Investigations on Na+, K+-ATPase energy consumption in ion flow of hydrophilic pores by THz unipolar stimulation

Summary Terahertz science and technology has recently shown new application prospects in artificial intelligence. It is found that terahertz unipolar stimulation can activate cell membrane hydrophilic pores. However, the behaviors of Na+, K+-ATPase and energy consumption during this period remain unknown. This paper investigates these behaviors by Na+, K+-ATPase and electroporation models, based on the interaction theory between terahertz fields and ions at the cellular level. The effective diameters of life ions are considered in the aqueous solution. From results, Na+, K+-ATPases can be activated and stay for a while before close after the stimulation. Their life ion flows are far lower than the flows via the pores. And their power dissipation is as low as 10−11 W in both rat neostriatal neurons and guinea pig ventricular myocytes. The results keep tenable in 0.1–1.2 THz. These lay the basis for investigations of information communication mechanisms in cells under terahertz stimulation.

As shown in Figures 3 and 4, 0.5 THz, 1 ps unipolar pulse train stimulation activates cell membrane hydrophilic pores in rat neostriatal neuron during the 1.2 ns stimulation.And the hydrophilic pores stay at least 11 ns after the shutdown of the stimulation.During the stimulation that is from 0 to 1.2 ns, the absolute values of the membrane potential at each polar angle q except q = p/2 increase significantly before the activation of hydrophilic pores at around 0.94 ns and then start to decrease.The reason for the exception at q = p/2 is that cell membrane is parallel to the stimulated terahertz electric field at this polar angle.The membrane conductivities keep zero before the activation of hydrophilic pores and increase significantly after the activation and finally tend to be nearly stable.After the stimulation (>1.2 ns), the absolute values of The cell and extracellular environment are marked.And the electric field (E-field) vector of the pulse train is depicted in the image.The polar angle q in the spherical coordinate system is marked and defined.The Na + , K + , Ca 2+ , and Cl À flows via cell membrane Na+, K+-ATPase and hydrophilic pores as well as their directions are respectively schematically illustrated in the image.It can be seen from Figures 5, 6, 7, and 8 that during the stimulation once the hydrophilic pores are activated at around 0.94 ns, the transmembrane ion flow of Na+, K+, ClÀ, and Ca2+ via hydrophilic pores increases from zero and shortly reaches each maximum.After that, the life ion flow starts to decrease exponentially due to the decrease of membrane potential (Figure 3) when the hydrophilic pores in cell membrane get nearly stable (Figure 4).Figures 9A-9D are respectively the normal averages (nonweighted averages) with respect to the angular direction q of Figures 5A, 6A, 7A, and 8A.From Figure 9, it can be seen that the average ion flows of Na+, K+, ClÀ, and Ca2+ in a whole cell finally tend to nonzero values in around 11 ns after the stimulation.
Figures 10 and 11 show the transmembrane ion flows of Na+ and K+ via Na+, K+-ATPase under the stimulation.During the stimulation, the flows vary as a result of the variation of membrane potentials before the activation of hydrophilic pores (Figure 3).After the activation of hydrophilic pores during the stimulation, the variation of ion concentrations due to the ion flows via the pores also contributes to the ion flows via Na+, K+-ATPase.The Na+ and K+ flows via Na+, K+-ATPase are nonzero when the membrane potential increases from resting potential to the positive direction in the case of rat neostriatal neuron (Figure 2A).Thus, based on the variation of the membrane potential with time by the stimulation shown in Figure 3, the Na+ and K+ flows are nonzero in the range of q from 0 to p/2 as shown in Figures 10 and 11.The Na+ and K+ flows increase first and then decrease with the increase of the membrane potential at q = 0, p/6, and p/3; this is because according to the I-V response characteristics of Na+, K+-ATPase in rat neostriatal neuron shown in Figure 2A, the positive peaks of membrane potential at q = 0 and p/6 are overlarge, and therefore the flows show an extraordinary opposite-direction-varying peak at q = 0 and p/6 at around 1 ns in Figures 10 and 11.This reflects an inhibition effect on Na+, K+-ATPase functions, which is similar to the case of voltage-gated calcium channels. 12In contrast, because the peak is much smaller, it does not show an extraordinary opposite-direction-varying peak when the membrane potential is reaching toward its peak at q = p/3.After reaching the peaks, the membrane potentials at q = 0 and p/6 decrease steeply toward to nearly zero soon within 12 ns, so the flows have extraordinary varies first and then decrease to zero soon.In contrast, after reaching the peak, the membrane potential at q = p/3 decreases comparably much slower and at 12 ns it still has a large magnitude, so the flows stay large and do not decrease to zero at q = p/3.So the maximum flows in Figures 10B and 11B are always reached when q is p/3.12, it can be seen that the variation of the average life ion flows via Na+, K+-ATPase tends to be gentle in around 11 ns after the stimulation.

