:17540576. 15 FCHO2:FCHO2 Human 2.5 PPIs and affinities: PMID:17540576. 16 FCHO1:FCHO2 Human 2.5 PPI: PMID:20448150. Affinity, homology (FCHO1<-FCHO2), PMID:17540576. 17 SYP1:SYP1 Yeast 2.5 PPI: PMID:19713939. Affinity, homology (SYP1<-FCHO2), PMID:17540576. 18 SLA2:SLA2 Yeast 0.001 PPI: PMID:21849475. Affinity, homology (SLA2<-HIP1), PMID:18790740. 19 OSH2:SWH1 (4) Yeast Used 0.01, 1.0 PPI: PMID:16554755. Affinity not known. 20 OSH2:OSH2 (4) Yeast Used 0.01, 1.0 PPI: PMID:22940862. Affinity not known. 21 SWH1:SWH1 (4) Yeast Used 0.01, 1.0 PPI: PMID:16554755,18467557. Affinity not known. 22 KES1:KES1 (2) Yeast Used 0.01, 1.0 PPI: PMID:22940862. Affinity not known. 23 VPS17:SNX4 Yeast Used 0.01, 1.0 PPI: PMID:15263065. Affinity not known. 24 SNX4:SNX41 Yeast Used 0.01, 1.0 PPI: PMID:22875988, 16554755, 16429126, 12554655, 20826334, 15263065, 11283351,19591838. Affinity not known. 25 VPS5:VPS17 Yeast Used 0.01, 1.0 PPI: PMID:16554755, 22940862, 11598206, 9285823, 9700157, 18467557, 12181349, 10688190, 15263065, 17696874. Affinity not known. 26 ATG20:SNX4 Yeast Used 0.01, 1.0 PPI: PMID:16429126, 12048214, 12554655, 18467557, 22615397, 10688190, 15263065, 18719252, 19591838. Affinity not known. 27 BOI2:CLA4 (3) Yeast Used 0.01, 1.0 PPI: PMID:11489916, 8666672. Affinity not known. 28 CLA4:SKM1 (2) Yeast Used 0.01, 1.0 PPI: PMID:14660704. Affinity not known. 29 BOI2:BEM1 Yeast 1.0 PPI: PMID:8666672. Affinity, homology (SH3/PRD interaction PMID14668868, PMID15834155, PMID19590096). 30 BOI1:BEM1 Yeast 1.0 PPI: PMID:8666672. Affinity, homology (SH3/PRD interaction PMID14668868, PMID15834155, PMID19590096). 31 BEM1:CLA4 Yeast Used 0.01, 1.0 PPI: PMID:19841731, 22277653, 21489982, 21118957, 11113154. Affinity not known. 32 VAM7:BEM1 Yeast Used 0.01, 1.0 PPI: PMID:16854988. Affinity not known. 33 SLA2:CLA4 Yeast Used 0.01, 1.0 PPI: PMID:11489916. Affinity not known. a) Repeated enhancement calculations because one or both protein bound multiple lipid types, or proteins bound each other through multiple domain pairs. b) See Datasets S2, S3 for further details, rates, and all results.

