Supporting Information s46

Supporting Information.

Synthetic Anionophores for Basic Anion as ‘Presumably OH-/Cl- antiporters’: From the

Synthetic Ion Channels to Multiion Hopping, Modified Anti-Hofmeister Selectivity and

Strongly Positive AMFE.

Sofya Kostina Berezin

[email protected] Table of Contents

SI1. Goldman-Hodgkin-Katz theory versus ‘ion hopping’ over a barrier (or transition- state theory). ‘One anion’ transporter, ‘multiion hopping’mechanism and AMFE theory.

SI2. Approximations.

SI3. Permeability of the ‘unstirred’ layer.

SI4. Weak vs strong acid: the pH “error” in 10 mM phosphate buffer.

SI5. Influx of the weak acid HAnion2 OUT into liposomes. A simple model, pH ≥ 7.

+ - SI6. Influx of the weak acid HAnion2 OUT and H /OH transport.

SI7. Anion1 IN / Anion2 OUT exchange, HAnion1 IN - is a strong acid, HAnion2 OUT - is a weak acid.

SI8. ‘Presumable OH-/Cl- exchange’. SI 1. GHK theory verus ‘ion hopping’ over a barrier (or transition-state theory). ‘One anion’ transporter, ‘multiion hopping’mechanism and AMFE theory.

GHK voltage equation (or just GHK equation) can be written as following:

  RT PM [M ]Out  PA[A ]In Erev  ln   + - F PM [M ]In  PA[A ]Out , where M A is a salt in solution.

GHK flux equation:

d[C] zU ([C] [C] e zU ) , where U = E F/(RT) J  V IN  PS IN OUT m dt 1 e zU GHK current equations:

d[C] zF Pz 2 EF 2 ([C] [C] e  zU ) I  V IN  IN OUT dt S RT zU 1 e (I = J*zF/S, Am-2 = C s-1 m-2= mol s-1C mol-1)

Goldman-Hodgkin-Katz equations is not the Eyring transport model but an approximate solution of the diffusion equation and Poisson's equation for electrostatic.

Because the ions are subject to the concentration gradients and the electrical potential gradients, their motion in the one-dimensional system can be described by a combination of Fick’s law and Poisson's equation as following: dC d J  D  uzFC , where D – diffusion coefficient, u – mobility (u = D/RT), C - dx dx concentration, z – valence of an ion, x – distance and ψ – local potential.

This equation simply expresses the additivity of diffusional and electrophoretic motions.

Let’s assume a constant electric field, i.e. – dψ /dx = constant = -(ψout- ψin)/d = E/d, where d – is thickness of the membrane, E – membrane potential difference. This implies that ψ will be a linear function of x as illustrated in Figure S1.

Let’s C' denote the concentration within the membrane (Figure S1). The concentrations just inside the membrane can be related to corresponding concentrations in the bathing media by a partition coefficient, ß as CIN = ßC'IN and C'OUT = ßCOUT'. In turn, the permeability coefficient can defined as P = ßD/d. Figure S1. Schematic concentration and voltage profiles through the membrane. The voltage is linear (constant field), while the concentration profile is distorted from linearity by the electric field. (Adapted from the references 1 and 2.)

Hence, there are only two forces that influence the movement of the charged particle as it crosses biomembrane. In our case, this charged particle is an (an)ion- receptor complex, which simply drifts down the concentration gradient and the potential gradient (electric field). The charge, size, diffusion and partitioning coefficients, concentrations inside and out are to determine the rate of the transmembrane passage through the regions of matter with different polarity. In turn, the height of the ‘energy barrier’ (with an exception of its electrical component) is preserved within the permeability coefficient in a form of partitioning coefficient. This model is known as solubility-electrodiffusion. At a glance, it is valid as long as the anion-receptor interactions are relatively weak.

