Kinetic Theory Model for Ion Movement through Biological Membranes: I. Field-Dependent Conductances in the Presence of Solution Symmetry

A model for ion movement through specialized sites in the plasma membrane is presented and analyzed using techniques from nonequilibrium kinetic theory. It is assumed that ions traversing these specialized regions interact with membrane molecules through central conservative forces. The membrane molecules are approximated as massive spherical scattering centers so that ionic fractional energy losses per collision are much less than one. Equations for steady-state membrane ionic currents and conductances as functions of externally applied electric field strength are derived and numerically analyzed, under the restriction of identical solutions on each size of the membrane and constant electric fields within the membrane. The analysis is carried through for a number of idealized ion-membrane molecule central force interactions. For any interaction leading to a velocity-dependent ion-membrane molecule collision frequency, the membrane chord conductance is a function of the externally applied electric field. Interactions leading to a collision frequency that is an increasing (decreasing) function of ionic velocity are characterized by chord conductances that are decreasing (increasing) functions of field strength. For ion-neutral molecule interactions, the conductance is such a rapidly decreasing function of field strength that the slope conductance becomes negative for all field strengths above a certain value.     

Determinants of time-dependent membrane conductance. The nonrole of classical ion-membrane molecule interactions

We have examined the steady-state and time-dependent electrical properties of a model membrane system. The model assumes that the directed velocity and energy of ions moving through the membrane are determined by the applied electric field, ionic diffusion forces, and central elastic collisions between ions and membrane molecules. A simple analysis of the steady-state electrical properties of the model yields results identical with ones obtained previously using a more complex analysis procedure. The time-dependent conductance changes of the model in response to a step change in electric field strength when there is solution symmetry display three qualitative patterns dependent on the nature of the ion-membrane molecule interaction. One of the patterns of conductance change is quite similar to that observed in the sodium conductance system of a number of excitable tissues: an initial conductance rise to a maximum (activation) followed by a decay to a final steady-state value (inactivation). However, the correspondence between the time-dependent model behavior and known experimental behavior of excitable systems is only qualitative. We conclude that the classical ion-membrane molecule interactions we consider are not involved in determining time-dependent conductance processes in the excitable systems for which comparison is possible.     

Kinetic Theory Model for Ion Movement through Biological Membranes: III. Steady-State Electrical Properties with Solution Asymmetry

An electrodiffusion model for plasma membrane ion transport, which takes into account the influence of high electric field strengths and ion-membrane molecule interactions, is presented and analyzed. A generalized Nernst-Planck equation for steady-state situations is derived which has electric field-dependent mobility and diffusion coefficients. Under the assumption of a constant electric field within the membrane, this equation is integrated to give a more general form of the Goldman equation. Based on this equation numerical computations of ionic chord conductance as a function of applied electric field strength were carried out for several permeant ion concentration ratios. The model is capable of yielding significantly larger rectification ratios than is the Goldman equation. Further, high field asymptotes to the current vs. electric field strength curve do not generally intersect at the origin.     

Generalized Bohm’s criterion and negative anode voltage fall in electric discharges

The value of the voltage fall across the anode sheath is found as a function of the current density. Analytic solutions are obtained in a wide range of the ratio of the directed velocity of plasma electrons v ₀ to their thermal velocity v _T . It is shown that the voltage fall in a one-dimensional collisionless anode sheath is always negative. At the small values of v ₀/v _T , the obtained expression asymptotically transforms into the Langmuir formula. Generalized Bohm’s criterion for an electric discharge with allowance for the space charge density ρ(0), electric field E(0), ion velocity v _i (0), and ratio v ₀/v _T at the plasma-sheath interface is formulated. It is shown that the minimum value of the ion velocity v _i ^* (0) corresponds to the vanishing of the electric field at one point inside the sheath. The dependence of v _i ^* (0) on ρ(0), E(0), and v ₀/v _T determines the boundary of the existence domain of stationary solutions in the sheath. Using this criterion, the maximum possible degree of contraction of the electron current at the anode is determined for a short high-current vacuum arc discharge.     

