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Cellular apoptosis by nanosecond, high-intensity electric pulses: Model evaluation of
the pulsing threshold and extrinsic pathway
Jiahui Songa, Ravindra P. Joshia,b,⁎, Stephen J. Beebeb
aDepartment of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529-0246, United States
bF. Reidy Research Center for Bioelectrics, 830 Southampton Ave., Suite 5100, Norfolk, VA 23510, United States
a b s t r a c ta r t i c l ei n f o
Received 21 October 2009
Received in revised form 2 March 2010
Accepted 3 March 2010
Available online 29 March 2010
A simple, bistable rate-equation based model is used to predict trends of cellular apoptosis following electric
pulsing. The caspase-8 extrinsic pathway with inherent delays in its activation, cytochrome c release, and an
internal feedback mechanism between caspase-3 and cleavage of Bid are incorporated. Results obtained
were roughly in keeping with the experimental cell-survival data and include an electrical pulse-number
threshold followed by a near-exponential fall-off. The extrinsic caspase-8 mechanism is predicted to be more
sensitive than the mitochondrial intrinsic pathway for electric pulse induced cell apoptosis. Also, delays of
about an hour are predicted for detectable molecular concentration increases following electrical pulsing.
Finally, our results suggest that multi-needle electrode systems with adjustable field orientations would
likely enhance apoptosis in the context of pulsed voltage-induced inactivation of tumor cells.
© 2010 Elsevier B.V. All rights reserved.
Electric pulses with applications to biomedical engineering and
drug/gene delivery have been in use for several years [1–4]. More
recently, high-intensity, nanosecond, pulsed electric fields (nsPEFs)
have been shown to be useful non-thermal tools capable of producing
a variety of specific cellular responses [5,6]. These include cellular
electroporation [7–11], electrically-triggered intracellular calcium
release [12,13], temporary blockage of action potential propagation
in nerves [14,15], activation of platelets and release of growth factors
for accelerated wound healing , shrinkage of tumors  and
cellular apoptosis [13,18–20].
While reversible and temporary changes are often desired based
on electromanipulation (e.g., for drug or gene delivery), irreversible
effects or apoptotic cell killing can also be important objectives (e.g.,
targetted elimination of tumor cells). Cell killing is also important for
bacterial decontamination and microbial inactivation [21–24].
Though cell survival and dose-related killing have been studied in
the context of radiation [25,26], electric pulsed survival studies and
data are relatively scant. Reported data reveals a threshold effect in
cell killing by electric fields, with survival being the eventual outcome
if either the field intensities or number of pulses (or both) are not
sufficiently high [27,28]. One of the most complete cell viability
studies under nanosecond electric pulsing was reported by Pakhomov
et al. [27,29]. In one study, the viability of human lymphoma cells
(Jurkat and U937 cells) to multiple 10 ns pulses was studied using
Trypan Blue uptake as the indicator for cell death in over 200 samples.
Results obtained at various electric field intensities versus the pulse
number revealed an initial horizontal plateau, followed by a near-
exponential fall-off beyond a characteristic threshold. In the other
study on U937 cell survival  to repetitive 50 kV/cm and150 kV/cm
pulses of 10-ns duration at 2 and 1 Hz, respectively, a threshold was
again observed with almost no effect on cell killing until about 1000
pulses for the 50 kV/cm case.
Despite its potential applications, the biophysical details and
mechanisms of electrically triggering cellular apoptotic pathways are
not well understood. From a high-level, systems standpoint, cell death
can be viewed as being caused by the inactivation of one (or several)
critical enzymatic sub-systems or process pathways. Such inactivation
should be regarded as a stochastic event given the variability in
growth-cycles of exposed cells, their age, individual orientations and
locations relative to the pulsing electrodes, differences in sizes and
shapes, and other heterogeneities (e.g., concentrations and molecular
states) that can affect various reaction rate constants. Assuming that
the inactivation times are random variables, and that the cellular
system consists of several components of which the most severe
defect leads to biological failure; then the Weibull distribution
becomes an appropriate descriptor for cell survivability [30–32].