Ion hopping over a barrier (transition-state theory or Eyring rate theory) is more familiar to a chemist. In the particular case, it becomes the most relevant if there is a second barrier associated with an anion release from the complex, or if we consider fixed binding site(s) inside the bilayer as an ion moves along an ion channel. Chemical forces strongly alter the energy profile along the way and so the movement across is not a simple electrodiffusion, or using formalism of the partitioning-electrodiffusion model described above we may say that the diffusion coefficient is no longer a constant. Let’s consider passage over a single barrier. In passing from one state to another an activation energy barrier ΔG# must be surmounted. The rate constant, k, is proportional to the fraction of molecules having the requisite energy, and accordingly is set equal to # koexp(-ΔG /RT). The exponential can be viewed as the probability of surmounting the energy barrier at given temperature, and ko as the frequency to attempts per unit time. ΔG# represents the work done in moving from a local energy minima to the peak. If the molecule is and ion and there is a potential difference, E ≠ 0, there are two parts of the # # energy barrier, chemical, ΔG , and electrical, ΔE . We assume a constant electric field, i.e. – dψ/dx = constant. If x = δ then ψ = E (Figure S2). As the ion hops from one local minimum to another, along the x axis, the gain (loss) in the electrical energy can be expressed as zFΔψ, where Δψ - the potential difference, to be surmounted, and zF - the charge carried by the ion.

Let’s consider a symmetrical case, where the rates for the reversed and forward processes are exactly the same. For instance, there is a single vacancy in an ionic crystal so as an ion hops between the two identical sites in the lattice. If this crystal is placed in the electric field, or charges are applied to its surface, the two sites are no longer the same but there is zFΔψ difference. In turn, the activation energy of the transition can be expressed # # as ΔG + zFΔψ/2 for the forward and ΔG - zFΔψ/2 for the reversed processes accordingly and the rate will be written as following:

# # -dCIN /dt = koexp(-ΔG /RT)exp(-zFΔψ/2RT)[C]IN -koexp(-ΔG /RT)exp(zFΔψ/2RT)[C]OUT= = k (exp(-zFΔψ/2RT) [C]IN - exp(zFΔψ/2RT) [C]OUT)

In turn, for instance, in the case depicted in Figure S6 the formalism of the transition-state theory will be written as following:

* * * -dC /dt=k1[C]IN exp(-zFΔψ/3RT) – k2[C ] exp(-zFΔψ/6RT) – 2k2[C ] exp(zFΔψ/6RT)+ k1[C]OUT exp(zFΔψ/3RT), * -dCIN /dt = - k1[C]IN exp(-zFΔψ/3RT)+ k2[C ] exp(zFΔψ/6RT), * -dCOUT /dt = - k1[C]OUT exp(zFΔψ/3RT)+k2[C ] exp(-zFΔψ/6RT),

# where k1 = ko1 exp(-ΔG1 /RT) # k2 = ko2exp(-ΔG2 /RT)

(Adapted from the references 1-3.) A hypothetical barrier model. The ion fluxes can be calculated from the free-energy barriers of transitions, which in turn, have two components: ‘chemical’ and electrical, δ – electrical distance. Upon desire or when it seems to be necessary, a combination of the two formalisms can be used to describe the transport phenomena. Thus, the ion transport across the bilayer can be viewed as alternating steps of the electrodiffusion (GHK theory) and hopping over barriers (rate theory).

References:

1. Hille, B. Ionic Channels of Excitable Membranes, 3rd ed., Sinauer Associates: Sunderland, MA, 2001. 2. MCB 137 Exercises and Solutions, Lesson 6, Complete Axon chapter. http://mcb.berkeley.edu/courses/mcb137/exercises/Axon_B104.pdf (accessed Nov. 4, 2013). 3. Yaroslavtsev AB Properties of solids through the eyes of a chemist. M. MUCTR. Mendeleev, 1992. Ярославцев А.Б. Свойства твердых тел глазами химика. М.: РХТУ им. Д.И.Менделеева, 1992. (Russian language)

For instance, we may consider a ‘one anion’ transporter using analogy of a classical ‘one ion’ channel. In contrast to Goldman-Hodgkin-Katz (GHK) theory that at a glance, describes permeation as passage over a single barrier, a ‘one anion’ transporter includes two symmetric barriers with one energy minimum in between (Figure S2, A and B). Therefore, it more accurately describes the behavior of the K+-valinomycin complex or a hypothetical Cl- - ‘valinomycin for anions’ complex inside the bilayer. (It is relevant to note that our model yet differs from the one of valinomycin, where the permeation of the free receptor and not of the anion-receptor complex is thought to be rate-limiting.) Being particularly interested in supramolecular chemistry of anions inside biomembrane, we wish to study the exact opposite so permeation of anion-receptor complex and not of the ‘unloaded’ carrier determines the rate of ion passage. We may also note that GHK theory may yet adequately describe the system depicted in Figure S2A (weak interactions) but not the case depicted in Figure S2B (strong interactions.) In turn, the ‘one anion’ transporter inevitably evolves to add one, two or more binding sites. Such systems correspond to numerous examples of the synthetic compounds, cation- or anion-selective, where a (multi)ion hopping mechanism has been proposed, implied, or could have been proposed. Anion-π slides, synthetic lipids that use relay mechanism for anion translocation (S. Matile), guanosine-based Na+ transporter (J.T. Davis), and helical peptides bearing two, three or more crown-ether units (N. Voyer), are just a few such systems to mention.

