Nanopore occlusion: A biophysical mechanism for bipolar cancellation in cell membranes
Thiruvallur R. Gowrishankar, Julie V. Stern, Kyle C. Smith, James C. Weaver
NNanopore occlusion: A biophysical mechanism forbipolar cancellation in cell membranes
Thiruvallur R. Gowrishankar a , Julie V. Stern a ,Kyle C. Smith a , James C. Weaver a, ∗ a Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute ofTechnology, Cambridge, MA, USA
Abstract
Extraordinarily large but short electric field pulses are reported by many exper-iments to cause bipolar cancellation (BPC). This unusual cell response occursif a first pulse is followed by a second pulse with opposite polarity. Possiblyuniversal, BPC presently lacks a mechanistic explanation. Multiple versions ofthe “standard model” of cell electroporation (EP) fail to account for BPC. Herewe show, for the first time, how an extension of the standard model can accountfor a key experimental observation that essentially defines BPC: the amountof a tracer that enters a cell, and how tracer influx can be decreased by thesecond part of a bipolar pulse. The extended model can also account for therecovery of BPC wherein the extent of BPC is diminished if the spacing betweenthe first and second pulses is increased. Our approach is reverse engineering,meaning that we identify and introduce an additional biophysical mechanismthat allows pore transport to change. We hypothesize that occluding moleculesfrom outside the membrane enter or relocate within a pore. Significantly, theadditional mechanism is fundamental and general, involving a combination ofpartitioning and hindrance. Molecules near the membrane can enter pores toblock transport of tracer molecules while still passing small ions (charge number ±
1) that govern electrical behavior. Accounting for such behavior requires anextension of the standard model.
Keywords:
Nanopore occlusion, bipolar cancellation, electroporation,hindrance, partitioning
1. Introduction
Over the past several years several publications have reported and partiallycharacterized the phenomenon of “bipolar cancellation” (BPC), using a varietyof in vitro experiments with isolated cells [1, 2, 3, 4, 5, 6, 7, 8]. BPC manifests ∗ Corresponding author
Email address: [email protected] (James C. Weaver)
Preprint submitted to Elsevier July 4, 2018 a r X i v : . [ q - b i o . S C ] J u l s reduction or cancellation of bioeffects, specifically the uptake of tracers suchas YO-PRO-1, propidium or calcium. BPC occurs when two pulses of oppositepolarity (not necessarily of same amplitude) are applied in rapid succession[1, 2, 3, 4, 5, 6, 7, 8]. The extent of cancellation decreases with increasedseparation of the two opposite polarity pulses.One striking feature is that BPC requires short, very large fields (nsPEFor nanosecond pulsed electric fields). These are not the longer, smaller fieldpulses used in conventional cell electroporation (EP) since the 1970s [9, 10, 11],but are nsPEF pulses used in supra-EP studies [12, 13, 14, 15, 16]. While notyet understood mechanistically, BPC is reported to mainly occur for widelyseparated mammalian cells in vitro, for applied electric field pulse strengths of4 - 100 kV/cm and durations of 10 to 600 ns.In some experiments pulse trains predominate, which greatly complicatesinterpretation because of memory effects due to pore lifetimes. Other stud-ies employ single pulses, which is more relevant to basic understanding, andtherefore the focus of the present work [17, 18].An unusual BPC feature is that the second part (reversed polarity) of thepulse should move tracer molecules “uphill”, against the concentration gradi-ent. The potential implications of BPC are tantalizing, but initial explanatoryhypotheses have failed. To our knowledge, the present paper is the first reportof a biophysical model that can account for functional features of BPC.Significantly, attempts to use the standard cell EP model to account forBPC all failed. The standard model always predicts a large number of poressuch that the diffusive influx always leads to an increase in intracellular tracermolecule. Essentially all EP delivery/extraction protocols accelerate transportdown a solute concentration gradient. For BPC the second pulse should do theopposite. This apparently simple change greatly increases the problem difficulty:how can tracer molecule entry be slowed?The standard EP model is based on lipidic transient pores (TPs) that formin lipid bilayer membranes in contact with aqueous electrolytes on both sides,and is consistent with many experimental observations [17, 19, 20, 21]. Thestandard model is essentially an extension of the Schwann model for eitherspherical or cylindrical cells [17, 20, 20]. By adding TP creation for supra-physiologic transmembrane voltages the resulting model exhibits non-linear TPcreation that begins at one (anodic) pole, followed by poration at the other(cathodic) pole, and then with time during a porating pulse, additional porecreation further away from the cell’s poles [17, 22].Here we propose a mechanism for BPC that is based on increased poreocclusion and a corresponding decrease in tracer transport due to the presenceof charged molecules within pores. The increased occlusion is represented in themodel by a decrease in the occlusion factor magnitude. We also account for thepossibility of a weak interaction of the inserted molecule with the membranepore by allowing the recovery of the occlusion factor.2 B C
Figure 1:
Isolated cell model.