Table S2. Scaffold-mediated PPIs and higher-order assemblies, with affinities a PS SP b PPI (distinct sets) Species Kd Literature Refs Kd Literature Refs (μM) (μM) 1 AP-2A:ITSN1:DAB2 Human 11 PPI and affinity: PMID: 0.07 PPI: PMID:12234931. 15496985. Affinity, homology (DAB:ITSNpartners on PRD): PMID:15834155. 2 AP-2A:ITSN1:FCHO1 Human 11 PPI and affinity: PMID: 3 PPI: PMID:20448150. 15496985. Affinity, homology (FCHO1:EPS15): PMID:27237791. 3 FCHO1:ITSN1:DAB2 Human 3 PPI: PMID: 20448150. 0.07 PPI: PMID:14596919. Affinity, homology Affinity, homology (EPS15:FCHO1): (DAB:ITSN partners on PRD): PMID:27237791. PMID:15834155. 4 AP-2:EPS15:AP-2 (2) Human 0.021&18 PPI and affinity: 0.021&18 PPI and affinity: PMID:15496985&16903783. PMID:15496985&16903783. 5 AP-2:EPS15:EPN1 (2) Human 0.021&18 PPI and affinity: 90 PPI and affinity: PMID: PMID:15496985&16903783. 18200045. 6 AP-2:EPS15:FCHO1 (2) Human 0.021&18 PPI and affinity: 3 PPI and affinity: PMID: PMID:15496985&16903783. 27237791. 7 ENT1:EDE1:SYP1 Yeast 90 PPI: PMID:12529323, 3 PPI: PMID:19713939, 18448668. Affinity, 19776351. Affinity, homology (Human homology (Human EPN:EPS15): PMID: FCHO:EPS15): PMID: 18200045. 27237791. 8 ENT2:EDE1:SYP1 Yeast 90 PPI: PMID:12529323. 3 PPI: PMID:19713939, Affinity, homology (Human 19776351. Affinity, EPN:EPS15): PMID: homology (FCHO:EPS15): 18200045. PMID: 27237791. 9 SLA2:SLA1:SYP1 Yeast Used 0.1, 10, PPI: PMID:12734398. Affinity 0.1 PPI: PMID:19841731. 100 not known. Affinity, homology (SH3-PRD interaction of with endocytic partners): PMID: 15834155. 10 SNX3:VPS5:VPS17 Yeast Used 0.01, 1.0 PPI: PMID: 17892535. Used 0.01, PPI: PMID:16554755, (Retromer Proxy) Affinity not known. 1.0 22940862, 11598206, 9285823, 9700157, 18467557, 12181349, 10688190, 15263065, Affinity not known.

Oligomers: Kd Dimer Kd Oligo 11 SH3GL2:SH3GL2:SH3GL2 Human 10 PPIs and affinities: 500 PPI: PMID: 20448150. Etc. PMID:16763559. Affinity: PMID: 17540576 (Estimated weaker 130μM, minimal solution oligomers) 12 FCHo1:FCHo2:FCHo1.. Human 2.5 PPI: PMID:20448150. 500 PPI: PMID: 20448150. Etc. Affinity, homology (FCHO1<- Affinity: PMID: 17540576 FCHO2), PMID:17540576. (Estimated weaker 130μM, minimal solution oligomers)

Polymerization: Kd AP-2:CLTC Kd CLC:CLC 13 AP-2:CLATH:CLATH.. Human 22 PPI: PMID:10944104. Used 1, 10, PPI: PMID: 26496610. Etc. Affinity, homology (AP-2<- 100, 1000 Affinity not known. AMPH): PMID:14981508. a) Repeated enhancement calculations because proteins bound each other through multiple domain pairs. b) See Dataset S4 for further details, rates, and all results.

Table S3. Volume and membrane surface area estimates for different cells and organelles. Reaction Total Surface Volume Volume Area V/A Compartment Type (µm3) (µm3) (µm2) (µm) Technique/Evidence Convex Plasma Membr. 3T3 Mouse Fibroblast 1200 2000 768 1.6 V:Coulter counter, SA: estimatea Human Chondrocyte 990 1650 730 1.4 CM, stereologyb Guinea pig Pancreatic 636 1060 581 1.1 c Exocrine TEM, stereology Rabbit Chondrocyte 1163 1939 1155 1.0 CM, stereologyd Human Erythrocyte* 54 90 136 0.4 Estimatee Euglena 5 7.8 7.2 0.7 Estimate: phylogeny+published dataf S. Cerevisiae 37 62 75.4 0.5 V:Coulter counter, SA: estimateg Human Neutrophil 120 200 300 0.4 TEM, stereologyh Human Lymphocyte 69 115 260 0.3 TEM, stereologyh Lamprey Motor Neuron 3578 5964 23430 0.2 CM, stereologyi E. Coli 1 1.0 6.0 0.1 Estimatej Convex Organelle Rat Hepatocyte Nucleus IM 204 204 135 1.5 Hepatocyte nucleus has 6% of total cell volumek,l 3T3 MVB IV 11 22 38 0.3 Assuming 1% of Cytosol volumem, ½ MVB OM SA S. Cerevisiae MVB IM 0.6 1.2 3.8 0.2 Assuming 1% of Cytosol volumem, ½ MVB OM SA S. Cerevisiae VAC IM 1.0 2.1 9.0 0.1 6% of cytosol volumen, assume ½ VAC OM SA 3T3 MIT IM 400 400 9222 0.04 Hepatocyte MIT VOL 20% of total cell volume, MIT IM SA 1200% of PM SAk,l