Variation of life ion concentrations in cell
Figures 13 and 14 show the variation of intracellular Na+ and K+ ion concentration at different polar angles q due to the ion flows via the cell membrane hydrophilic pores and Na+, K+-ATPase under the 1.2 ns stimulation of 5 3 10 7 V/m, 0.5 THz, 1 ps unipolar pulse train.From the figures, the intracellular ion concentrations of Na+ and K+ both decrease near q = 0 and increase near q = p during the stimulation.The reason is as follows.Because the ion flow component due to the electric field across the cell membrane is far larger than the component due to the concentration difference across the membrane in the case of the ion flows via hydrophilic pores, 19 the variation of the concentration at different polar angles q is mainly because of the ion flow component due to the electric field.Furthermore, the direction of the stimulated THz electric field is pointing to extracellular environment near q = 0 and intracellular environment near q = p (see Figure 1).And Na+ and K+ ions are both positive charges.Thus, during the stimulation, Na+ and K+ ions are both transported from the cell to extracellular environment near q = 0 and from the extracellular environment to the cell near q = p, leading to the corresponding variation of the ion concentrations of Na+ and K+.And the trend of the variation of the ion concentrations at different q keeps for a short time after the stimulation (Figures 13  and 14); this is because during this time the membrane potentials are still large enough (Figure 3).At the relatively long time after the stimulation, the Na+ concentrations near q = 0 and p both start to increase, and the K+ concentration near q = 0 and p both start to decrease; this is because at this time the membrane potentials are close to 0 (Figure 3), and then the ion flow component due to the electric field becomes negligible compared with that due to the concentration difference.Thus, the variation of the concentration at different q is mainly because of the ion flow component due to the concentration difference across the cell membrane.It is worth mentioning that there is an exception at q = p/6 in the case of Na+ (Figure 13B), and this is because the membrane potential is not close to 0 at this moment so the ion flow component due to the electric field at q = p/6 is still large and nonnegligible.
Figure 15 shows the variation of the average ion concentrations of Na+, K+, Ca2+, and ClÀ in cell under the stimulation.It can be seen that there are abnormal variation rates or tendencies at the time during and shortly after the stimulation (before around 3 ns in Figure 15) for each type of the ions; this is because of the effect of the ion flow component due to the electric field across the cell membrane on the transmembrane ion flow. 19And at a relatively long time after the stimulation, the variation tendency for each type of the ions is compliant with the tendency due to their concentration differences across the cell membrane.This is because the ion flow component due to the electric field becomes negligible at this time in comparison to that due to the concentration difference.
It should be noted that the variations of the intracellular ion concentrations for Na+, K+, and ClÀ seem to be trivial compared with their large basal ion concentration.And owing to the tiny basal ion concentration in cell for Ca2+, the variation of intracellular Ca2+ concentration is nonnegligible, nearly two times the basal ion concentration in around 11 ns after the stimulation.It should also be noted that the effect of Na+, K+-ATPase on the Na+ and K+ ion concentration in cell during the life ion flow via hydrophilic pores is negligible (Figures 15A and 15B).This is consistent with the fact that the life ion flows via Na+, K+-ATPase are much smaller than the flows via hydrophilic pores (Section life ion flows via Na+, K+-ATPase and hydrophilic pores).

