Calcium bursts induced by nanosecond electric pulses

We report here real-time imaging of calcium bursts in human lymphocytes exposed to nanosecond, megavolt-per-meter pulsed electric fields. Ultra-short (less than 30 ns), high-field (greater than 1 MV/m), electric pulses induce increases in cytosolic calcium concentration and translocation of phosphatidylserine (PS) to the outer layer of the plasma membrane in Jurkat T lymphoblasts. Pulse-induced calcium bursts occur within milliseconds and PS externalization within minutes. Caspase activation and other indicators of apoptosis follow these initial symptoms of nanosecond pulse exposure. Pulse-induced PS translocation is observed even in the presence of caspase inhibitors. Ultra-short, high-field, electroperturbative pulse effects differ substantially from those associated with electroporation, where pulses of a few tens of kilovolts-per-meter lasting a few tens of microseconds open pores in the cytoplasmic membrane. Nanosecond pulsed electric fields, because their duration is less than the plasma membrane charging time, develop voltages across intracellular structures without porating the cell.     

Nanoelectropulse-induced phosphatidylserine translocation

Nanosecond, megavolt-per-meter, pulsed electric fields induce phosphatidylserine (PS) externalization, intracellular calcium redistribution, and apoptosis in Jurkat T-lymphoblasts, without causing immediately apparent physical damage to the cells. Intracellular calcium mobilization occurs within milliseconds of pulse exposure, and membrane phospholipid translocation is observed within minutes. Pulsed cells maintain cytoplasmic membrane integrity, blocking propidium iodide and Trypan blue. Indicators of apoptosis-caspase activation and loss of mitochondrial membrane potential-appear in nanoelectropulsed cells at later times. Although a theoretical framework has been established, specific mechanisms through which external nanosecond pulsed electric fields trigger intracellular responses in actively growing cells have not yet been experimentally characterized. This report focuses on the membrane phospholipid rearrangement that appears after ultrashort pulse exposure. We present evidence that the minimum field strength required for PS externalization in actively metabolizing Jurkat cells with 7-ns pulses produces transmembrane potentials associated with increased membrane conductance when pulse widths are microseconds rather than nanoseconds. We also show that nanoelectropulse trains delivered at repetition rates from 2 to 2000 Hz have similar effects, that nanoelectropulse-induced PS externalization does not require calcium in the external medium, and that the pulse regimens used in these experiments do not cause significant intra- or extracellular Joule heating.     

Thresholds for Phosphatidylserine Externalization in Chinese Hamster Ovarian Cells following Exposure to Nanosecond Pulsed Electrical Fields (nsPEF)

High-amplitude, MV/m, nanosecond pulsed electric fields (nsPEF) have been hypothesized to cause nanoporation of the plasma membrane. Phosphatidylserine (PS) externalization has been observed on the outer leaflet of the membrane shortly after nsPEF exposure, suggesting local structural changes in the membrane. In this study, we utilized fluorescently-tagged Annexin V to observe the externalization of PS on the plasma membrane of isolated Chinese Hamster Ovary (CHO) cells following exposure to nsPEF. A series of experiments were performed to determine the dosimetric trends of PS expression caused by nsPEF as a function of pulse duration, τ, delivered field strength, E_D, and pulse number, n. To accurately estimate dose thresholds for cellular response, data were reduced to a set of binary responses and ED50s were estimated using Probit analysis. Probit analysis results revealed that PS externalization followed the non-linear trend of (τ*E_D ²)⁻¹ for high amplitudes, but failed to predict low amplitude responses. A second set of experiments was performed to determine the nsPEF parameters necessary to cause observable calcium uptake, using cells preloaded with calcium green (CaGr), and membrane permeability, using FM1-43 dye. Calcium influx and FM1-43 uptake were found to always be observed at lower nsPEF exposure parameters compared to PS externalization. These findings suggest that multiple, higher amplitude and longer pulse exposures may generate pores of larger diameter enabling lateral diffusion of PS; whereas, smaller pores induced by fewer, lower amplitude and short pulse width exposures may only allow extracellular calcium and FM1-43 uptake.     