The 5 µ m radius cylindrical cell (A) is contained in a200 µ m × µ m system model (B). The cell mesh transport network model (MTNM) [20] isrepresented by 150 transmembrane node-pairs (C) that describe local transmembrane voltages,pore distributions, hindrance, partitioning of molecules and ions into the pores, and moleculartransport. The 4-nm thick membrane has a resting potential of -50 mV due to a fixed currentsource [20]. The field is created by applying external pulse generator voltages to the topand bottom rows of nodes of the simulation box. Each of the local areas associated with atransmembrane node-pair is regarded as a very small planar membrane patch (a Voronoi cell)endowed with a resting potential source and a complete dynamic EP model [20].
2. Methods
Cell EP inescapably involves spatially distributed, highly nonlinear and hys-teretic interactions throughout a cell system model. We use a cylindrical cellmembrane contacting electrically conducting extracellular and intracellular me-dia [23, 20, 24, 18, 21]. These complex interactions are solved computationallywith an isolated cylindrical cell model (Fig. 1). We describe the system usingthe meshed transport network model (MTNM) elsewhere (above publications).The cylindrical plasma membrane (PM) has 5 µ m radius, 6 . µ m height, and4 nm thickness (Fig. 1A). The extracellular region is represented by 2077 nodes(or Voronoi cells. which are the local regions), and the intracellular region isrepresented by 891 nodes. Of these, 150 node pairs (one extracellular and oneintracellular) span the PM (Fig. 1B). The two electrolytes are represented bypassive models that describe charge transport and storage within the electrolyte[25]. The PM node pairs (Fig. 1C) contain a complete dynamic EP model thatprovides the local kinetics of membrane pore creation, evolution, and destruc-tion, and include associated changes in transmembrane voltage and membraneconductance.We use D p = 2 × − m / s, for the diffusion coefficient in pore radiusspace and a maximum pore radius, r p , max of 12 nm with a pore lifetime of100 s. The details of the local membrane EP model are described elsewhere[23, 20, 24, 18]. The local membrane models also include a -50 mV restingtransmembrane voltage source. Other parameters for describing membrane EPwithin local membrane areas (regions associated with a transmembrane nodepair) and adjacent aqueous media are given elsewhere [26].3 .2. Occluded transport We assume that once a lipidic transient pore (TP) is created in the mem-brane, one or more charged molecules enter the pore. The presence of a chargedmolecule in the pore causes occlusion that hinders the movement of ions andtracer molecules. Some of the molecules are weakly bound to the pore wall andwith time leave the pore. However, in the case of a bipolar pulse, the secondpulse draws more molecules into the pores, increasing occlusion.We modify the standard model of electroporation by introducing an occlusionfactor, O(t), that accounts for a decrease in pore-mediated transport of bothsmall ions and tracer molecules. O(t) represents the total occlusion due toexternal molecule hindrance and partitioning. In addition, O(t) kinetics canaccount for the partial recovery of the membrane by the release of weakly boundmolecules from the pore walls. O(t) accounts for the decrease in tracer transportthrough a pore in the presence of external molecules in the pore.