Survivability based on such a Weibull distribution yields a threshold
followed by either a concave, convex or an exponential fall-off based
on the characteristic Weibull parameters. However, such analytical
descriptions ignore the underlying physical details.
From a more biophysical standpoint, two pathways to apoptosis
are recognized. An “extrinsic pathway” which is instigated at the
Bioelectrochemistry 79 (2010) 179–186
⁎ Corresponding author. Department of Electrical and Computer Engineering, Old
Dominion University, Norfolk, VA 23529-0246, United States.
E-mail address: firstname.lastname@example.org (R.P. Joshi).
1567-5394/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/bioelechem
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cellular plasma membrane through death receptors; and the “intrinsic
pathway,” which responds to intracellular cues through mitochon-
drial-initiated processes. The former pathway can be triggered by
extracellular death signals linked with CD95 molecules and tumor
necrosis factor (TNF)-related apoptosis-inducing ligands. Apoptosis
(which is important in maintaining homeostatic balance [33–35]) can
be activated by deprivation of survival signals, genetic or toxicological
damage , or through external electrical pulsing. A common
observation in response to these stimuli is the activation of caspases,
a group of cysteine proteases that serve as the main initiators and
effectors of apoptosis. For example, death receptors, such as CD95,
enable the binding or clustering of molecules to form the death-
inducing signaling complex [37,38]. Trimerization of death receptors
upon cross-linking recruits procaspase-8. Subsequent proteolytic
activation through several cleavage steps (based on proximity
interactions) leads to caspase-8 (C8) activation. A series of biochem-
ical reactions are then set into motion leading to apoptosis.
The mitochondria-dependent activation (intrinsic pathway)
involves cytochrome c release from mitochondria induced by stress,
irradiation, or inflammation [39,40]. In the more recent electrical
pulsing context [28,41], it is postulated that the externally applied
electric field modulates the transmembrane mitochondrial potential.
This can directly open the mitochondrial permeability transition pore
[42,43], leading to cytochrome c release, with subsequent down-
stream apoptotic events. There is also a linkage between the electric
field-initiated events at the plasma membrane and the mitochondrial
processes. For example, caspase-8 has been shown to cleave the Bcl-2
family member Bid, causing release of cytochrome c . A
mathematical model of this cascade leading to the activation of
caspase-3 and the eventual DNA fragmentation and cell death was
recently discussed by Bagci et al. .
The role and extent of electric field modifications to the apoptotic
pathways is unclear. Hard experimental data is lacking, in part due to
the complexity of the biophysical mechanisms and the underlying
competition between various processes. However, possible conse-
quences of the applied field from a biophysical standpoint can be
conjectured. This should help drive and focus experimental studies on
specific hypothesis. Consequences of the applied voltage include the
stimulation of CD95 and recruitment of procaspase-8 through
enhanced dipole-interactions. Another possibility is that membrane
poration by the external field leads to molecular diffusion through the
pore bottleneck as observed with phosphatidylserine externalization
[17,46]. Such molecular transport towards local pores (in keeping
with the fluid mosaic model ), should increase the proximity
between molecules and enhance their interactions. So for instance,
denoting [C8⁎] as the concentration of activated caspase8, one can
roughly write the following rate equation due to the co-operative
action of “n” molecules of caspase8:
½?= dt = −kdC8*
½? + k U
ð Þ C8
½?nX ½ ?m;
where [C8] denotes inactive procaspase-8 concentration, while [X]m
represents concentration arising from “m” death receptor molecules.
In the above equation, k(U) is a production rate constant that depends
on the external signal U, i.e., the electrical pulse in the present case,
while kdis the destruction rate of the activated caspase-8. Unfortu-
nately, values for k(U), or its functional dependence on the electrical
signal U remain unknown. Apart from dipolar orientation, factors that
would shape k(U) include electrostatic-driven repulsion of antago-
nistic molecules such as c-FLIP that compete with procaspase-8 for
membrane binding. Furthermore, the apoptotic effect can be expected
to depend on the magnitude of the electric field at specific membrane
sites. Assuming that molecular clustering and dimerization is a
discrete, distributed event, the activation of C8⁎can be expected to
depend on the electric field orientation and its value at critical,
discrete sites. Thus, the response magnitude could vary, depending on
the electric field oreintation within cells. Another germane question is
the relative importance of the extrinsic process vis-a-vis the
mitochondrial pathway. Last but not least, is the threshold behavior
observed with regards to cell survival and its exponential decrease
with pulse number beyond the threshold.