Figure S2. Simple barrier models. The ion fluxes can be calculated from the free-energy barriers of transitions, which in turn, have two components: ‘chemical’ and electrical, δ – electrical distance. Even if ‘chemical’ energy profile is symmetric as depicted the total free energy profile would be asymmetric. A. A ‘one anion’ transporter, weak binding. B. A ‘one anion’ transporter, strong binding. C. A (multi)ion hopping mechanism, strong binding - two ions in the adjacent binding sites efficiently destabilize each other, lowering the kinetic barriers. SI2. Approximations. Table S1. Hydration energies and permeabilities of the selected inorganic anions.

9 -1 -1 Anion PAnion *10 cm s ∆GHydr (Anion) kJ mol Cl- 2.2 -363 Br- 7.3 -328 NO3- 19 -311 I- 60 -278 ClO4- 116 -228

The literature data in Table S1 have been used to construct the dependence of PAnion- on ∆GHydr as depicted in Figure S3. This approximate relation y = 6020.5*exp (-0.0302*x) - - has been used to obtain the permeability values for anions of the weak acids, N3 , SCN , - - F and CH3COO , tabulated in Table 1 in the article.

Figure S3. Dependence of PAnion- on ∆GHydr Table S2. Experimental and theoretical values of the partition coefficient (hydrophobicity) for the weak acids HAnion, Poctanol/water (reported by Walter et al) -1 and LogPHAnion (ACD Lab); experimental values of the permeability PHAnion, cm s reported by Walter et. al.

HAnion LogPHAnion Poct/water -1 (ACD Lab) (experimental) PHAnion, cm s -6 HF 4.2*10 3.1*10-4 -1 HSCN 0.429 3.2*10 2.6 -4 C2H4O2 -0.322 5.3*10 5.0 * 10-3

HN3 -0.068 -2 HCl 6.0*10 2.9 -5 HNO3 -0.773 6.9*10 -4 9.2*10 The data in Table S2 have been used to construct the dependence of log PHAnion on

LogPHAnion depicted in Figure S4.

0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.5

-1 y = 2.9471x - 0.9865 R2 = 0.969 -1.5 -2

Figure S4. Dependence of log PHAnion on LogPHAnion

This approximate relation y = 2.9471*x - 0.9865 has been used to obtain/approximate the -2 -1 permeability values for hydrazoic acids HN3, PHN3 = 6.5 *10 cm s , depicted in Table 1.

SI 3. Permeability of the ‘unstirred’ layer.

P unstirred layer can be estimated as following: -5 2 -1 -9 2 -1 -6 -5 -1 -5 P unstirred layer = D/δ = 10 cm s / 1000 nm = 10 m s / 10 m = 10 cm s where D = 10 cm2 s-1 - typical value for the diffusion coefficient in water for small molecule, δ = 1000 nm - thickness of the unstirred layer. Therefore, if speed at which the molecule moves across the unstirred layer is much higher than the speed at which it moves across the membrane (P unstirred layer >> P m) than unstirred layer effect is negligible.

- -9 -1 For instance, P m (F ) = 0.83 *10 cm s >> P unstirred layer However, if speed at which the molecule moves across the unstirred layer and the speed at which it moves across the membrane are comparable than apparent permeability should be expected as a combination of the two phenomena.

-4 For instance, P m (HF) = 3.1 * 10 > P unstirred layer SI4. Weak vs strong acid: the pH “error” in 10 mM phosphate buffer.