Our model can readily accommodate experimental waveforms with complexcharacteristics, including a decaying sinusoid. We model the response of two dif-ferent but related electric field pulses: bipolar (BP; + and - 24 kV/cm, 200+200ns; Fig. 2A) and unipolar (UP; 24 kV/cm, 200 ns; Fig. 2B). These pulses aredigitized version of the experimental pulses of Gianulis et al. [3].
The extracellular and intracellular media have electrical conductivities of1.2 S / m and 0.3 S / m, respectively. The extracellular medium also contains1 µ M YO-PRO-1 (YP), a fluorescent dye with molecular properties: chargenumber: +2, molecular length: 1.7 nm, molecular radius: 0.53 nm, extracellulardiffusion coefficient: 5 . × − m / s, and intracellular diffusion coefficient:1 . × − m / s [20].
3. Results
The uptake of YP in an isolated cell model is compared to the experimentaluptake from UP and BP pulses [3]. The effect of changing hindrance due toentry of external molecules is also presented. Our model’s response can thereforeaccount for the reported experimental BPC behavior.
Figure 2A and 2B show transmembrane voltage (∆ φ m ) at the anodic andcathodic poles of the cell in response to the BP (A) and UP (B) pulses of Fig. 2.∆ φ m increases with the onset of the applied field until the associated increasein membrane conductance causes the reversible electrical breakdown (REB) ofthe membrane. The REB peak occurs within 25 ns from the start of the pulse.Only the first peak of the pulse causes REB of the membrane. The magnitudesof the subsequent peaks of the applied field are not large enough to cause REBgiven persisting conductance. ∆ φ m responses for BP and UP at the poles arealso bipolar and unipolar, respectively.4 (BP 5 peaks) B (UP 3 peaks) C D
Figure 2:
Electrical response to bipolar (BP) and unipolar (UP pulses.
The BP (A)and UP (B) pulses are digitized versions of experimental waveforms [3]. Each pulse of thecomplex waveform is approximately 200 ns long and the amplitude of the first positive peakis 24 kV/cm. The BP has 5 peaks (A) and UP has 3 peaks (B). Peaks 2 and 4 in the BPare not present in the UP. The UP is derived from the BP by rectification. voltage, ∆ φ m ,response is shown at the anodic (red) and cathodic (black) poles for the BP (C) and UP (D)pulses. In both unipolar and bipolar cases, ∆ φ m increases rapidly at the onset of the pulse.This rise initiates a burst of pore creation, increasing the conductance of the membrane. Theconductance increase brings down ∆ φ m to a plateau of 0.7 V before the pulse starts declining. Figure SI-1 (Supplemental Information) shows the hindrance factor as afunction of pore radius for YP. The hindrance factor, H (0 ≤ H ≤
1) withoutoccluding molecules is determined by the size of YP molecule relative to thepore radius [20]. When H →
0, transport is significantly hindered, close tozero. However, when H →
1, transport is largely unhindered, which leads totransport rates approaching bulk electrolyte values. In other words, a highervalue of hindrance factor corresponds to less transport. For YP and pore radiiless than 2 nm, YP molecules experience significant hindrance for transportthrough a minimum-sized (0.85 nm radius) pore. In this example, transport ofYP is reduced by a factor of 0.007 for a pore radius of 0.85 nm and by a factorof 0.2 for a pore radius of 2 nm. However, if the pore is obstructed by external5 B Figure 3:
Cell model YP uptake compared to experiment[3].
Experimental uptakeof YP in CHO cells subject to a BP (blue) and UP (black) pulses are shown (A). The cor-responding uptake in the cell model is shown in (B) normalized to the initial extracellularconcentration of YP. Hindrance, quantified by the H-factor (hindrance factor) was increasedat 200 ns for UP by 100 times and for BP by 1000 times. Our model reasonably accounts forbipolar cancellation (decreased uptake for a BP) as seen in experiments[3]. molecules, the increased hindrance extends to larger pores. Both BP and UPpulses considered here cause pores to expand to no more than 2 nm in poreradius (Fig. SI-2).
