Effects of Shock Strength

The pore number and distribution depend on the shock strength V0 applied to the membrane, and the model is used to explore this dependence. Figure 12 illustrates the effect of

(a) Number of pores

(b) Number of large pores

(c) Average radius

(a) Number of pores

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4

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(c) Average radius

(d) Area of pores

(e) Conductivity

(f) Pore creation

LL 4

(d) Area of pores

LL 4

stimulus strength (V)

stimulus strength (V)

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2 4 6 stimulus strength (V)

stimulus strength (V)

2 4 6 stimulus strength (V)

Figure 12: Dependence of electroporation on shock strength. (a) Number of all pores (K) and number of small (Ksm) and large (Kig) pores. The lines corresponding to K and Ksm overlap. (b) Number of large pores (Klg) shown on an expanded vertical scale. (c) Average radius (f) of the large pore population. The vertical bars indicate standard deviation. The range of the shock strengths was truncated to 4.125 V because there are no large pores for stronger shocks. (d) Total area of pores reported as a fraction of the membrane surface area for all (F), small (Fsm), and large (Flg) pores. (e) Conductivity of the membrane for all (G), small (Gsm), and large (Glg) pores. (f) Beginning (tbeg) and end (tend) of the pore creation phase. Note the logarithmic scale of the vertical axis. All results except those in (f ) were collected at the end of a 1-ms shock. The legend in (a) applies also to (b), (d), and (e). The dotted vertical lines indicate the shock of 3 V, that is, the default shock strength used previously in this chapter

shock strength on the number of pores, their average radius, the area of pores, membrane conductivity, and the timing of the pore creation phase. The shock V0 ranges from 0.975 V (below the apparent threshold) to 7.5 V, and all data except Fig. 12f were collected at the end of a 1-ms shock.

As expected, the number of pores increases with the shock strength but, except for very weak shocks, this increase is due to the creation of small pores. In Fig. 12a, curves representing all pores and small pores overlap and large pores appear to be a negligible fraction of all pores. As seen on the expanded vertical axis in Fig. 12b, the number of large pores initially increases, but above 4 V, large pores disappear altogether and only small pores are being created. This prediction was confirmed by experiments in which high-voltage, short pulses were shown to create a large number of pores with radii not substantially larger than 1 nm.31,67,68 Additional confirmation came from the studies that observed decrease in the uptake of macromolecules (i.e., DNA) for strong pulses.64,69

The average radius of large pores decreases as the number of large pores grows but increases again once fewer large pores are created (Fig. 12c). Despite their relatively small number, large pores contribute significantly to the fractional pore area (Fig. 12d) and to the increase in membrane conductivity (Fig. 12e) for shocks below 4 V. As the shock strength increases, the contribution of small pores increases, and above 4 V, all pore area and all membrane conductance are due to small pores. Figure 12f shows that the pore creation phase begins earlier, and its duration is shorter for stronger shocks (note that the vertical axis is logarithmic).

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