Quantitative modeling of the overall electric field-induced cellular
apoptosis is an extremely difficult task. Details of the various bio-
mechanisms, their temporal dynamics and mutual interactions are
not known, and many of the parameters and rate constants have not
been measured. Given these difficulties, here we attempt to
qualitatively probe some of the above issues through simple model
simulations. The objectives of this study are: (1) to demonstrate that a
pulse-number threshold naturally emerges for cell killing by nano-
second, high-intensity pulses, (2) to assess whether the intrinsic or
the extrinsic pathway is more dominant following electric pulsing,
and (3) to examine the hypothesis that cell apoptosis might be
associated with discrete events initiated at specific sites.
Here, the pulse number-dependent cell-survival trends are
quantified based on a simple biophysical model of the apoptotic
processes. Time-dependent evolution of the caspase concentrations
and the various molecular species are simulated. The numerical
evaluations provide qualitative predictions of pulse number depen-
dence of cell survival, and rough predictions of the time duration for
irreversibility initiated by the electric pulses.
2. Modeling details
As already stated, quantitative modeling of electric field-induced
apoptosis is an arduous task. Additionally, the lack of parameters
characterizing the bio-components and the inherent cell-to-cell
variability, make precise predictions virtually impossible. Conse-
quently, we take a less-ambitious and fairly simplified systems-level
approach. Our current modeling objectives are limited to the
following: (a) ascertain whether a pulse-number threshold emerges
for cell killing by the nanosecond, high-intensity pulses. Such a result
would lend a qualitative biophysical explanation of the experimental
observations. (b) Gauge the relative importance of the extrinsic
mechanism relative to the intrinsic, mitochondrial pathway. This
become germane, given that the ultrashort (nanosecond) pulsing
might be expected to have a stronger effect on intracellular organelles
. (c) Lend qualitative support to the hypothesis that cell apoptosis
is due to discrete events initiated at specific sites. By extrapolation,
use of multi-prong electric pulsing systems would then be more
effective in cell killing (or in triggering cellular electro-biochemistry)
due to the variable field orientations and the possibility to affect
Time-dependent kinetics of the caspases and the various molec-
ular species within the apoptotic pathway, were simulated using the
rate-equation model proposed by Bagci et al. ; in part because of
the availability of published rate parameters. This model contains a
system of 31 coupled rate equations for the temporal evolution of the
various concentrations. The initial equilibrium concentrations were
determined by running the time-dependent rate-equation simulation
until steady state. This model includes the C3-Bid positive feedback
process, wherein increases in [C3] lead to enhanced cleavage of Bid,
which in turn feed into enhancing the [C3] concentrations through
release of cytochrome c and caspase-9 activation.
The role of the externally applied electric field in our model is
to trigger C8 release from specific sites within the plasma membrane.
On the assumption that C8 release occurs at discrete sites on the
plasma membrane, one can expect different cells to exhibit varying
degrees of C8 activation depending on their orientation with respect
to the external field. Our notion of discrete sites and specific death-
signaling domains ties in with emerging evidence that lipid micro-
environments on the cell surface, known as lipid rafts, may be
critically involved in the ultimate cell fate [48,49]. Death-inducing
J. Song et al. / Bioelectrochemistry 79 (2010) 179–186
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signaling receptor (DISC) molecules are known to be located at
membrane rafts and act as the linchpins from which apoptosis signals
are launched . From a modeling standpoint, assignment of
random caspase-8 release concentrations to each cell through a
stochastic, Monte Carlo type implementation, can take this discrete
nonuniformity into account. Hence, for our simulations, the caspase-
8 concentration released in each cell was assigned a value “r [Cmax],”
with “r” being a random number and [Cmax] a preset concentration
upperbound. Clearly, a large caspase-8 release can be expected to lead
to irreversible increases in caspase-3, and predictions of cell death. In
keeping with previous values , initial concentrations of all
compounds in our simulation were taken to be zero, except for
procaspase-3, procaspase-9, Apaf-1, Bid, Bax, Bcl-2, inhibitor of
apoptosis (IAP), and cytochrome c_mito, which were all set to 4.0 nM.