Submicrosecond pulses cause supra-EP (large number of small pores) [22].Small pores limit the uptake of molecules like YP. But even pores as small as 2nm radius allow YP (length: 1.7 nm, radius: 0.53 nm) to cross the membranewith a small hindrance factor. Both BP and UP create nearly identical distri-bution of pores (size and number) (Fig SI-2). However, when H decreases, theuptake decreases. Both BP and UP show similar uptake profiles for different Hvalues because of similar pore distribution for both pulses.
Gianulis et al. [3] show that bipolar and unipolar nanosecond electric fieldpulses (Fig. 2) enable electroporative uptake of YP in CHO cells (Fig. 3A). Theexperimental study shows that uptake from a BP is three times smaller thanthat from a corresponding UP.The intracellular YP concentration in the isolated cell model shows thata decreased uptake from a BP (compared to a corresponding unipolar pulse)corresponds to increased occlusion (less uptake). Figure 3B shows YP uptakefor UP (O(t >
200 ns) = 0.01) and for bipolar pulse (O(t >
200 ns) = 0.001). Thedecrease in YP uptake for a BP compared to the UP agrees with experimentalresults [3]. However, the uptake ratio (BP:UP) at t = 300 s is nearly twice aslarge in our model compared to the experimental values.6 BC Figure 4:
Occlusion recovery in a single cell model. (A)
The UP is an idealizedtrapezoidal pulse (24 kV/cm, 200 ns). An identical pulse of opposite polarity occurs after aninterpulse interval, t i . (B) Occlusion factor, O(t) is scaled linearly increasing from 10 − to10 − during a t i of 0 to 50 µ s. As a large number of pores (10 ) is created at the start ofthe pulse, occluding molecules enter some pores causing significant occlusion. But after thepulse, loosely bound molecules depart leading to larger O(t) for wider interpulse intervals. (C) Uptake of YP at t = 5 s and t = 300 s for different interpulse intervals, normalized to initialextracellular YP concentration. Uptake from having no interpulse interval is shown in theinset. The large X at 0 represents the level of normalized uptake from the UP, since for a UPno interpulse interval applies. The dotted line gives the maximum relative YP concentrationratio.
BPC is demonstrated by reduced uptake when a second pulse of oppositepolarity follows a first pulse. However, if the second pulse is applied after a delay,BPC is diminished [2]. We accordingly extend the mechanistic hypothesis ofmolecular pore occlusion to include a binding strength effect. Following the first7ulse, weakly interacting occluding molecules leave the pore with an assumedlinear time dependence over 50 µ s. However, if a second pulse of oppositepolarity is applied sooner (t i < µ s) after the first pulse (Fig. 4 (A)), it slowsoccluding molecules exiting the pore and thus extends time of occlusion (Fig. 4(B)), where YP uptake is shown at 5 s and 300 s after a BP in Fig. 4 (C). Uptakefrom a BP is smaller than UP (denoted by x) on black curve for short interpulseintervals demonstrating BPC. However, when the interpulse interval is longerthan 10 µ s, BPC is diminished, with uptake approaching the UP values. Therecovery of BPC effect is faster for fields of larger amplitude (Fig. SI-3).
4. Discussion
Different versions of standard cell EP models all focus on the lipidic por-tion of the plasma membrane [17, 19, 20, 21]. However, the standard EP modelcannot explain BPC in cells as it does not involve non-membrane molecules (con-taminants [27], extracellular molecules [28, 29, 30] or intracellular molecules).The revised EP model takes into account such molecules by considering ex-ternal sources of occluding molecules. The model could be partially tested bypurposefully adding occluding molecule candidates to the extracellular medium.