Nanoelectropulse-driven membrane perturbation and small molecule permeabilization

Background  

Nanosecond, megavolt-per-meter pulsed electric fields scramble membrane phospholipids, release intracellular calcium, and induce apoptosis. Flow cytometric and fluorescence microscopy evidence has associated phospholipid rearrangement directly with nanoelectropulse exposure and supports the hypothesis that the potential that develops across the lipid bilayer during an electric pulse drives phosphatidylserine (PS) externalization.     

Molecular Dynamics Simulations of Lipid Membrane Electroporation

The permeability of cell membranes can be transiently increased following the application of external electric fields. Theoretical approaches such as molecular modeling provide a significant insight into the processes affecting, at the molecular level, the integrity of lipid cell membranes when these are subject to voltage gradients under similar conditions as those used in experiments. This article reports on the progress made so far using such simulations to model membrane—lipid bilayer—electroporation. We first describe the methods devised to perform in silico experiments of membranes subject to nanosecond, megavolt-per-meter pulsed electric fields and of membranes subject to charge imbalance, mimicking therefore the application of low-voltage, long-duration pulses. We show then that, at the molecular level, the two types of pulses produce similar effects: provided the TM voltage these pulses create are higher than a certain threshold, hydrophilic pores stabilized by the membrane lipid headgroups form within the nanosecond time scale across the lipid core. Similarly, when the pulses are switched off, the pores collapse (close) within similar time scales. It is shown that for similar TM voltages applied, both methods induce similar electric field distributions within the membrane core. The cascade of events following the application of the pulses, and taking place at the membrane, is a direct consequence of such an electric field distribution.     

Transient Features in Nanosecond Pulsed Electric Fields Differentially Modulate Mitochondria and Viability

It is hypothesized that high frequency components of nanosecond pulsed electric fields (nsPEFs), determined by transient pulse features, are important for maximizing electric field interactions with intracellular structures. For monopolar square wave pulses, these transient features are determined by the rapid rise and fall of the pulsed electric fields. To determine effects on mitochondria membranes and plasma membranes, N1-S1 hepatocellular carcinoma cells were exposed to single 600 ns pulses with varying electric fields (0–80 kV/cm) and short (15 ns) or long (150 ns) rise and fall times. Plasma membrane effects were evaluated using Fluo-4 to determine calcium influx, the only measurable source of increases in intracellular calcium. Mitochondria membrane effects were evaluated using tetramethylrhodamine ethyl ester (TMRE) to determine mitochondria membrane potentials (ΔΨm). Single pulses with short rise and fall times caused electric field-dependent increases in calcium influx, dissipation of ΔΨm and cell death. Pulses with long rise and fall times exhibited electric field-dependent increases in calcium influx, but diminished effects on dissipation of ΔΨm and viability. Results indicate that high frequency components have significant differential impact on mitochondria membranes, which determines cell death, but lesser variances on plasma membranes, which allows calcium influxes, a primary determinant for dissipation of ΔΨm and cell death.     

Leukemic cell intracellular responses to nanosecond electric fields

Intense, nanosecond (ns) pulsed electric fields (PEFs) are known to affect the intracellular structures of cells. The probability of preferentially inducing subcellular effects increases with decreasing pulse length while effects on the plasma membrane are diminished. This has been demonstrated by applying electrical pulses of 60 and 10 ns duration with electric field intensities of up to 6.5 MV/m to HL-60 cells. Using confocal microscopy, PEF-induced changes in the integrity of the plasma membrane and nucleus were measured by recording fluorescence changes with propidium iodide (PI) and acridine orange (AO), respectively. Results suggest that high voltage, nsPEFs target the nucleus and modify cellular functions while plasma membrane effects are delayed and become smaller as pulse duration is shortened. Cell viability was not affected by these pulses. In spite of the high pulsed electric fields, thermal effects can be neglected because of the ultrashort pulse duration. The results suggest application of this ultrashort pulse technology to modulate nuclear structure and function for potential therapeutic benefit.     