S. Cerevisiae MIT IM 12.4 12.4 905 0.01 Hepatocyte MIT VOL 20% of total cell volume, MIT IM SA 1200% of PM SAk,l Concave Organelle 3T3 MVB OM 1200 - 77 15.6 Assuming MVB SA 10% of PM SA 3T3 RE 1200 - 77 15.6 Assuming total RE SA 10% of PM SA 3T3 EE 1200 - 77 15.6 Assuming total EE SA 10% of PM SA 3T3 LYS 1200 - 154 7.8 Hepatocyte LYS SA 20% of PM SAk,l S. Cerevisiae EE 37 - 7.5 4.9 Assuming EE SA 10% of PM SA S. Cerevisiae MVB OM 37 - 7.5 4.9 Assuming EE SA 10% of PM SA S. Cerevisiae VAC OM 37 - 18 2.1 CM, image analysis 3T3 MIT OM 1200 - 1921 0.6 Hepatocyte MIT OM SA 2.5 times of PM SA k,l 3T3 Golgi 1200 - 2690 0.4 Hepatocyte Golgi SA 3.5 times of PM SA k,l S. Cerevisiae MIT OM 37 - 189 0.2 Hepatocyte MIT OM SA 2.5 times of PM SA k,l S. Cerevisiae Golgi 37 - 264 0.1 Hepatocyte Golgi SA 3.5 times of PM SA k,l 3T3 ER 1200 - 13832 0.1 Hepatocyte ER SA 18 times of PM SAk S. Cerevisiae ER 37 - 1358 0.03 Hepatocyte ER SA 18 times of PM SAk (*)Cytoplasmic volume assumed to be the same as total cell volume. Abbreviations: EE-Early endosomes, RE-Recycling endosomes, IV- Intraluminal vesicles of endosomes, VAC-Vacuoles, G-Golgi, PM-Plasma membrane, NUC-Nucleus, ER-Endoplasmic reticulum, LE-Late endosomes, LYS-Lysosomes, MVB-Multivesicular bodies, MIT-Mitochondria, OM-Outer membrane, IM-Inner membrane, CM-Confocal microscopy, TEM-transmission electron microscopy. (a) PMID1366595 & PMID1614815 (b) PMID15970445 (c) PMID4363955 (d) DOI: 10.1111/j.1365-2818.1994.tb03447.x (e) PMID3565597 (f) PMID19443453 (g) PMID12089449 (h) PMID6775712 (i) DOI:10.1006/ncmn.1993.1016 (j) PMID14681416,ISBN: 9781134111589 (k) ISBN: 9780815344322 (l) PMID833203 (m) PMID862008 (n) PMID27151661.