When an external electric field is applied to a cell, pore size distributionsevolve from a thermalized distribution around 0.85 nm to larger pore radii. But,the pulses of Fig. 2A and 2B exist only for 200 ns, not long enough to causesignificant pore expansion. Given the long pore lifetime ( τ p = 100 s), the poredistribution does not change significantly during the pulse.Further, rapid creation of nearly 10 pores causes several orders of magni-tude increase in membrane conductance. This sudden new electrical load (largemembrane conductance) holds down ∆ φ m ( t ) and leads to the creation of onlya small number of additional pores with subsequent pulses. Although the totalpore number, N(t), is large, most pores are less than 1.5 nm in radius. Thesesmall pores offer significant hindrance to the uptake of YP. Here we propose a mechanism for bipolar cancellation based on pore oc-clusion due to entry of external molecules into the membrane [28, 29, 27, 30].Occlusion can be caused by initial entrance into the pore or movement (re-location) of occluding molecules within an existing nanopore (conformationalchange). This is similar to protein-bound ion channel conformational changes.The magnitude of occlusion depends on the extent of interaction of the oc-cluding molecules with the pores and the tracer molecule. Occluding moleculesmay enter the pore partially, weakly bind to the membrane or fully inserted intothe membrane. Molecules that are weakly bound may leave the pore quickly. Ifa pulse of opposite polarity is applied before the occluding molecules leave thepore, they can be reinserted into the pore, further increasing occlusion.8e compared our model results with single pulse experimental results ofBPC [3] that show a decreased uptake with a BP (compared to a UP of sameamplitude) up to 300 s after the pulse (Fig. 3). The experimental 300 s time-scaleis consistent with our model’s τ p = 100 s. Our model suggests that occludingmolecules entering pores during a UP (24 kV/cm, 200 ns) can hinder transportby a factor of 100 compared to standard pore transport. In contrast, a BP ofequal amplitude (24 kV/cm, 200+200 ns) hinders transport by a further factorof 10 (overall factor of 1,000). Bipolar cancellation effects have been demonstrated experimentally as de-creased net uptake of calcium, propidium, and Yo-Pro-1 due to a bipolar pulsecompared to a unipolar pulse [1, 2, 3, 4, 5, 6, 7, 8]. Here we concentrate onYP because of comparable single pulse experimental results [3]. Modeling ofintracellular calcium, in contrast, is more complicated. The (assumed) negativecharge of most occluding molecules should affect the transit of doubly chargedcalcium (z s = +2) through nanopores because of partitioning. Also, the largensPEF pulses can cause supra-EP of not only the PM, but also the endoplasmicreticulum (ER) membranes [22], which may release calcium from internal stores,a potentially significant complication. BPC is the only EP application that attempts to move a tracer against itsconcentration gradient. For this reason alone, the standard model has been suc-cessful in accelerating a “downhill” tracer transport. According to the standardEP model, cellular uptake is largely determined by post-pulse pore distributionsbecause the post-pulse duration (100s of seconds) dominates behavior over theduration of the pulse (200 ns) [31]. For uptake to persist for 100s of seconds,pores must remain open for an order of 100 s. If pore life time is much longerthan the pulse duration, subsequent pulses (of same or opposite polarity) willnot create new pores as the membrane conductance can remain large, and holddown ∆ φ m [21]. In such cases, post-pulse diffusive uptake is nearly equal forboth UP and BP pulses. Even if a small difference exists, it will only cause agreater uptake for a bipolar pulse. The new, extended EP model that accountsfor occlusion is essential for describing bipolar cancellation. Acknowledgment