Na+, K+-ATPase power dissipation
Figure 16 shows the power dissipation of Na+, K+-ATPase during the life ion flows via hydrophilic pores under the stimulation.It can be seen that the power dissipation varies a lot during and shortly after the stimulation (before around 3 ns) when the membrane potentials vary  drastically.And the variation of the power dissipation tends to be gentle at a relatively long time after the stimulation.It is clear that the average power dissipation is as low as around the level of 10 À11 W. However, it is qualitatively several orders of magnitude larger than the power dissipation that is at the level of 10 À18 W in the ion flow via protein Ca2+ channels. 20The reasons are as follows: the life ion flow via hydrophilic pores in Figures 5, 6, 7, and 8 is far larger than the ion flow via voltage-gated Ca2+ channels (VGCCs) as seen in literature. 14hus, the variations of membrane potentials and intracellular ion concentrations are more drastic due to ion flow via hydrophilic pores seen in Figures 3 and 15 than due to ion flow via VGCCs as seen in literature 14 ; this leads to a much larger ion flow via the ion ATPase in the case of  hydrophilic pores compared with that in the case of VGCCs.As a result, the power dissipation in the case of ion flow via hydrophilic pores is much larger than that in the case of ion flow via the VGCCs.

Comparison in different cell types
In addition to the rat neostriatal neuron, the Na+ and K+ flow and the power dissipation of Na+, K+-ATPase during the life ion flow via hydrophilic pores are investigated in another cell type, guinea pig ventricular myocyte.Because the changes in ion concentrations are nearly negligible for Na+ and K+ ions (see Figure 15), the variations of the ion flow via Na+, K+-ATPase are mainly determined by the variations of membrane potentials.As the membrane potentials continue to increase toward their peaks (see Figure 3), the ion flows reach their maximums more shortly and then decrease more shortly even to zero in the case of guinea pig ventricular myocyte (Figures 17 and 18) compared with the case of rat neostriatal neuron (Figures 10 and 11).This is because the I-V characteristics in guinea pig ventricular myocyte has a narrower shape compared with that in rat neostriatal neuron (see Figure 2).Thus, the increase and the decrease vary more shortly in the case of guinea pig ventricular myocyte than in the case of rat neostriatal neuron.Besides, the ion flows at most of the q do not decrease to zero at the time from 4 ns to around 12 ns compared with the rat neostriatal neuron.This is because the I-V curve has a shift toward more negative membrane potential compared with that in rat neostriatal neuron (see Figure 2).Thus, at those membrane potentials at the time from 4 ns to around 12 ns, the ion flows in guinea pig ventricular myocyte are nonzero.The difference of ion flows in these two different cell types leads to the difference of power dissipation of Na+, K+-ATPase between Figures 16 and 19 according to Equation 21.
From Figures 17, 18, and 19, it can be seen that the Na+ flow, K+ flow, and power dissipation in the case of guinea pig ventricular myocyte vary a lot during and shortly after the stimulation when the membrane potentials vary drastically.And at a relatively long time after the stimulation, the variations of ion flows and power dissipation tend to be gentle.Those are the same as the case of rat neostriatal neuron.Besides, the average power dissipation of Na+, K+-ATPase in guinea pig ventricular myocyte has the similar order of magnitude as that in rat neostriatal neuron, namely, the level of 10 À11 W, although the specific values are different.As a result, the Na+, K+-ATPase in rat neostriatal neuron and guinea pig ventricular myocyte behaves similar during the life ion flow via hydrophilic pores under the stimulation.