The activation and release of C8 by the voltage pulse takes time
since a sequence of processes such as the formation of the death-
inducing signaling complex (DISC) , clustering followed by
cleavage of C8 etc. are involved. Consequently, the physics-based
model needs to account for a finite time delay in the availability of
caspase-8 following the external pulsing. Furthermore, in response to
an electric field impulse, the concentration of C8 must gradually rise
as a function of time and eventually saturate. This aspect, not treated
by the Bagci model, was included based on a CD95 activation
proposed by Bentele et al. . As a result, these time-dependent
C8 concentrations following an excitation electrical pulse were used
as input to the rate-equation model for caspases.
3. Simulation results
3.1. Single cell results
Calculation results are first presented for a single cell based on the
above approach. Later we provide results using an ensemble of 1000
cell-entities for more meaningful and realistic predictions of cell
survival. Fig. 1a and b shows caspase-3 concentrations as a function of
time starting from two different assumed levels of C8. At the lower
0.01 nM caspase-8concentration, a decayin C3 over timeis predicted;
while increased values of C3 with time are seen in Fig. 1b for the
higher 0.1 nM caspase-8. These results are indicative of a bi-stability
in the apoptotic process and the requirement of a critical C8 level for
cell death induction. For the higher 0.1 nM caspase-8 value, appre-
ciable C3 activation is predicted to occur roughly in the 1–2 hour time
frame. This time scale turns out to be approximately in keeping with
our preliminary experimental data (not shown, but is becoming
available within our group) that gauges caspase activity and gathers
intracellular data. For example, a cell-permeable, fluorescent inhibitor
of caspases is being utilized to monitor caspase activity, while data on
the mitochondrial membrane potentials is measured using either JC-1
or tetramethylrhodamine ethyl ester (TMRE). In any event, the
simulationresult of Fig. 1 suggeststhat if moreC8 were to be activated
(e.g., either due to a highervoltagepulse or through multiple pulsing),
then the probable outcome for cell death in the overall population
would be enhanced.
To gauge the response of C8 over time to multiple pulsing and
evaluate possible cumulative effects, simulations were next carried
out with low, but repetitive, 0.4 pM caspase-8 injections. Simulation
results for the time-dependent [C3] concentration are shown in Fig. 2
in response to 1 and 10 pulses (at 1 Hz), respectively. The injections
were taken to begin after 10,000 s (∼2.7 h) from the initial time to
allow the system to reach an initial steady state. The 10-pulse case
points towards unstable cell behavior as reflected through the [C3]
increase, despite the low caspase-8 injection levels.
The above calculations were based on instantaneous caspase-
8 release following a voltage pulsing event for a cell. However, as
already mentioned, the caspase-8 concentration should be taken to
rise gradually in a time-dependent fashion. Using the Bentele model,
Fig. 1. Single cell simulation results for the caspase-3 concentration ([Casp3]/nM)
versus time in hours (t/h) for two different starting caspase-8 values. (a) Caspase-
8 value of 0.01 nM, and (b) initial caspase-8 value of 0.1 nM.
Fig. 2. Predicted logarithm of concentration C3 ([Casp3]/nM) versus time in hours (t/h)
following 1- and 10-injections at 1 Hz of 0.4 pM caspase-8 in a single cell. The injections
were taken to begin after 10,000 s.