- Let’s imagine that we replaced all Anion1 in a 100 mM solution, 10 mM phosphate - buffer at pH = 7 with CH3COO . (Anion1- corresponds to a strong acid.) The concentration of CH3COOH in the medium can be obtained as following:

- pH = pKa + Log[Anion2 ]/[HAnion2], pH = pKa(CH3COOH) + Log( 0.1 - [CH3COOH]/[ CH3COOH]), 7 = 4.8 + Log(0.1 – [CH3COOH]/[ CH3COOH]), which gives [CH3COOH] = 0.000627. But if the anion of the weak acid undergoes hydrolysis, the pH of the medium should also - - rise. There is 0.006131 mM of H2PO4 at pH = 7 in 10 mM buffer in Anion1 solution, - - which drops to [H2PO4 ]’ = 0.006131 - 0.000627 = 0.005504 mM in CH3COO , which in turn, corresponds to pH’ = 7.1. Therefore, we can say that the actual concentration of the acetic acid in the solution is less than 0.015846 mM and the actual pH change is less than 0.1.

Log pH- - Anion2- HAnion2 % pH (Anion2-/HAnion2) pKa [H2PO4 ] [H2PO4]' pH' [F- ] 0.1 0.099999984 1.58489E-08 1.58E-05 10 6.800000806 6.8 1.582E-05 1.58E-05 10.0004 0.1 0.099984154 1.58464E-05 0.015846 7 3.800000834 3.8 0.006131 0.006115 7.00297

[CH3COO-] 0.1 0.099999369 6.30952E-07 0.000631 10 5.200000938 5.2 1.582E-05 1.52E-05 10.0177 0.1 0.099373 0.000627 0.627 7 2.20000086 2.2 0.006131 0.005504 7.11215 SI5. Influx of the weak acid HAnion2 OUT into liposomes. A simple model, pH ≥ 7.

- - Let’s consider Anion1 IN / Anion2 OUT system in the absence of an ionophore, 10 mM phosphate buffer, HAnion2 is a weak acid and HAnion1 is a strong acid.

- - We have a liposomal suspension, Anion1 IN/Anion1 OUT, 10 mM phosphate buffer, pHIN = - pHOUT = 6.4 and an isoosmotic solution containing F , 10 mM phosphate buffer, pH = 6.4. As soon as a small aliquot of this liposomal suspension is diluted into the isoosmotic medium containing the anion of a weak acid, the intravesicular pH drops due to the influx of HF. Because HF is the only permeant specie, the influx of HF terminates as soon as concentrations of it inside and out equalize. We note that 1) it takes several ms (or s) to establish the equilibrium, 2) Em = 0 during this process because charged species do not permeate across the bilayer on a relevant time scale.

Figure S5. The equilibrium that establishes upon dilution of liposomal suspension, 100 mM NaClIN and 100 mM NaClOUT, pH = 10 into the isoosmotic medium containing NaF at pH = 10.

Flowchart S1. Equations.

{Reservoirs} d/dt (R1) = + J1 INIT R1 = 0 d/dt (R2) = - J1 INIT R2 = 0.1*0.002 d/dt (R3) = + J2 INIT R3 = 0.000005*4.3*10^(-19)*7.1*10^12 d/dt (R4) = - J2 INIT R4 = 0.000005*0.002

{Flows} J1 = F2*2.8*10^(-14)*7.1*10^12*(F3-F1) * 10^3 J2 = J1

{Functions} F1 = F6 * 10^(-F4)/10^(-3.2) F2 = 0.31*10^(-5) F3 = F7 * 10^(-F5)/10^(-3.2) F4 = 7.2+log10((0.01-F8)/(F8)) F5 = 7.2+log10((0.01-F9)/(F9)) F6 = R1/(4.3*10^(-19)*7.1*10^12) F7 = R2/(0.002) F8 = R3/(4.3*10^(-19)*7.1*10^12) F9 = R4/0.002

Equations + Explanation.

d/dt (R1) = J1 J1, mol s-1 – HF flow R1 – N(F-), mol – amount of the fluoride anion in liposomes

INIT R1 = 0 d/dt (R2) = - J1

R2 – N(F-), mol – amount of the fluoride anion in the extravesicular solution

INIT R2 = 0.1*0.002 - INIT R4 = [F ]OUT Initial, M * V, L d/dt (R3) = J2 INIT R3 = 0.000005*4.3*10^(-19)*7.1*10^12

-1 - J2, mol s – ‘flow’ of [H2PO4 ] into liposomes. - - R3 – N(H2PO4 ), mol – amount of H2PO4 anions in liposomes At pH = 10.5 in 10 mM phosphate buffer we have [NaH2PO4] = 0.000005, M