This work was partially supported by an AFOSR MURI grant FA9550-15-1-0517. We thank P. T. Vernier and E. B. S¨ozer for many discussions, E. C.Gianulis for waveform data and K. G. Weaver for continued computer support.9 eferences [1] B. L. Ibey, J. C. Ullery, O. N. Pakhomova, C. C., I. Semenov, H. T. Beier,M. Tarango, S. Xiao, K. H. Schoenbach, A. G. Pakhomov, Bipolar nanosec-ond electric pulses are less efficient at electropermeabilization and killingcells than monopolar pulses, Biochem. Biophys. Res. Commun. 443 (2014)568–573.[2] A. G. Pakhomov, I. Semenov, S. Xiao, O. N. Pakhomova, B. Gregory,K. H. Schoenbach, J. C. Ullery, H. T. Beier, S. R. Rajulapati, B. L. Ibey,Cancellation of cellular responses to nanoelectroporation by reversing thestimulus polarity, Cellular Molecular Life Sci. 22 (2014) 4431–4441.[3] E. C. Gianulis, J. Lee, C. Jiang, S. Xiao, B. L. Ibey, A. G. 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Occlusion and Molecular transport through poresOccluding molecules decrease tracer influx
Our aim is to estimate the diminished influx of tracer molecules that occurs dur-ing the second part of a bipolar pulse that causes bipolar cancellation (BPC).Accordingly, we modify a standard model of electroporation [20] by introducingan occlusion factor, O ( t ), that accounts for a decrease in pore-mediated trans-port of ions and tracer molecules. Consistent with notation in [20, 32, 18], weconsider a tracer as a solute, “s”, but recognize that the concepts of hindranceand partitioning are more general, applying also to tracers (e.g. YP) that movealong an interior pore surface or pore wall. The tracer flux through a pore, J s , p ,is related to the flux in bulk electrolyte, J s by J s , p = [ O ( t ) HK ] J s where H and K are the hindrance and partition factors of the nanopore withoutoccluding molecules [20]. The occlusion factor, O ( t ), represents the total tracerocclusion due to entry and relocation of external occlusion molecules. Theseexternal molecules reside for various times within pores, altering hindrance andpartitioning for tracers. In addition, with a time dependence, O ( t ) accounts forthe partial recovery of the membrane by the release of weakly bound occludingmolecules from within pores. Occlusion effect for tracers and for small ions
The small, highly mobile ions that dominate electrical behavior are Na + , Cl − and K + . Bipolar cancellation experiments emphasize tracer influx, not electri-cal behavior. We expect the effects on tracers such as YO − PRO − ++ (YP),propidium ++ (Pro), and Ca ++ to be larger than for the ubiquitous, small ionswith charge number ±
1. Put simply, these small ions are likely get through re-stricted (occluded) pathways more readily than the tracers with charge number+2. For YP and Pro tracers size also favors a larger occlusion effect.Altered occlusion represents alteration of both hindrance to molecular trans-port and also alteration of partitioning of different tracer molecules in the pore-occluding molecule complex. 13 igure SI-1:
Hindrance factor, H ( r s , r p ) , as a function of pore radius, r p , for YP which has a radius of 0.53 nm and a length of 1.71 nm. For pore radii less than 2 nm, YPmolecules experience a significant hindrance for transport through the pore. If the pore iseven partially obstructed by an external (non-membrane constituent) molecule, the hindranceextends to larger pores. A) Before pulse (B)
Peak 1 (C)
Peak 2 (D)
Peak 3 (E)
Peak 4 (F)
Peak 5 (G)
Before pulse (H)
Peak 1 (I)
Peak 2 (missing) (J)
Peak 3 (K)
Peak 4 (missing) (L)
Peak 5
Figure SI-2:
Pore histogram at the five peaks of the BP (bipolar pulse; top tworows) and the three peaks of the UP (unipolar pulse; bottom two rows).
Thehistograms show the number of pores as distributed by their radius (in nm). The panels (A)and (G) show the thermalized distribution of pores at t= 0. Pore histograms show evolutionof pore distribution from the resting potentialand the associated thermalized distribution forr p ≤ A)(B)
Figure SI-3:
Model uptake of YP as a function of duration between the two pulses of abipolar pulse at t = 5 s (left) and t = 300 s(right). The recovery of BPC effects is faster forlarger field strengths.as a function of duration between the two pulses of abipolar pulse at t = 5 s (left) and t = 300 s(right). The recovery of BPC effects is faster forlarger field strengths.