Close of Na+, K+-ATPase
Section cell life ion flow and Na+, K+-ATPase power dissipation under the stimulation shows that Na+, K+-ATPase does not close at around 11 ns after the stimulation.In order to investigate whether Na+, K+-ATPase closes during the life ion flow via hydrophilic pores, a longer time  (A) Variation of intracellular K+ concentration with respect to polar angle q versus time.(B) Variation of intracellular K+ concentration at q = 0, p/6, p/3, p/2, 2p/3, 5p/6, and p versus time.
around 80 ns simulation is conducted.And meanwhile the stimulation duration is reduced from 1.2 ns to 1.1 ns to increase the ratio of the time after the stimulation to the time during the stimulation.
As we can see from Figures 22 and 23, the membrane potential of the cell keeps approaching nearly to zero, and the life ion flow via hydrophilic pores tends to be stable after 11 ns after the 1.1 ns stimulation of 5 3 10 7 V/m, 0.5 THz, 1 ps unipolar pulse train.After a drastic variation during and shortly after the stimulation, the flow via Na+, K+-ATPase tends to be gentle and slowly decreases to zero with time mainly due to the decrease of membrane potentials.Na+, K+-ATPase closes at around 80 ns.Besides, from Figure 23, the intracellular K+ concentration keeps decreasing slowly in a relatively long time after the stimulation, because the flow via Na+, K+-ATPase is far smaller than that via hydrophilic pores.Nevertheless, the change in intracellular K+ concentration keeps negligible at around 80 ns after the stimulation.The power dissipation of Na+, K+-ATPase is at the level of 10 À11 W, and it decreases to zero when Na+, K+-ATPase closes.

DISCUSSION
The activation of hydrophilic pores by THz unipolar picosecond pulse train stimulation causes enormous transmembrane life ion flows.Those ion flows are able to be far larger than the ion flow via protein ion channels and thus mask the other ion flows.The prevail of ion flow via hydrophilic pores leads to a drastic change in membrane potential, that is, a significant increase followed by a relatively slower but persistent decrease to approximately zero.In comparison, in the case where hydrophilic pores are not being activated, the change in membrane potential has much smaller amplitude. 12,14,20The membrane potentials vibrate with terahertz frequency around resting potential. 12,14,20Those lead to the fact that the ion flow via the ion ATPase with activation of hydrophilic pores is far larger than the flow via the ATPase without the activation of hydrophilic pores.Those lead to a tremendous energy consumption with the activation of hydrophilic pores compared with the case where hydrophilic pores are not activated.Besides, the hydrophilic pores show no signs of turning off for around 80 ns after the 1.1 ns stimulation.Then, the ion flow via the pores stays so the membrane potential keeps nearly zero instead of being back to resting potential for at least 80 ns.In this case, the cell physiological functions [21][22][23] might be essential to make the hydrophilic pores closed before the cell is able to respond to the next stimulation.Hence, some time is necessary for the restoration of the cell back to resting conditions when it is ready for another stimulation or information communication.As a result, the THz unipolar picosecond pulse train stimulation might serve as an end signal of last communication or a reset signal for next communication in cells.

Conclusions
Cell membrane Na+, K+-ATPases are activated during the life ion flows via cell membrane hydrophilic pores under the terahertz unipolar picosecond pulse train stimulation.After the stimulation, the Na+, K+-ATPase and hydrophilic pores can stay open for tens of nanoseconds before the close of Na+, K+-ATPase.The life ion flow via Na+, K+-ATPase is several orders of magnitude smaller than the flow via hydrophilic pores and has opposite transmembrane transport direction to the flow via the pores at a relatively long time after the stimulation.The life ion flow via the pores and Na+, K+-ATPase causes a negligible change in intracellular Na+ and K+ concentration even at a relatively long time 80 ns after the stimulation when the Na+, K+-ATPase closes.In two different types of cells, rat neostriatal neuron and guinea pig ventricular myocyte, the power dissipations of Na+, K+-ATPase during the life ion flow via hydrophilic pores are both at as low as around the level of 10 À11 W. And the power dissipation becomes zero after the close of Na+, K+-ATPase.This level of power dissipation is still qualitatively far larger than the power dissipation (the level of 10 À18 W) of cell membrane Ca2+ ATPase during the flow via voltage-gated calcium channels under terahertz bipolar picosecond pulse train stimulation where no hydrophilic pore is formed. 20This might indicate that the activation of hydrophilic pores may cause a drastic increase in energy consumption of cell metabolic energy during the information communication of cells.The results also show that the conclusions are tenable under different stimulation frequencies in 0.1-1.2THz.The theoretical studies lay the foundations for the research on the information communication mechanisms in the cell under terahertz stimulation.