DNA electrophoretic migration patterns change after exposure of Jurkat cells to a single intense nanosecond electric pulse

Intense nanosecond pulsed electric fields (nsPEFs) interact with cellular membranes and intracellular structures. Investigating how cells respond to nanosecond pulses is essential for a) development of biomedical applications of nsPEFs, including cancer therapy, and b) better understanding of the mechanisms underlying such bioelectrical effects. In this work, we explored relatively mild exposure conditions to provide insight into weak, reversible effects, laying a foundation for a better understanding of the interaction mechanisms and kinetics underlying nsPEF bio-effects. In particular, we report changes in the nucleus of Jurkat cells (human lymphoblastoid T cells) exposed to single pulses of 60 ns duration and 1.0, 1.5 and 2.5 MV/m amplitudes, which do not affect cell growth and viability. A dose-dependent reduction in alkaline comet-assayed DNA migration is observed immediately after nsPEF exposure, accompanied by permeabilization of the plasma membrane (YO-PRO-1 uptake). Comet assay profiles return to normal within 60 minutes after pulse delivery at the highest pulse amplitude tested, indicating that our exposure protocol affects the nucleus, modifying DNA electrophoretic migration patterns.     

Microdosimetry for conventional and supra-electroporation in cells with organelles

Conventional electroporation (EP) by 0.1 to 1 kV/cm pulses longer than 100 micros, and supra-electroporation by 10 to 300 kV/cm pulses shorter than 1 micros cause different cellular effects. Conventional EP delivers DNA, proteins, small drugs, and fluorescent indicators across the plasma membrane (PM) and causes moderate levels of phosphatidylserine (PS) translocation at the PM. We hypothesize that supra-EP is central to intracellular effects such as apoptosis induction and higher levels of PS translocation. Our cell system model has 20,000 interconnected local models for small areas of the PM and organelle membranes, small regions of aqueous media, appropriate resting potentials, and the asymptotic EP model. Conventional EP primarily affects the PM, but with a hint of endoplasmic reticulum involvement. Supra-EP can involve all of a cell's membrane at the largest fields. Conventional EP fields tend to go around cells, but supra-EP fields go through cells, extensively penetrating organelles.     

Transmembrane molecular transport during versus after extremely large, nanosecond electric pulses

Recently there has been intense and growing interest in the non-thermal biological effects of nanosecond electric pulses, particularly apoptosis induction. These effects have been hypothesized to result from the widespread creation of small, lipidic pores in the plasma and organelle membranes of cells (supra-electroporation) and, more specifically, ionic and molecular transport through these pores. Here we show that transport occurs overwhelmingly after pulsing. First, we show that the electrical drift distance for typical charged solutes during nanosecond pulses (up to 100 ns), even those with very large magnitudes (up to 10 MV/m), ranges from only a fraction of the membrane thickness (5 nm) to several membrane thicknesses. This is much smaller than the diameter of a typical cell (∼16 μm), which implies that molecular drift transport during nanosecond pulses is necessarily minimal. This implication is not dependent on assumptions about pore density or the molecular flux through pores. Second, we show that molecular transport resulting from post-pulse diffusion through minimum-size pores is orders of magnitude larger than electrical drift-driven transport during nanosecond pulses. While field-assisted charge entry and the magnitude of flux favor transport during nanosecond pulses, these effects are too small to overcome the orders of magnitude more time available for post-pulse transport. Therefore, the basic conclusion that essentially all transmembrane molecular transport occurs post-pulse holds across the plausible range of relevant parameters. Our analysis shows that a primary direct consequence of nanosecond electric pulses is the creation (or maintenance) of large populations of small pores in cell membranes that govern post-pulse transmembrane transport of small ions and molecules.     

Membrane disorder and phospholipid scrambling in electropermeabilized and viable cells

Membrane electropermeabilization relies on the transient permeabilization of the plasma membrane of cells submitted to electric pulses. This method is widely used in cell biology and medicine due to its efficiency to transfer molecules while limiting loss of cell viability. However, very little is known about the consequences of membrane electropermeabilization at the molecular and cellular levels. Progress in the knowledge of the involved mechanisms is a biophysical challenge. As a transient loss of membrane cohesion is associated with membrane permeabilization, our main objective was to detect and visualize at the single-cell level the incidence of phospholipid scrambling and changes in membrane order. We performed studies using fluorescence microscopy with C6-NBD-PC and FM1-43 to monitor phospholipid scrambling and membrane order of mammalian cells. Millisecond permeabilizing pulses induced membrane disorganization by increasing the translocation of phosphatidylcholines according to an ATP-independent process. The pulses induced the formation of long-lived permeant structures that were present during membrane resealing, but were not associated with phosphatidylcholine internalization. These pulses resulted in a rapid phospholipid flip/flop within less than 1 s and were exclusively restricted to the regions of the permeabilized membrane. Under such electrical conditions, phosphatidylserine externalization was not detected. Moreover, this electrically-mediated membrane disorganization was not correlated with loss of cell viability. Our results could support the existence of direct interactions between the movement of membrane zwitterionic phospholipids and the electric field.     