Table S4. Phosphoinositide (PtdInsPn) and phosphatidylserine concentrations across various organelles in a mammalian and a yeast cell. Lipid Lipid SA Conc. SA Conc. % #Lipid 3T3 3T3 #Lipid S.C. S.C. Lipid 3T3 (µm2) (µm-2) Notes S.C. (µm2) (µm-2) Notes

PtdIns(3)P Total lipids: 1.69 106 Total lipids: 2.79 106 MVB IV (3T3) 20%(a) 3.4 105 38 2.94 104 Total lipids calculated from - - - (j) (a) ratio to PI(4,5)P2 6 4 VAC OM (B.Y.) 41% - - - 1.14 10 18 6.3 10 Set total lipids of PI(3)P to (a) 6 5 (k),(l) VAC IM (B.Y.) 41% - - - 1.14 10 9 1.27 10 same as total PI(4,5)P2 Cyt Vesicles (B.Y.) 9%(a) - - - 2.51 105 8 3.3 104 Total lipids: 3.73 107 Total lipids: 2.79 106 PtdIns(4)P G 45%(b) 1.68 107 2,687 6.25 103 1.25 106 265 4.7 103 PM total lipids from PM 35%(b) 1.31 107 768 1.7 104 (i) 9.75 105 76 1.29 104 (SAxPM Lipid Conc.) Total Set total lipids of PI(4)P to (b) 6 4 5 4 (k),(l) LYS 15% 5.6 10 154 3.64 10 lipids from fraction on PM. 4.18 10 18 2.32 10 same as total PI(4,5)P2 EE 10%(b) 3.73 106 77 4.86 104 2.8 105 8 3.68 104 Total lipids: 1.19 106 Total lipids: Undetected PtdIns(5)P PM total lipids from (SAxPM Lipid Conc.) Total PM 27%(c) 3.2 105 768 420 (i) lipids from fraction on PM. - - - Total lipids: 8.06 104 Total lipids: Undetected PtdIns(3,4)P2 PM total lipids from (SAxPM Lipid Conc.) Total PM 40%(d) 3.2 104 768 42 (i) lipids from fraction on PM. - - - Total lipids: 2.64 105 Total lipids: 2. 105 PtdIns(3,5)P2

Set total lipids of PI(3,5)P2 Total lipids calculated from 14x lower than total (e) 5 3 (j) 5 3 (k),(l),(m) LYS/VAC 85% 4.8 10 153.7 3.1 10 ratio to PI(4,5)P2 1.69 10 18 9.4 10 PI(4,5)P2 Total lipids: 2.82 107 Total lipids: 2.79 106 PtdIns(4,5)P2 PM 68%(f) 1.92 107 768 2.5 104 (h) 1.89 106 75.4 2.5 104 (f) 6 4 5 4 MVB OM 4% 1.13 10 77 1.47 10 PM total lipids from 1.11 10 7.5 1.47 10 Used same PM lipid conc. (SAxPM Lipid Conc.) Total as 3T3(h), then see Notes for (f) 6 4 5 4 MVB IV 4% 1.13 10 38 2.94 10 lipids from fraction on PM. 1.11 10 3.8 2.94 10 PI(4,5)P 2 3T3. Total lipids: 3.07 104 Total lipids: Undetected PtdIns(3,4,5)P3 PM 70%(g) 2.15 104 768 28 (i) PM total lipids from - - - (SAxPM Lipid Conc.) Total RE 25%(g) 7.68 103 77 100 lipids from fraction on PM. - - -

PhosphatidylSerine Set PM total lipids to 5x that Set PM total lipids to 5x that 7 5 (n) 6 5 (n) PM NA 9.6 10 768 1.25 10 of PM total PI(4,5)P2 9.47 10 76 1.25 10 of PM total PI(4,5)P2

Abbrev: 3T3/NIH fibroblast cells, (S.C.) Saccharomyces Cerevisiae. SA Surface Area. Compartment abbreviations same as Table S1. (a) PMID10970851 (b) PMID24711504 (c) PMID20370717 (d) PMID14604433 (e) PMID24324172 (f) PMID11964166 (g) PMID19864464, PMID25345859. (h) PMID22024883 (i) Ref.(13) (j) PMID22621786 (k) PMID11854411 (l) PMID17392273. (m) PMID11889142 (n) ~9% of lipids on PM are PS: PMID24007978, 1-1.5% are PI(4,5)P2.