- INIT R3 = [H2PO4 ]IN initial, M * Vliposome, L * Nliposomes

d/dt (R4) = - J2 INIT R4 = 0.000005*0.002

- - R4 – N(H2PO4 ), mol - amount of H2PO4 anions in the extravesicular solution - INIT R4 = [H2PO4 ]OUT initial, M * Vliposome, L * Nliposomes J1 = F2*2.8*10^(-14)*7.1*10^12*(F3-F1) * 10^3

-1 2 3 J1 = PHF, m s * Aliposome, m * Nliposomes * ([HF]OUT - [HF]IN), mol L * 10 J2 = J1 - J2([H2PO4 ]) = J1(HF) -1 F2 – PHF, m s F1 - [HF]IN, M F3 – [HF]OUT, M F2 = 0.31*10^(-5) F1 = F6 * 10^(-F4)/10^(-3.2) F3 = F7 * 10^(-F5)/10^(-3.2) - + [HF] IN = [F ]IN * [H ]IN /Ka(HF) - + [HF]OUT = [F ]OUT * [H ]OUT / Ka(HF)

F4 – pHIN F5 – pHOUT F4 = 7.2+log10((0.01-F8)/(F8)) F5 = 7.2+log10((0.01-F9)/(F9)) - F6 – [F ]IN, M - F7 – [F ]OUT, M F6 = R1/(4.3*10^(-19)*7.1*10^12) F7 = R2/(0.002) - - [F ]IN = N(F )IN, M / (Vliposome, L * Nliposomes) - - [F ]OUT = N(F )OUT , mol / VOUT, L - F8 - [H2PO4 ]IN, M - F9 - [H2PO4 ]OUT, M F8 = R3/(4.3*10^(-19)*7.1*10^12) F9 = R4/0.002 - - [H2PO4 ]IN = N(H2PO4 )IN, M / (Vliposome, L * Nliposomes) - - [H2PO4 ]OUT = N(H2PO4 )OUT, M / V, L

+ - SI6. Influx of the weak acid HAnion2 OUT and H /OH transport.

Figure S6. The equilibrium that establishes upon dilution of liposomal suspension, 100 mM NaClIN and 100 mM NaClOUT, pH = 10 into the isoosmotic medium containing NaF at pH = 10; H+ and OH- ions permeate on a relevant time scale.

- - Let’s consider the same Anion1 IN / Anion2 OUT system in the absence of an ionophore, 10 mM phosphate buffer, HAnion2 is a weak acid and HAnion1 is a strong acid. However, + - here HAnion2 is not the only permeant specie but H and OH ions may also permeate across on a relevant time scale. If H+/OH- permeate fast enough, the new equilibrium is established. In turn, if H+/OH- do not permeate fast enough, we are looking at the kinetics as the liposome slowly gets positively charged on the outside. The Flowchart S2 that describes this process is partly analogous to Flowchart S1. Only the difference between the two is explained in details.

HAnion2 = HF

Flowchart S2.

d/dt (R6) = + J3 INIT R6 = 0 J3, mol s-1 – H+ flow + + R6 – N(H )Excess, mol – amount of the H that accumulates in the extravesicular medium due to passage of H+ ions across the bilayer

d/dt (R5) = - J4 INIT R5 = 0 J4, mol s-1 – OH- flow - - R5 – N(OH )Excess, mol – amount of the OH anion that accumulates in the extravesicular medium due to passage of OH- ions across the bilayer

{Flows} J1 = F2*2.8*10^(-14)*7.1*10^12*(F3-F1) * 10^3

J2 = J1 - J3 - J4 - + - J2([H2PO4 ]) = J1(HF) - J3(H ) - J4(OH )

J3 = F13*3*10^(-14)*7.1*10^12 *(10^(-F4)*F11-10^(- F5)*F12) * 10^3 J4 = F13*3*10^(-14)*7.1*10^12 *(10^(F5-14)*F11-10^(F4-14)*F12) * 10^3

-1 2 -pH OUT -pH IN 3 J3 = PH+, m s * Aliposome, m * Nliposomes * (10 *F11 – 10 *F12)* 10 -1 2 (pH OUT -14) (pH IN -14) 3 J4 = POH-, m s * Aliposome, m * Nliposomes * (10 * F11– 10 *F12)* 10