Electroporation of DC-3F Cells Is a Dual Process

Treatment of biological material by pulsed electric fields is a versatile technique in biotechnology and biomedicine used, for example, in delivering DNA into cells (transfection), ablation of tumors, and food processing. Field exposure is associated with a membrane permeability increase usually ascribed to electroporation, i.e., formation of aqueous membrane pores. Knowledge of the underlying processes at the membrane level is predominantly built on theoretical considerations and molecular dynamics (MD) simulations. However, experimental data needed to monitor these processes with sufficient temporal resolution are scarce. The whole-cell patch-clamp technique was employed to investigate the effect of millisecond pulsed electric fields on DC-3F cells. Cellular membrane permeabilization was monitored by a conductance increase. For the first time, to our knowledge, it could be established experimentally that electroporation consists of two clearly separate processes: a rapid membrane poration (transient electroporation) that occurs while the membrane is depolarized or hyperpolarized to voltages beyond so-called threshold potentials (here, +201 mV and −231 mV, respectively) and is reversible within ∼100 ms after the pulse, and a long-term, or persistent, permeabilization covering the whole voltage range. The latter prevailed after the pulse for at least 40 min, the postpulse time span tested experimentally. With mildly depolarizing or hyperpolarizing pulses just above threshold potentials, the two processes could be separated, since persistent (but not transient) permeabilization required repetitive pulse exposure. Conductance increased stepwise and gradually with depolarizing and hyperpolarizing pulses, respectively. Persistent permeabilization could also be elicited by single depolarizing/hyperpolarizing pulses of very high field strength. Experimental measurements of propidium iodide uptake provided evidence of a real membrane phenomenon, rather than a mere patch-clamp artifact. In short, the response of DC-3F cells to strong pulsed electric fields was separated into a transient electroporation and a persistent permeabilization. The latter dominates postpulse membrane properties but to date has not been addressed by electroporation theory or MD simulations.     

Plasma membrane voltage changes during nanosecond pulsed electric field exposure

The change in the membrane potential of Jurkat cells in response to nanosecond pulsed electric fields was studied for pulses with a duration of 60 ns and maximum field strengths of approximately 100 kV/cm (100 V/cell diameter). Membranes of Jurkat cells were stained with a fast voltage-sensitive dye, ANNINE-6, which has a subnanosecond voltage response time. A temporal resolution of 5 ns was achieved by the excitation of this dye with a tunable laser pulse. The laser pulse was synchronized with the applied electric field to record images at times before, during, and after exposure. When exposing the Jurkat cells to a pulse, the voltage across the membrane at the anodic pole of the cell reached values of 1.6 V after 15 ns, almost twice the voltage level generally required for electroporation. Voltages across the membrane on the side facing the cathode reached values of only 0.6 V in the same time period, indicating a strong asymmetry in conduction mechanisms in the membranes of the two opposite cell hemispheres. This small voltage drop of 0.6-1.6 V across the plasma membrane demonstrates that nearly the entire imposed electric field of 10 V/mum penetrates into the interior of the cell and every organelle.     

Numerical study of lipid translocation driven by nanoporation due to multiple high-intensity,ultrashort electrical pulses

The dynamical translocation of lipids from one leaflet to another due to membrane permeabilization driven by nanosecond, high-intensity (> 100 kV/cm) electrical pulses has been probed. Our simulations show that lipid molecules can translocate by diffusion through water-filled nanopores which form following high voltage application. Our focus is on multiple pulsing, and such simulations are relevant to gauge the time duration over which nanopores might remain open, and facilitate continued lipid translocations and membrane transport. Our results are indicative of a N^½ scaling with pulse number for the pore radius. These results bode well for the use of pulse trains in biomedical applications, not only due to cumulative behaviors and in reducing electric intensities and pulsing hardware, but also due to the possibility of long-lived thermo-electric physics near the membrane, and the possibility for pore coalescence.     

