Biophysics-based critique of the assisted discharge mechanism hypothesis
Julie V. Stern, Thiruvallur R. Gowrishankar, Kyle C. Smith, James C. Weaver
BBiophysics-based critique ofthe assisted discharge mechanism hypothesis
Julie V. Stern , Thiruvallur R. Gowrishankar , Kyle C. Smith , and James C. Weaver , ∗ , Harvard-MIT Division of Health Sciences and Technology, Institute for Medical Engineering and Science,Massachusetts Institute of Technology, Cambridge, MA, USA; ∗ Corresponding author
Cell experiments with large, short electric field pulses of opposite polarity reveal a remarkable phe-nomenon: Bipolar cancellation (BPC). Typical defining experiments involve quantitative observation oftracer molecule influx at times of order 100 s post pulsing. Gowrishankar et al. BBRC 2018 503:1194-1199shows that long-lived pores and altered partitioning or hindrance due to inserted occluding moleculescan account for BPC. In stark contrast, the Assisted Discharge (AD) hypothesis, Pakhomov et al. CellMol-LifeSci 2014 71(22):4431-4441; Fig. 6, only involves early times of a microsecond down to nanoseconds.Further, well established terminology for cell membrane discharge relates to membrane potential decaysshortly after pulsing. Discharge is silent on molecular or ionic transport, and does not address the factthat tracer molecule uptake vs time is measure at about 100s after pulsing ceases. Our critique of ADnotes that there can be an association of AD with BPC, but associations are only necessary, not sufficient.A BPC mechanism hypothesis must be shown to be causal, able to describe time-dependent molecularinflux. The two hypotheses involve very different time-scales (less than a microsecond vs 100 s) andvery different quantities (volts/s vs molecules/s). Unlike pore-based hypotheses the AD hypothesis lacksexplicit molecular transport mechanisms, and does not address the greatly delayed measured molecularuptake. We conclude that AD is an implausible candidate for explaining BPC.Basic approach:
Use general features of established science for plausibility estimates. This biophysics/physicsmethod has often been used to obtain rough estimates of the plausibility of reported results, new concepts,theoretical constructs, etc. Testing is widely used, and can be extended to biophysics, including bioelectrics. Inthe present (biophysics of bioelectrics) order of magnitude (OOM) estimates can be compelling.
Four examples of order of magnitude estimates of plausibility using generally accepted science.
Theseare:(1) Implausibility of small 50-60 Hz fields causing cancer [1],(2) Plausibility of animal sensing of very small electric fields [2],(3) Plausibility of biological detection of small chemical reaction rates [3], and(4) Plausibility of nsPEF causing ∼
100 to 1000-fold more pores than conventional electroporation [4].Here we argue that AD (Assisted Discharge) is an implausible mechanism of bipolar cancellation (BPC). Ourcritique does not presently apply to excitable cells, as it considers only what is generally known about electro-poration (EP), or nanopores, in non-excitable cells. We consider generally accepted science found in the EP
Page 1 a r X i v : . [ phy s i c s . b i o - ph ] A p r igure 1: “Bipolar pulses may assist cell membrane discharge and reduce the membrane time above the criticalvoltage. Cell membrane is charged ( bottom ) by a monopolar pulse ( a , top ) or a bipolar pulse ( b , top ). The mem-brane voltage (arbitrary units) goes from the baseline ( solid line ) to the critical electroporation voltage ( dashedline ) and above it. The time when the membrane voltage exceeds the critical level is shown by shading . The bipo-lar pulse reduces this time but does not bring the voltage below the negative critical value. See text for details.”This figure is Figure 6 from [5].literature. We purposefully do not include experiments carried out by MURI investigators, before and during theMURI funding. The rationale is simple and basic: We want to understand what can be expected given estab-lished science, mainly publications in the biophysics literature before BPC was considered. Accepted sciencedoes not change just because someone wants to assume that BPC observed at ∼
100 s is part of AD. ”Assisteddischarge” means discharge is faster (assisted) because of very large nsPEF fields that make so many pores thatthe membrane conductance is greatly increased. And that increased conductance is the cause of the more rapid(assisted) discharge through the heavily porated regions of the cell membrane. It has nothing to do with tracermolecule data and observations that occur much later, viz. at ∼
100 s. Here the established scientific facts are:(1) What is generally known about passive and porated cell membrane charging and discharging [6, 7, 8]. SeeFig. 2, with both passive (150 mV/cm) and heavily porated (24 kV/cm) examples.(2) What is known broadly about nanoporation due to nsPEF. Here a number of quantitative models that arebroadly consistent with experiments are considered [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. The gen-eral, established fact is that many small pores (nanopores) are created, which creates large membraneconductances.
Basic background and key definitions for BPC.