{Functions} F1 = F6 * 10^(-F4)/10^(-3.2) F2 = 0.31*10^(-5) F3 = F7 * 10^(-F5)/10^(-3.2) F4 = 7.2+log10((0.01-F8)/(F8)) F5 = 7.2+log10((0.01-F9)/(F9)) F6 = R1/(4.3*10^(-19)*7.1*10^12) F7 = R2/(0.002) F8 = R3/(4.3*10^(-19)*7.1*10^12) F9 = R4/0.002

F10 = (F16-F14) *96480/(8.314*298)

F10 – U – reduced membrane potential -1 -1 -1 U = Em, V * F, Coulomb mol /(R, J mol K * T, K), where Em, V = F16 – F 14

F11 = IF F10 >0.01 OR F10 <-0.01 then F10/(1-2.72^(-F10)) else 1/(1+F10/2+F10^2/6) F12 = F11*2.72^(-F10)

F13 = 10^(-8) F17 = 4*10^(-11) -8 -1 F13 – PH+ = 10 , m s -11 -1 F17 – POH- = 4*10 , m s F15 = F16 – F 14 F15 – Em, V = EH+, V – EOH-, V

F14 = R6/(7.1*10^12) *96480/(10^(-2)*3*10^(-14)) + -1 -1 -2 2 F14 - EH+, V = N(H )Excess/Nliposomes * F, Coulomb mol /(C, Coulombs V m * A, m )

F16 = R5/(7.1*10^12)*96480/(10^(-2)*3*10^(-14)) - -1 -1 -2 2 F16 - EOH-, V = N(OH )Excess/Nliposomes * F, Coulomb mol /(C, Coulombs V m * A, m )

SI7. Anion1 IN / Anion2 OUT exchange, HAnion1 IN - is a strong acid, HAnion2 OUT - is a weak acid.

- Anion1 IN / F OUT exchange, HAnion1 - is a strong acid.

Flowchart S3. Flowchart S3 is largely analogous to Flowchart S2. Only the difference between the two is explained in details.

- INIT R4(3) = [H2PO4 ]OUT(IN) initial, M * Vliposome, L * Nliposomes At pH = 6.87 in 10 mM phosphate buffer we have [NaH2PO4] = 0.006815, M At pH = 8.25 in 10 mM phosphate buffer we have [NaH2PO4] = 0.0008182, M

d/dt (R6) = + J3 INIT R6 = 0 d/dt (R5) = - J4 INIT R5 = 0 d/dt (R7) = - J5 INIT R7 = 0.1*4.3*10^(-19)*7.1*10^12

- R7- N(Anion1 ), mol – amount of Anion1 in liposomes.

d/dt (R8) = + J5 INIT R8 = 0.1*0.04*10^(-3)

- R8 - N(Anion1 ), mol – amount of Anion1 in the extravesicular solution (40 μL of the liposomal suspension 100 mM NaAnion IN/NaAnion OUT is injected into 2 ml solution)

d/dt (R9) = + J6 INIT R9 = 0

- - R9 - N(F )anionophoretic, mol – amount of the F anion in liposomes that accumulates using aniophoretic pathway

{Flows} J1 = F2*2.8*10^(-14)*7.1*10^12*(F3-F1) * 10^3+J6

J1 (HF +F-), mol s-1 – total flow of F- anion into liposome as a combination of the electronetutral (HF) and electrogenic (J6 (F-)) pathways.

J2 = (J1-J3-J4-J6) - - + - - J2([H2PO4 ]) = J1(HF+F ) - J3(H ) - J4(OH ) – J6(F ) J3 = F13*3*10^(-14)*7.1*10^12 *(10^(-F4)*F11-10^(- F5)*F12) * 10^3 J4 = F17*3*10^(-14)*7.1*10^12 *(10^(F5-14)*F11-10^(F4-14)*F12) * 10^3

J5 = F18*3*10^(-14)*7.1*10^12*(F19*F12-F20*F11) * 10^3 J6 = F21*3*10^(-14)*7.1*10^12*(F7*F11-F6*F12) * 10^3

- -1 2 - - J5 = PAnion , m s * Aliposome, m * Nliposomes * ([Anion1 ]IN, M*F12 - [Anion1 ]OUT, M *F11)*103

-1 2 - - 3 J6 = PF-, m s * Aliposome, m * Nliposomes * ([F ]OUT, M*F11 – [F ]IN, M *F12)*10