Mechanistic analysis of electroporation-induced cellular uptake of macromolecules

Pulsed electric field has been widely used as a nonviral gene delivery platform. The delivery efficiency can be improved through quantitative analysis of pore dynamics and intracellular transport of plasmid DNA. To this end, we investigated mechanisms of cellular uptake of macromolecules during electroporation. In the study, fluorescein isothiocyanate-labeled dextran (FD) with molecular weight of 4,000 (FD-4) or 2,000,000 (FD-2000) was added into suspensions of a murine mammary carcinoma cell (4T1) either before or at different time points (ie, 1, 2, or 10 sec) after the application of different pulsed electric fields (in high-voltage mode: 1.2-2.0 kV in amplitude, 99 microsec in duration, and 1-5 pulses; in low-voltage mode: 100-300 V in amplitude, 5-20 msec in duration, and 1-5 pulses). The intracellular concentrations of FD were quantified using a confocal microscopy technique. To understand transport mechanisms, a mathematical model was developed for numerical simulation of cellular uptake. We observed that the maximum intracellular concentration of FD-2000 was less than 3% of that in the pulsing medium. The intracellular concentrations increased linearly with pulse number and amplitude. In addition, the intracellular concentration of FD-2000 was approximately 40% lower than that of FD-4 under identical pulsing conditions. The numerical simulations predicted that the pores larger than FD-4 lasted <10 msec after the application of pulsed fields if the simulated concentrations were on the same order of magnitude as the experimental data. In addition, the simulation results indicated that diffusion was negligible for cellular uptake of FD molecules. Taken together, the data suggested that large pores induced in the membrane by pulsed electric fields disappeared rapidly after pulse application and convection was likely to be the dominant mode of transport for cellular uptake of uncharged macromolecules.     

The effects of intense submicrosecond electrical pulses on cells

A simple electrical model for living cells predicts an increasing probability for electric field interactions with intracellular substructures of both prokaryotic and eukaryotic cells when the electric pulse duration is reduced into the sub-microsecond range. The validity of this hypothesis was verified experimentally by applying electrical pulses (durations 100 micros-60 ns, electric field intensities 3-150 kV/cm) to Jurkat cells suspended in physiologic buffer containing propidium iodide. Effects on Jurkat cells were assessed by means of temporally resolved fluorescence and light microscopy. For the longest applied pulses, immediate uptake of propidium iodide occurred consistent with electroporation as the cause of increased surface membrane permeability. For nanosecond pulses, more delayed propidium iodide uptake occurred with significantly later uptake of propidium iodide occurring after 60 ns pulses compared to 300 ns pulses. Cellular swelling occurred rapidly following 300 ns pulses, but was minimal following 60 ns pulses. These data indicate that submicrosecond pulses achieve temporally distinct effects on living cells compared to microsecond pulses. The longer pulses result in rapid permeability changes in the surface membrane that are relatively homogeneous across the cell population, consistent with electroporation, while shorter pulses cause surface membrane permeability changes that are temporally delayed and heterogeneous in their magnitude.     

Plant actin controls membrane permeability

The biological effects of electric pulses with low rise time, high field strength, and durations in the nanosecond range (nsPEFs) have attracted considerable biotechnological and medical interest. However, the cellular mechanisms causing membrane permeabilization by nanosecond pulsed electric fields are still far from being understood. We investigated the role of actin filaments for membrane permeability in plant cells using cell lines where different degrees of actin bundling had been introduced by genetic engineering. We demonstrate that stabilization of actin increases the stability of the plasma membrane against electric permeabilization recorded by penetration of Trypan Blue into the cytoplasm. By use of a cell line expressing the actin bundling WLIM domain under control of an inducible promotor we can activate membrane stabilization by the glucocorticoid analog dexamethasone. By total internal reflection fluorescence microscopy we can visualize a subset of the cytoskeleton that is directly adjacent to the plasma membrane. We conclude that this submembrane cytoskeleton stabilizes the plasma membrane against permeabilization through electric pulses.     

