Quantitative Limits on Small Molecule Transport via the Electropermeome — Measuring and Modeling Single Nanosecond Perturbations

The detailed molecular mechanisms underlying the permeabilization of cell membranes by pulsed electric fields (electroporation) remain obscure despite decades of investigative effort. To advance beyond descriptive schematics to the development of robust, predictive models, empirical parameters in existing models must be replaced with physics- and biology-based terms anchored in experimental observations. We report here absolute values for the uptake of YO-PRO-1, a small-molecule fluorescent indicator of membrane integrity, into cells after a single electric pulse lasting only 6 ns. We correlate these measured values, based on fluorescence microphotometry of hundreds of individual cells, with a diffusion-based geometric analysis of pore-mediated transport and with molecular simulations of transport across electropores in a phospholipid bilayer. The results challenge the “drift and diffusion through a pore” model that dominates conventional explanatory schemes for the electroporative transfer of small molecules into cells and point to the necessity for a more complex model.

Rate of uptake is another way to look at the data reported in Figure 2. In Figure S1 we plotted time derivative of the same data, showing the decrease in rate of uptake with time. Rate of uptake at time point t, R t is filtered in this plot using moving average difference filter, such that (S1) where φ t is the uptake at point t and Δt is the timestep of the recording.
Distribution plots of rate of uptake in Figure S2 show that the shape of the distribution is maintained, meaning there are no irregular jumps in rate of uptake during the time course causing broadening or narrowing of the distribution. Moreover, consistent with maintained width of the distribution, an inspection of changes in rate of uptake for individual cells showed that as the population average is decreasing with time, cell-to-cell variation of rates of uptake is maintained. In other words, cells with higher rate of uptake at 20 seconds are also the same ones with higher rate of uptake at 180 seconds after the field exposure.

YO--PRO--1 Uptake versus cell location with respect to electrodes
We looked at correlation of cell location between the electrodes to the total uptake of YP1 molecule at different time points (Fig. S3) and found no direct correlation. This observation is consistent with the uniform electric field distribution we expect to have between the parallel wire electrodes based on electrostatic simulations of the electrode assembly reported in Wu et al. 2 .

Diffusion Coefficient for YO--PRO--1
An experimental value for the diffusion coefficient of YO-PRO-1 (YP1) was not found in the literature, instead we used an estimate based on the geometrical properties of the YP1 molecule. For a spherical particle with a well-established diffusion coefficient we used the sodium ion as a reference. From its diffusion coefficient (D Na ), and radius (r Na ), we can extract an estimate for the diffusion coefficient of an ellipsoid particle with longer radius (l YP1 /2) and shorter radius (r YP1 ).
. Diffusion coefficient (D) and friction coefficient (ξ) are related 3 : where k, and T are Boltzmann's constant, and absolute temperature. For a spherical particle like the sodium ion the friction coefficient is where η is viscosity of the solvent. For ellipsoid solutes moving sideways with longer radius (l YP1 /2) and shorter radius of (r YP1 ) the friction coefficient is Using S2, S3, and S4, we can get diffusion coefficient for YP1: Sensitivity of diffusive uptake calculations to hindrance and partitioning effects As described under section "Modeling YO-PRO-1 uptake as diffusive transport through membrane pores", J s,p , diffusive uptake through a single cylindrical pore can be described as: , where J s is the diffusive uptake due to a concentration gradient (without any interaction of the solute with the pore walls) and H and K are hindrance and partitioning factors that account for solute-pore interactions 4 .
Hindrance (H) arises from two factors, decreased effective area when solute is passing through the pore (f A ), and the drag exerted on the solute by the pore walls (f D ), as developed by Bungay and Brenner 5 . For a detailed explanation of the calculation of each factor please refer to Smith 4 . Here we give the specific equations that we used for calculations that generated Fig. 8 of the main text. (S7) where effective area f A is given by with λ = r s /r p where r p is the radius of the pore, and is the drag factor (f D ) modified for a cylindrical solute according to where l s and r s are solute dimensions.
Partitioning (K) accounts for the energetic cost of moving a charged solute from a high dielectric constant medium to the low dielectric constant interior of a lipid bilayer. (S12) where A, B, C are factors given below and (S13) where z s is the valence of the solute, q e is the elementary charge, V m is the membrane potential, k is the Boltzmann constant and T is the absolute temperature. (S14) with n = 0.25, and the Born energy (S15) In this calculation, small changes in pore radius and solute radius can lead to large changes in diffusive uptake because of how hindrance and partition factors change with pore size. Figure S4 shows hindrance and partitioning for a solute with radius of r s = 0.53 nm together with the combined effect of these factors on total transport is in red. Note that Fig. S4 is a semilog plot, and when the pore size approaches to solute size on the left hand side of the plot, both factors decrease dramatically with a small change in pore size. For example, a 0.05 nm change in pore size-a fraction of the size of a water molecule -from 0.6 nm to 0.65 nm causes, more than a tenfold change in the transport rate, while a change from 0.9 nm to 1.0 nm in pore size ends up in a three-fold change in the transport rate for a solute with a cross-sectional radius of 0.53 nm, approximately the size of YO-PRO-1. This sensitivity in calculations is important to note since, up to now, there is no evidence of such sensitivity experimentally. Figure S4. Hindrance and partitioning as a function of pore radius, for a solute of radius r s = 0.53 nm. Figure S5 shows the total number of interfacial (bound) and bulk (free) YP1 molecules in a 128-POPC system containing 52 YP1 molecules as a function of time. Figure S5. Redistribution of YP1 from the bulk solution to the bilayer interface Similar interfacial YP1 concentrations are found in systems containing NaCl or KCl. In systems containing NaCl, YP1 displaces Na + from the bilayer interface (Fig. S6). Figure S6. Displacement of interfacial Na + by YP1. K + ions do not affect the binding behavior of YO-PRO-1 Figure S7. Radial distribution function of YP1 showing strong binding affinity between positively charged YP1 nitrogens and negatively charged POPC phosphate residues, while interactions with positively charged choline groups were three times less likely.