Limitations of the study
This investigation is based on the interaction theory between terahertz fields and ions at the cellular level, 5,14 so the stimulation frequency is confined in the low-frequency range of THz range in order to satisfy that the wavelength of the THz stimulation in the cellular environment is far larger than the cell system size as mentioned in Section cell model of ion flow by the stimulation in method details in STAR methods.Besides,  for the frequency lower than 0.1 THz, which is beyond the scope of the terahertz frequency range, there might be some unknown microwave effects that are not taken into considerations in the model.Thus, current model is unsuitable for the investigations in the case that the frequency is below THz range.As a consequence, this investigation is focused on the stimulation of the narrow THz frequency band in 0.1-1.2THz.
5][26][27] Then, under the terahertz stimulation, the interaction of the electromagnetic stimulation at sub-THz frequencies and the natural vibration motions in protein molecules would have impact on the protein functions and thus lead to a potential amplification/deamplification of the protein activity.This, in the case of the ion channel protein in the cell membrane, is probably the amplification/deamplification of ion flow via the ion channel protein.Thus, the evaluation of the life ion flows via Na+, K+-ATPase by the stimulation might be overestimated or underestimated a few.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

Cell model of ion flow by the stimulation
A cell with 6.6 mm diameter as shown in Figure 1 is stimulated by terahertz unipolar picosecond pulse train stimulation.The stimulation duration is 1.1 ns and 1.2 ns.The terahertz repetition frequency of the unipolar picosecond pulse train is respectively 0.1 THz, 0.21 THz, 0.3 THz, 0.5 THz, 0.51 THz, 0.7 THz, 0.9 THz and 1.2 THz.The duty cycle of the pulse train is 0.5 so the pulse width of each unipolar pulse in the train is 5 ps, 2.38 ps, 1.67 ps, 1 ps, 0.98 ps, 0.71 ps, 0.55 ps and 0.41 ps, respectively.Based on the frequency spectrum profile of the unipolar picosecond pulse train with terahertz repetition frequency, 19 the electromagnetic frequency of those pulse train stimulation in terahertz range is mainly concentrated on the repetition frequency.
During the stimulation with those terahertz frequencies, the shortest wavelength of the terahertz electromagnetic wave in the cellular aqueous environment is far larger than the size of the cell (diameter of 6.6 mm) and also larger than the cell system in the simulation (diameter of 19.8 mm).It belongs to quasi-magnetostatic problem.And then according to the electromagnetic interaction theory between terahertz fields and physiological ions at the cellular level, 5,14 the effects of magnetic fields can be ignored in the study of the life ion flow.
The capacitive current of the cell membrane is taken into account. 18The life ion flow in the intracellular and extracellular environments is driven by concentration gradients, and the ion flow across the cell membrane is depicted as follows.