F1 = F6 * 10^(-F4)/10^(-3.2) F2 = 0.31*10^(-5) F3 = F7 * 10^(-F5)/10^(-3.2) F4 = 7.2+log10((0.01-F8)/(F8)) F5 = 7.2+log10((0.01-F9)/(F9)) F6 = R1/(4.3*10^(-19)*7.1*10^12) F7 = R2/(0.00204) F8 = R3/(4.3*10^(-19)*7.1*10^12) F9 = R4/0.00204

F10 = (F16-F14+F23-F22)*96480 /(8.314*298)

Em, V = F16 - F14 + F23 - F22 = EH+ – EOH- + EAnion- – EF-

F11 = IF F10 >0.01 OR F10 <-0.01 then F10/(1-2.72^(-F10)) else 1/(1+F10/2+F10^2/6) F12 = F11*2.72^(-F10) F13 = 10^(-3) F14 = R6/(7.1*10^12)*96480/(10^(-2)*3*10^(-14)) F15 = (F16-F14) F16 = R5/(7.1*10^12)*96480/(10^(-2)*3*10^(-14)) F17 = 4*10^(-11) F18 = -1 F18 - PAnion1- = , m s F19 = R7/(4.3*10^(-19)*7.1*10^12) F20 = R8/(2.04*10^(-3))

- F19 – [Anion1 ]IN, M - F20 – [Anion1 ]OUT, M

F21 = 0.83*10^(-11) -11 -1 F21 - PF- = 0.83 *10 , m s

F22 = R9/(7.1*10^12)*96480/(10^(-2)*3*10^(-14)) F23 = (0.1*4.3*10^(-19) - R7/(7.1*10^12))*96480/(10^(-2)*3*10^(-14))

- -1 -1 -2 2 F22 = EF-,V = N(F )anionophoretic/Nliposomes * F, Coulomb mol /(C,Coulombs V m *A, m )

- - F23 = EAnion1-,V = ([Anion1 ]IN initial * VLiposome, L - (N(Anion1 )IN/Nliposomes)) * F, Coulomb mol -1/(C, Coulombs V-1 m-2 * A, m2) SI8. ‘Presumable OH-/Cl- exchange’.

Figure S7. Presumable OH-/Cl- exchange.

Here we consider a classical experiment (‘presumable Cl-/OH- exchange’) where the anion gradient as well as the pH gradient are imposed. We ignore the electrogenic nature of the phenomena, and the goal is to consider and compare just the initial fluxes of the anions in solution.

-11 -1 If PAnion- is in a range about (2.2-116)*10 m s , the ion transport will proceed on a relevant time scale. Because hydration energies for Cl- and OH- are similar we could have -11 -1 assigned POH- ≈ PCl- = 2.2*10 m s . However, because reported values POH- for pure phospholipid bilayer (without anionophore) equal 10-9 – 4*10-11 m s-1 we use them instead.

- - -1 2 - -1 3 J(Anion ) = PAnion , m s * Aliposome, m * Nliposomes * ([Anion ]OUT, mol L ) * 10 =

= 116 * 10-11 * 3 *10-14 * 7.1*1012 * 0.1 *103 = 2.47*10-8 mol s-1

- - -1 3 J(Cl ) = PCl- * Aliposome * Nliposomes * ([Cl ]IN, mol L ) * 10 =

= 2.2 * 10-11 * 3 *10-14 * 7.1*1012 * 0.1 *103 = 4.69*10-10 mol s-1

- - -1 3 J(OH ) = POH- * Aliposome * Nliposomes * ([OH ]OUT , mol L ) * 10 =

= 4 * 10-11 * 3 *10-14 * 7.1*1012 * 10-4 *103 = 8.5 * 10-13 mol s-1 or = 10-9 * 3 *10-14 * 7.1*1012 * 10-4 *103 = 2 * 10-11 mol s-1

-9 Therefore, even if we assume the pHOUT = 10 and use the largest reported value POH- =10 m s-1, the flux of OH- ion is way below the flux rate for the least permeant inorganic anions of the salts. An interested researcher can also take a look at the phosphate buffer, knowing that - 2- concentration of H2PO4 + HPO4 is only 10 mM and hydration energy follows an order - - - 2- Cl < CH3COO < H2PO4 / HPO4 .