J. Song et al. / Bioelectrochemistry 79 (2010) 179–186
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the normalized concentrations of caspase-8 and the blocked DISC
states obtained through numerical simulations are shown in Fig. 3. As
expected, both increase over time. However, a saturating trend is
obtained for the concentration [C8]. This is due to a regulatory
mechanism associated with the role of c-FLIP, which efficiently blocks
caspase-8 activation at the DISC. The characteristic time delay seen in
Fig. 3 is roughly 5 min. This is quite small compared to much longer
period spanning hours over which C3 activation and eventual cell
death occurs. This thus confirms that to a good approximation,
biochemical triggering by an electric pulse can be taken to be a very
3.2. Predictions of ensemble population dynamics
Having discussed some aspects of single cell response, ensemble
simulations were carried out next to include the statistical variability
inherent in actual experiments. Thousand cells were used, and the C8
injection in each cell was randomly varied between zero and a
maximum value (Cmax) by assigning random numbers. Predictions of
cell survival versus pulse number for low level C8 injection (with
[Cmax]=0.04 pM) are shown in Fig. 4. The injections, corresponding
to the pulse numbers, were set at a frequency of 1 Hz, in keeping with
the experimental data of Pakhomov et al. . Fig. 4 clearly shows a
threshold effect, and virtually all cells are predicted to survive until
about50 pulsesare incidentonthecells.Beyondthethreshold,a near-
exponential fall-off in survival is predicted, which again is in keeping
with the nanosecond electric pulsing experiments. However, at the
very large pulse numbers, a shift towards a somewhat saturating
trend can be seen in Fig. 4. Physically, this outcome arises from our
choice of a fixed set of random numbers for each C8 injection at the
1 Hz frequency. In other words, those cells assigned a relatively high
random number, were always associated with higher C8 activation,
leading to their more likely (and faster) outcomes of cell death. Those
with low random numbers continued to survive. This constant
random number assignment to the cells is a likely scenario under in
vivo conditions using electrical pulsing that is fixed in location and
One possibility for circumventing this effect and ensuring strong,
continued cell killing might be to use multi-pronged or multi-
electrode pulsing systems. Application of pulses via a multi-electrode
system would offer changes in the field magnitude and local
orientation, thereby ensuring greater activation from the pulsing
over the entire population. Alternatively, electrorotation of cells 
under in vitro conditions might be a simple and practical technique to
test out differences experimentally.
3.3. Comparisons between extrinsic and intrinsic pathways
In the above simulations, the extrinsic pathway was triggered by
allowing for caspase-8 activation. This extrinsic pathway accommo-
dates a role for mitochondria through the influence of truncated Bid
and the p53 protein. However, it is postulated that external fields can
directly modulate the mitochondrial transmembrane potential, affect
anion channels, open the mitochondrial permeability transition pore,
and lead to cytochrome c release . It therefore, becomes germane
to evaluate the role of such field-induced cytochrome c release and
gauge its relative importance with regards to the plasma membrane-
based caspase-8 process. Towards that end, simulation runs were
carried out to evaluate the pulse number dependence of cell survival
starting only with the intrinsic process.
Fig. 5 shows simulation results for two different values (0.4 nM
and 2 nM) of cytochrome c release. Since details of the cytochrome c
concentrations released due to mitochondrial transmembrane poten-
tial shifts are unknown, values were chosen on an ad hoc basis. The
goal was simply to facilitate a comparison with the C8 concentrations
for gauging the relative importance between the extrinsic and
intrinsic mechanisms in elevating cellular caspase-3 levels. In
addition, the effect of fixed-versus-random targeting of cells by the
Fig. 3. Single cell simulation results for the temporal evolution of the normalized
concentration (NC [nM/nM]) for caspase-8 and blocked DISC states versus time in
minutes (t/min). The normalization is with respect to the maximum value of 0.2 nM for
Fig. 4. Predicted logarithm of cell-survival ratio (Log f(s)) versus pulse number for 1000
cells. Survival ratio f(s)=N(s)/Ntotwith N(s) the number of surviving cells and Ntotthe
total cell number.
Fig. 5. Cell-survival fraction f(s) versus pulse number predicted for two different values
of cytochrome c release.
J. Song et al. / Bioelectrochemistry 79 (2010) 179–186
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electric pulsing was probed by varying the random number
assignment in the algorithm. Specifically, in two of the three cases,
fixed random numbers were used to assign the level of cytochrome c
release from each cell following a pulsing event. In the third case,
shown in Fig. 5, a variable random number assignment to cellular
cytochrome c release was used. All the plots of Fig. 5, in a general
sense, exhibit similar trends. A pulse-number threshold is followed by
an exponential fall-off that gradually reaches a saturating trend.