Flow via the pores by the stimulation
The activation of cell membrane hydrophilic pores by the stimulation at the whole cellular level is numerically calculated with Neu and Krassowska electroporation model 18,19,31  where N(t, q) is the density of hydrophilic pores in cell membrane at the polar angle q at time t, V ep is the characteristic voltage of hydrophilic pores, a is the creation rate of hydrophilic pores, N eq (V m (t, q)) is the equilibrium density of hydrophilic pores at the membrane potential V m (t, q), N 0 is the equilibrium density of hydrophilic pores at zero membrane potential.q p is the rate constant of the pore creation, q p = (r m /r*), 2 r m is the radius of the pore at the minimum energy at zero membrane potential, and r* is the minimum radius of the hydrophilic pores.
And the evolution of the radii of the hydrophilic pores is numerically evaluated by, 18,19,31 r j À 2pg + 2ps eff r j # ; ðj = 1; 2; :::; KÞ (Equation 2) where r j is the pore radius of the j th hydrophilic pore, V m,j is the membrane potential at the position of the j th hydrophilic pore, D p is the diffusion coefficient in the variation of the pore radius, k B is the Boltzmann constant, T is the absolute temperature, F max is the maximum electric force at V m,j = 1, r t and r h are constants in the variation of pore radius, b is the steric repulsion energy, g is the edge energy, s eff is the effective tension density of the membrane, 18,19,31 where s 0 is the tension density at the interface between hydrocarbon chain of phospholipid molecules and water molecules, s 0 is the tension density of the phospholipid bilayer without hydrophilic pores in cell membrane, A p is the total area of all the hydrophilic pores in the whole cell membrane, A cell is the area of the whole cell membrane.
The membrane potential at the whole cellular level is numerically estimated based on the principle of current continuity at the whole cell membrane by, 4) and the Laplace equation of electrical potential by, V 2 F = 0 (Equation 5) where C m is the membrane capacitance, F i and F o are respectively intracellular and extracellular electrical potentials which are the functions of space and time, V rest is the resting membrane potential, g 1 is the membrane conductance of total physiological ion channels, I p is the current of life ions via hydrophilic pores.At the time and after the activation of the hydrophilic pores, each type of the life ion flow via the pores is numerically computed with the generalized modified Poisson-Nernst-Planck model 19,32 12) 13) (Equation 14) k À 3 c P ,10 ð3 À pHÞ 1+c MgATP k d;MgATP (Equation 15) (Equation 16) where F c is a factor that is correlated with membrane capacitance and the number density of Na+, K + -ATPase protein channels in the cell membrane.And v cyc is steady-state cycle rate of Na+, K + -ATPase.The factor F c and the parameters in v cyc are determined as the best fit values based on the whole-cell current-voltage experimental data of Na+, K + -ATPase.Those parameters in the v cyc include the rate con-  28 and guinea pig ventricular myocyte, 29 so as to study the work of Na+, K + -ATPase and the energy consumption in these two cell types.

Figure 1 .
Figure 1.Illustration of cell system under the stimulation of terahertz unipolar picosecond pulse trainThe cell and extracellular environment are marked.And the electric field (E-field) vector of the pulse train is depicted in the image.The polar angle q in the spherical coordinate system is marked and defined.The Na + , K + , Ca 2+ , and Cl À flows via cell membrane Na+, K+-ATPase and hydrophilic pores as well as their directions are respectively schematically illustrated in the image.

Figure 12 .
Figure 12.Average life ion flows via Na+, K+-ATPase of rat neostriatal neuron under the 1.2 ns stimulation of 5 3 10 7 V/m, 0.5 THz, 1 ps unipolar pulse train After the stimulation, the numerical calculations continue for around 11 ns.(A and B) (A) Average Na+ flow, (B) average K+ flow.

Figure 20
Figure20shows the variation quantities of intracellular Na+ and K+ concentrations as a result of life ion flow via hydrophilic pores and Na+, K+-ATPase with respect to frequency in 0.1-1.2THz.In Figure20, the variation quantity without the THz stimulation is also plotted.The cell is under 1.2 ns stimulation of 5 3 10 7 V/m, 1 ps unipolar pulse train, and the variation quantities are accumulated at 12.3 ns.It is apparent that the variation quantities of the Na+ and K+ ion concentrations are both nearly invariant with respect to the frequency.And the effect of the THz stimulation is obvious by comparing the variation quantities with and without the stimulation.