A defining feature of BPC is experimentally measured de-crease in the ratio of tracer molecule influx into a cell for a bipolar pulse (BP) compared to a unipolar pulse (UP).Electric field pulses are followed by cell membrane electrical discharge within a few microseconds or less. Insharp contrast, tracer influx occurs over a long time (1 - 100 s) after the pulses. This is not trivial: after theproposed important discharge, the measured effect is seen 6-8 orders of magnitude displaced in time. Thismeans the electrically initiated molecule (tracer) transport is an exasperatingly slow process. What can accountfor this?! How can an early electrical event (discharge) lead to a greatly delayed tracer influx that defines BPC?This essential basic feature is missing. Further, for both UP and BP 24 kV/cm there is immediate poration. Anon-porated (passive) membrane is not involved, inconsistent with Fig. 6 of Pakhomov et al. 2014 [5].
Page 2 igure 2: Response of small and large amplitude electric fields.
These results show that assisted dischargeonly occurs for a passive membrane with negligible conductance change (zero electroporation; low strengthelectric field small channel conductance). The 150 mV/cm, 200 ns unipolar pulse (top left) creates 26 pores incontrast to a 24 kV/cm, 200 ns unipolar pulse (bottom left) that creates . × pores in a 5 µ m radius cell.As in Fig. 6 of Pakhomov 2014 [5], the bipolar case has a much faster discharge after the first half of the BPpulse. However, this occurs only for small electric fields that cause negligible electroporation. But to elicit BPClarge fields ( >
10 kV/cm) are used, it is a contradiction. Response of two unipolar pulses (with no gap) for the 150mV/cm and 24 kV/cm fields are shown in the right column. In all cases pores are created early (rapidly) on thefirst pulse and the large conduction is “remembered”.For perspective, passive (normal) discharge time constant of a cell is about 100 ns to 1 µ s for typical mammaliancells [6, 7, 8]. Electroporated cells have spatially distributed pores of various lifetimes, so the effective, localconductivity varies spatially and temporally, a complication that is readily addressed by using integrated cellsystem models [9, 10, 11, 12, 13, 14, 15, 16, 18, 19].For the nsPEF (nanosecond pulsed electric fields) needed to elicit BPC there is an additional feature: As shownby the Schoenbach-MURI (ODU) [4] a broad finding is that nsPEF with field strengths of order 10-100 kV/cmand sufficiently short pulses (of order 2-1,000 ns) approximately 100-1,000 more pores are created, not limitedto the outer, plasma membrane (PM), but pores are also created in many organelles within the cell, includingbacterial-size mitochondria with double membranes. This means that the discharge times are much more rapid.All of the above is a condensed version of what is now established nsPEF biophysics.To our knowledge the Assisted Discharge (AD) mechanism hypothesis for bipolar cancellation (BPC) was intro-duced by Pakhomov and co-workers, see their Fig. 6 and associated text, included here as Fig. 1, but it has Page 3 o equations [5]. Subsequent publications cite the AD hypothesis. We find six significant flaws, identified anddefined below.Flaw
Figure 3: Passive and Standard EP model response of an isolated cell model in response to a 10 kV/cm, 5ns rise/fall time, 60 ns unipolar pulse (left) and a 60 ns + 60 ns 10/-10 kV/cm bipolar pulse (right). The passivemodel response is shown in solid line and the EP model response is shown by the dashed curve. The passivemodel response for a unipolar pulse shows the transmembrane at the pole increasing to over 4 V (for illustrationonly) and discharging with a time constant of around 100 ns. However, when EP is included, the response showsa reversible electrical breakdown (REB): a rapid increase in transmembrane voltage followed by a decreaseto a plateau which rapidly reaches zero after the pulse ends ( < ∆ φ m (membrane potential or transmem-brane voltage). The horizontal dashed line(s) in Fig. 6 in [5] are detection or measurement thresholds that dependon both pore creation rates at different cell membrane locations, and also on experimental measurement capa-bilities. There is nothing “critical” about these events. Instead they are measurement thresholds for either actualor Gedanken experiments, governed by signal-to-noise ratio (S/N). Continuum theories and molecular dynamics Page 4 imulations are consistent regarding the conditions needed to observe effects due to significant poration for par-ticular experimental conditions (cell geometry and size, pulse waveform, etc.). Detection (measurement) theoryis well known in physics (and therefore biophysics involving bioelectrics) [1, 3, 21, 22, 23].Flaw e.g. nsPEF). But influx of tracer molecules occurs long afterwards, with tracer influxtime scales of 1 to 100 seconds. The AD mechanism offers no explanation for this huge discrepancy.Flaw pores, avery large number. These pores cause a much faster membrane discharge ( ∼
10 ns) after the pulse.In general, the literature contains lots of results for pore behavior after pore creation. This undercuts the idea thatone should avoid treating what happens above the critical membrane potential, which is the implication of the ADmechanism hypothesis.
Acknowledgments
Supported partially by AFOSR MURI grant FA9550-15-1-0517.
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