Comparing the two curves obtained using fixed random number
assignments, a lower threshold is associated with the higher 2 nM
cytochrome c release and the fall-off is faster. Between the fixed- and
variable random number cases, a smaller threshold is predicted with
fixed random numbers but the survival fall-off is slower. Physically,
this is to be expected since those cells that are randomly chosen to
have larger cytochrome c release undergo a higher and faster caspase-
3 elevation; while the others with low random number assignments
continue to survive. The important point arising from these simula-
tions though is that in comparison to caspase-8 activation, signifi-
cantly higher levels of cytochrome c release seem to be necessary for
cell killing. Thus, the extrinsic mechanism can be regarded as having a
more dominant role than the intrinsic pathway.
Additionally, since changes in transmembrane potential are harder
to attain in internal organelles due to their smaller size and relative
shielding by the plasma membrane, the role of the mitochondrial
process can be expected to be even less critical. This inference is
qualitatively in keeping with some of the experimental data emerging
from our experiments on cell with the nanosecond pulsing. For
example, in E4 squamous carcinoma cells treated in vitro with nsPEFs,
it hasbeen possible to observethe appearance of active caspasesusing
a fluorescent, cell-permeable inhibitor. This observation is typical at
relatively lower electric fields for which cells do not exhibit
cytochrome c release. However, at higher electric fields, active
caspases and cytochrome c appear together (Ren and Beebe,
manuscript in preparation). This suggests that under lower electric
field conditions, the activation ofcaspasesis observedin a cytochrome
c independent manner — typical of mediation through the extrinsic
More direct comparisons of the relative role of cytochrome c and
the timing under various conditions are shown in Fig. 6. This single
pulse simulation result for cellular caspase-3, used 20 nM cytochrome
c release and a C8 activation set at 4 pM. In the simulations, these
injections were taken to occur after 10,000 s after the initial time. A
number of interesting features are seen from the results of Fig. 6. As
before, the extrinsic pathway can be seen to have a stronger influence
on elevating C3 levels. In fact, the curve with C8 injection alone nearly
overlaps the plot obtained with both C8 and cytochrome c release
combined. The outcome with C8 is also much faster, with caspase-3
predicted to be elevated in less than 1 h following an electrical pulsing
event. Experimentally, caspase markers should detect such C3
The results of Fig. 6, though obtained on the basis of a model
containing 31 rate equations, can roughly be understood and
interpreted by utilizing a simple representation of the overall system.
Ultimately, the dynamics are controlled by the interplay between the
C8, C3 and IAP concentrations. The applied electric field augments the
caspase-8 release rate, which then leads to C3 generation, while IAP
inhibits caspase3 production. Thus crudely, these concentrations can
be expressed as:
½?=dt = −R3C3
½? + FAC8
½?=dt = −R8C8
½? + FAC3
ðÞ + FAU
½?= dt = −RIAPIAP
½? + FIIAP
ðÞ + FAU
In the above, R3, R8, and RIAP represent degradation rates for
caspase3, caspase8, and IAP, respectively, FA(x) denotes an activation
function controlled by the variable x, while FI(x) is an inhibitory
function of the x-variable. These activation and inhibitory functions
are invoked to better represent the influences of the various variables.
IgnoringtheroleofIAP toa firstapproximation, andassumingthatthe
strong electric field enhances the [C8] magnitude relatively quickly,
the following equation for the slower C3 dynamics is obtained:
½? + F*
Furthermore, assuming that the field-induced activation function
roughly acts as a fast switch turning quickly to some limiting value KA,
yields the following solution for C3(t):
C3 t ð Þ½? = C3 0
ð Þ½?exp −R3t
ðÞ + KA= R3
ðÞ 1−exp −R3t
where [C3(0)] is the initial cellular caspase3 concentration. Thus,
under conditions of a fast, “switch-like” turn-on of caspase-8, the
rapid increase in caspase-3 versus time can be explained. This
predicted exponential rise in caspase-3, followed with a saturating
value, is qualitatively similar to the numerical plot of Fig. 6. Physically,
since it takes a finite time for field-activated switching, and there are
also other processes between active C8 production and caspase3
activation, a temporal delay is quite expected. Comparing Eq. (6) with
Fig. 6 yields a rate constant R3of about 1.04/h and a KAvalue of
roughly 0.8 nM/h.