Figure 21
Figure21shows the average power dissipation Na+, K+-ATPase with time during the life ion flow via hydrophilic pores at different frequencies.It can be seen from the figure that the variation of the power dissipation is nearly the same under different frequencies in 0.1-1.2THz.And the effect of the THz stimulation on the power dissipation is significant by comparing with that of no THz stimuli.The activation of Na+, K+-ATPase and hydrophilic pores in the cell is mainly due to the increase of the absolute values of membrane potentials under terahertz unipolar picosecond pulse train stimulation in the range of 0.1-1.2THz.Because the duty cycles of the pulse trains are the same at different frequencies, the integrals of the electric fields delivered to the cell in terms of time are the same.Therefore, the frequency of the terahertz stimulation has no impact on the life ion flows, the variation quantities of ion concentrations accumulated, and the power dissipation in this narrow frequency range.As a result, the results in Section cell life ion flow and Na+, K+-ATPase power dissipation under the stimulation keep tenable under different stimulation frequencies in 0.1-1.2THz.

Figure 15 .
Figure 15.Variation of average intracellular ion concentrations of Na+ c Na-i and K+ c K-i due to the transmembrane life ion flow via hydrophilic pores and Na+, K+-ATPase in rat neostriatal neuron under the 1.2 ns stimulation of 5 3 10 7 V/m, 0.5 THz, 1 ps unipolar pulse train (A-D) The c Na-p-i , c K-p-i , c Cl-p-i , and c Ca-p-i are respectively the Na+, K+, ClÀ, and Ca2+ concentration due to the ion flow via exclusive hydrophilic pores.After the stimulation, the numerical calculations continue for around 11 ns.(A) c Na-i and c Na-p-i , (B) c K-i and c K-p-i , (C) c Cl-p-i , (D) c Ca-p-i .

Figure 16 .
Figure 16.Power dissipation of Na+, K+-ATPase during the transmembrane life ion flow in rat neostriatal neuron under the 1.2 ns stimulation of 5 3 10 7 V/m, 0.5 THz, 1 ps unipolar pulse train After the stimulation, the numerical calculations continue for around 11 ns.(A) The power dissipation with respect to polar angle q versus time.(B) The power dissipation at q = 0, p/6, p/3, p/2, 2p/3, 5p/6, and p versus time.

Figure 19 .
Figure 19.Power dissipation of Na+, K+-ATPase during the transmembrane life ion flow in guinea pig ventricular myocyte under the 1.2 ns stimulation of 5 3 10 7 V/m, 0.5 THz, 1 ps unipolar pulse train After the stimulation, the numerical calculations continue for around 11 ns.(A)The power dissipation with respect to polar angle q versus time.(B) The power dissipation at q = 0, p/6, p/3, p/2, 2p/3, 5p/6, and p versus time.

Figure 20 .
Figure 20.Variation quantity of ion concentration induced by the flow via hydrophilic pores and Na+, K+-ATPase versus frequency with and without the stimulation (A and B) Variation quantity of intracellular ion concentration due to the life ion flow via cell membrane hydrophilic pores and Na+, K+-ATPase at around 12.3 ns with respect to different stimulation frequencies under the 1.2 ns stimulation of 5 3 10 7 V/m, 1 ps unipolar pulse train, the variation quantity without the THz stimulation is also plotted (''no THz stimuli'') in each figure: (A) variation quantity of intracellular Na+ concentration [Na+]i versus frequency, (B) variation quantity of intracellular K+ concentration [K+]i versus frequency.

stants k 1 + , k 1 - 4 -,
the dissociation constants for binding of Na+, K+ and ATP, k 0 d,Nao , k 0 d,Nai , k 0 d,Ko , k 0 d,Ki , k d,MgATP , and the coefficients that determine the voltage dependencies for the Na+ and K+ concentrations in the inside and outside of the cell D Nai , D Ki , D Nao , D Ko .The experimental data are measured in the cases of two different cell types, rat neostriatal neuron

TABLE
d RESOURCE AVAILABILITY B Lead contact B Materials availability B Data and code availability qÞ N eq ðV m ðt; qÞÞ N eq ðV m ðt; qÞÞ = N 0 e qp ðVmðt;qÞ=VepÞ 2(Equation1)