Pleiotropic Actions of Forskolin Result in Phosphatidylserine Exposure in Primary Trophoblasts

Forskolin is an extract of the Coleus forskholii plant that is widely used in cell physiology to raise intracellular cAMP levels. In the field of trophoblast biology, forskolin is one of the primary treatments used to induce trophoblastic cellular fusion. The syncytiotrophoblast (ST) is a continuous multinucleated cell in the human placenta that separates maternal from fetal circulations and can only expand by fusion with its stem cell, the cytotrophoblast (CT). Functional investigation of any aspect of ST physiology requires in vitro differentiation of CT and de novo ST formation, thus selecting the most appropriate differentiation agent for the hypothesis being investigated is necessary as well as addressing potential off-target effects. Previous studies, using forskolin to induce fusion in trophoblastic cell lines, identified phosphatidylserine (PS) externalization to be essential for trophoblast fusion and showed that widespread PS externalization is present even after fusion has been achieved. PS is a membrane phospholipid that is primarily localized to the inner-membrane leaflet. Externalization of PS is a hallmark of early apoptosis and is involved in cellular fusion of myocytes and macrophages. We were interested to examine whether PS externalization was also involved in primary trophoblast fusion. We show widespread PS externalization occurs after 72 hours when fusion was stimulated with forskolin, but not when stimulated with the cell permeant cAMP analog Br-cAMP. Using a forskolin analog, 1,9-dideoxyforskolin, which stimulates membrane transporters but not adenylate cyclase, we found that widespread PS externalization required both increased intracellular cAMP levels and stimulation of membrane transporters. Treatment of primary trophoblasts with Br-cAMP alone did not result in widespread PS externalization despite high levels of cellular fusion. Thus, we concluded that widespread PS externalization is independent of trophoblast fusion and, importantly, provide evidence that the common differentiation agent forskolin has previously unappreciated pleiotropic effects on trophoblastic cells.     

Intracellular localization of Herpes simplex virus type 1 thymidine kinase fused to different fluorescent proteins depends on choice of fluorescent tag

Recognition signals are displayed on the cell surface during apoptosis that enable macrophages to engulf and dispose of the dying cell. A common signal is the externalization of phosphatidylserine (PS). Studies in erythrocytes and platelets have suggested that PS exposure requires the concomitant activation of a phospholipid scramblase (PLS) and inhibition of an adenosine triphosphate (ATP)-dependent aminophospholipid translocase. However, the molecular mechanism underlying PS exposure during apoptosis remains poorly understood. In this study, we provide evidence that expression of PLS is neither necessary nor sufficient for PS exposure during Fas-triggered apoptosis. On the other hand, egress of PS is shown to correlate with a decline in intracellular ATP and inhibition of aminophospholipid translocase activity upon Fas stimulation. Moreover, suppression of intracellular ATP levels by the glucose anti-metabolite, 2-deoxyglucose, alone or in combination with glucose-free medium, potentiates Fas-induced PS exposure in the PLS-expressing Jurkat cell line and enables PLS-defective Raji cells to externalize PS in response to Fas ligation. These studies suggest that intracellular ATP levels can modulate the externalization of PS during apoptosis, and implicate the ATP-dependent aminophospholipid translocase in this process.     

On the molecular mechanisms implicated in the bipolar cancellation of membrane electroporation

Bipolar cancellation is the phenomenon in which the permeability of cell membranes subjected to high intensity short pulsed electric field (ns-μs range) is reduced or eliminated when the system is subjected to bipolar instead of monopolar pulses. Although several studies have tried to explain bipolar cancellation, the underlying mechanisms remain unclear. Very few articles study bipolar cancellation by means of molecular dynamics (MD) simulation. In this paper, we investigated the molecular mechanisms underlying the difference in electroporation induced by bipolar and monopolar picosecond electric pulses (EPs) using MD simulation. The electric field gradients and electric forces on water molecules of the two pulses were analyzed in detail for the first time. For a certain pulse width, when the field intensity is relatively small, the direction of bipolar electric force on the interfacial water molecule reverses as the bipolar EPs reverse, while the electric force on interfacial water molecules of the cathode side remains in the same direction as that of applied monopolar EPs. The bipolar electric force reversal delays the water protrusion and increases the pore formation time. Therefore, this phenomenon could correspond to bipolar cancellation. When the field intensity is relatively large, although the bipolar electric force direction still reverses, half of the total time of the monopolar EPs has no electric fields. The electric forces of monopolar no-field half-cycles are much smaller than those of the bipolar EPs. Therefore, the pore formation time of bipolar EPs reduces, and this phenomenon is called bipolar enhancement. The occurrence of bipolar cancellation or bipolar enhancement depends on conditions such as the width and intensity of the pulse.