The simulation result of Fig. 6 is in keeping with experimental
results with HL-60 cells that were exposed to five 10 ns pulses at
150 kV/cm, and 60 ns pulses at 60 kV/cm and analyzed 25 or 40 min
post-pulse as shown in Fig. 7. The time duration and corresponding
electric fields were chosen to ensure roughly equal energy input for
both the 10 ns and 60 ns pulses. A time-dependent increase in the
appearance of active caspases could be seen for both the 10 ns and
60 ns cases. However, with the shorter 10 ns pulses, the activation
time line was slower. In data not shown, cytochrome c was released
from HL-60 cells. However, because of the constraints of the
experimental designs, we have not yet been able to determine in
HL-60, which comes first: caspase activation or cytochrome c release,
and continued efforts are underway. Finally, in data not shown for E4
squamous cell carcinoma, the appearance of active caspases was seen
between 20 and 60 min, which is again in keeping with the simulation
predictions of the present report.
Fig. 6. Caspase 3 ([Casp3]/nM) versus time in hours (t/h) from single cell simulations
under various conditions of caspase-8 activation and cytochrome c release.
J. Song et al. / Bioelectrochemistry 79 (2010) 179–186
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In the above, an attempt has been made to probe and quantify the
experimentally observed pulse number-dependent cell-survival
trends on the basis of a biophysical model of apoptotic processes.
Additionally, a relative assessment between extrinsic and intrinsic
pathways, and rough predictions of the time duration over which
irreversible activation at the molecular level might be initiated, has
been carried out. A feature of this rate-equation modeling is the
predicted delay of about an hour in the time taken for molecular
concentration increases following electrical pulsing. This delayed
biochemical process in response is similar to a recent report on
cellular dye update upon electric pulsing . The experiments by
Kennedy et al.  identified two distinctive electroporative uptake
signatures: an initial almost negligible dye absorption immediately
after the pulse exposure, followed by a high-level, accelerating uptake
at much longer times. This result is generally in line with earlier
reports (for example, Neumann et al. ) indicating multi-stage
evolution following electrical pulsing.
It must be re-emphasized that the biophysics of the overall process
is quite complex and many issues remain unanswered. For example,
the electric pulsing can be expected to trigger and influence a wide
number of processes, not limited simply to caspase-8 activation,
regulation of the mitochondrial transmembrane potential, or electro-
poration. These would include, for example, induced electron
transfers between molecules leading to possible dissociation or
conformational changes, facilitation of oxidation-reduction (redox)
reactionsand influence ontheir rate kinetics,alterations of membrane
pumps , or calcium release from the endoplasmic reticulum .
Hence, the primary electrical event could lead to several downstream
biochemical modifications, initiation of inter-dependent pathways,
and interplay between multiple secondary processes.
A number of aspects were ignored in our simple treatment. For
example, it was assumed in the simulations that a chosen amount of
cytochrome c release would result from each electrical pulsing. This
assumes that the cytochrome c outflow is roughly similar to field-
induced intracellular calcium release , and that its concentration
within the mitochondria is large enough to discount depletion effects.
Similarly, it was assumed that in the multiple-pulsing scenario, the
continued presence of strong external fields would not alter the rates
and that the reaction kinetics would continue to follow the
parameters of the Bagci model. In theory, other effects, such as
nanoporation, can also be expected to change the dynamics of the
apoptotic pathway. For example, upon pore creation, the lipid
molecules which are in a state of constant flux could begin to diffuse
through an effective “membrane sink-hole.” It is very likely then that
diffusion and transport of the lipid molecules in the localized vicinity
of electropores would tend to increase molecular proximity, and
enhance inter-molecular interactions. Consequently, the dimerization
and clustering processes that initiate procaspase-8 cleavage could
augment the extrinsic pathway. The role of reactive oxygen species
(ROS) generation by the electric pulsing has also been ignored in the
present treatment. Reports in the literature  suggest that
application of electric fields could elevate ROS. This, in turn, would
alter apoptotic destruction through the ROS-mediated pathways
involving oxidative stress [61,62]. For example, ROS is known to
induce dissociation of cytochrome c from cardiolipin on the inner
mitochondrial membrane, and facilitate its release via mitochondrial
permeability transition-dependent mechanisms. Last but not least,
our numerical implementation of the simple multiple-pulsing
scenario assumed a fixed amount of caspase-8 activation repeatedly
in response to the external pulsing. However, quite conceivably, there
could be a depletion effect and the CD95 initiated process might not
produce as much C8 after multiple pulses. However, the activation
could physically arise from different discrete sites within the plasma
membrane. A multitude of such sites would alleviate the depletion
issue and provide an electrically-induced effect after each electrical
pulse. This hypothesis of multi-targets and sites would be in keeping
delivery through multi-electrode systems . Such multi-electrode
systems would provide sufficiently high electric fields at different
locations and orientations within cells for greater bio-effects.
5. Summary and conclusions
In summary, a simple model-based rate-equation treatment of the
various cellular biochemical processes was used to qualitatively
predict the pulse number-dependent caspase activation and cell-
survival trends. The model incorporated the caspase-8 associated
extrinsic pathway, the delay inherent in its activation, cytochrome c
release, and the internal feedback mechanism between caspase-3 and
Bid. Time-dependent evolution of the caspase concentrations and the
various molecular species (including caspase-3, Bid, t-Bid, cyto-
chrome c , caspase 9, and apoptosome formation) were simulated.
Results obtained were roughly in keeping with the experimental
cell-survival data. In particular, a pulse-number threshold was
predicted followed by a near-exponential fall-off. The analysis is
more insightful and based on biophysics instead of the statistical
treatments that invoke survival distributions. Also, the intrinsic
pathway was shown to be much weaker as compared to the extrinsic
mechanism for electric pulse induced cell apoptosis. In addition,
delays of about an hour are predicted for detectable molecular
concentration increases following electrical pulsing. Furthermore,
since cell killing depends on the amounts of caspase-8 activation and
cytochrome c released, differing survival thresholds are to be
expected between different cell types. For instance, our previous
experimental reportson electric pulsing of cells showed a relative lack
of PS externalization in B16 cells, whereas Jurkat cells showed strong
PS effects . This underscores inherent differences in cell
parameters and their responses to external stimuli. Our PS observa-
tion postulated various factors such as a more stable plasma
membrane and higher energies required for electroporation and
molecular transport. Quite conceivably then, one can expect B16 cells
to have a lower degree of caspase-8 activation and hence, cell death.
This has been confirmed in our experiments, and Jurkats shown to be
more susceptible to electric pulse killing. It must be mentioned that
the predictedvariability associatedwithrandom number assignments
suggests that multi-electrode systems with adjustable field orienta-
tions would likely enhance cell apoptosis. Finally, the relative success
in predicting the pulse number-dependent trends and the thresholds
based on random number assignments to various cells, lends support
to the notion of discrete death-signaling sites on the cell membranes.
This is in keeping with recent reports in connection with cancer
Fig. 7. The appearance FITC-VAD-fmk fluorescence (F) as an active caspase marker with
two different pulse durations of 10 ns and 60 ns, measured at 25 and 40 min post-pulse
for HL-60 cells. Data for cell number (Nc) versus Log (F/a.u.).
J. Song et al. / Bioelectrochemistry 79 (2010) 179–186
Author's personal copy
therapy, that apoptosis-inducing ligand receptors are located at
discrete membrane sites .
The authors thank the Office of Naval Research for partial support.
Useful conversations with A. Pakhomov and R. Heller (Old Dominion
University) are acknowledged. One of us (RPJ) also thanks I. Bahar
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