The Effects of Alkali Metal Cations and Common Anions on the Frog Skin Potential

The effects on the potential difference across isolated frog skin (R. catesbeiana, R. pipiens) of changing the ionic composition of the bathing solutions have been examined. Estimates of mean values and precision are presented for the potential changes produced by substituting other alkali metal cations for Na at the outside border and for K at the inside border. In terms of ability to mimic Na at the outside border of bullfrog skin, the selectivity order is Li > Rb, K, Cs; at the outside border of leopard frog skin, Li > Cs, K, Rb. In terms of ability to mimic K at the inside border of bullfrog and leopard frog skin: Rb > Cs > Li > Na. Orders of anion selectivity in terms of sensitivity of the potential for the outside border of bullfrog skin are Br > Cl > NO₃ > I > SO₄, isethionate and of leopard frog skin are Br, Cl > I, NO₃, SO₄. An effect of the solution composition (ionic strength?) on the apparent Na-K selectivity of the outside border is described. The results of the investigation have been interpreted and discussed in terms of the application of the constant field equation to the Koefoed-Johnsen-Ussing frog skin model. These observations may be useful in constructing and testing models of biological ionic selectivity.     

Thresholds in field-induced reactions of linear biopolymers: Strong chain-length dependence of field effects in DNA

We have analysed the field-induced conformation change of DNA by absorbance measurements at the magic angle. Conformation changes are observed when the electric field strength exceeds a clearly defined threshold value. The threshold values increase with increasing salt concentration and show a linear dependence upon the logarithm of the ionic strength. Measurements with homogeneous DNA samples of different chain lengths N show that the threshold increases with decreasing N; at a given ionic strength the threshold is a linear function of the logarithm of N. The threshold value observed for a circular DNA molecule with a chain length N_c fits to these data with an effective length N_c/2. This result indicates that the length of maximal extension is important for the field-induced reaction and suggests, together with the other results, that the field-induced reaction is mainly driven by a polarization of the ion atmosphere along the axis of DNA, Some data are also given for the dynamics of the reaction: at high electric field pulses the first step is a fast deslacking and lilting of the bases followed by a slow unwinding process. For short pulses the reaction is almost completely reversible with a characteristic time constant of about 3 μs for the back reaction.     

Nonquasineutral model of an equilibrium Z-pinch

A fundamentally new approach is proposed for describing Z-pinches when the pinch current is gov-erned to a large extent by strong charge separation, which gives rise to a radial electric field in the nonquasineutral core of the pinch. In the central pinch region with a characteristic radius of about $r_0 \sim \sqrt {J_0 /en_e c}$ , part of the total pinch current J ₀<J, is carried by the drifting electrons and the remaining current is carried by ions moving at the velocity v _iz ～c(2eZJ/m _i c ³) in the peripheral region with a radial size of c/ω_pi. In the nonquasineutral core of a Z-pinch, the radial ion “temperature” is on the order of ZeJ ₀/c. The time during which the non-quasineutral region exists is limited by Coulomb collisions between the ions oscillating in the radial direction and the electrons. Since the magnetic field is not frozen in the ions, no sausage instability can occur in the non-quasineutral core of the Z-pinch. In the equilibrium state under discussion, the ratio of the radial charge-separation electric field E ₀ to the atomic field E _a may be as large as $E_0 /E_a \sim 137^2 (a_0 \omega _{pe} /c)\sqrt {J/J_{Ae} }$ , where a ₀ is the Bohr radius.     

The effects of external electric field: creating non-zero first hyperpolarizability for centrosymmetric benzene and strongly enhancing first hyperpolarizability for non-centrosymmetric edge-modified graphene ribbon H2N-(3,3)ZGNR-NO2

How to generate a non-zero first hyperpolarizability for a centrosymmetric molecule is a challenging question. In this paper, an external (pump) electric field is used to make a centrosymmetric benzene molecule generate a non-zero value of the electric field induced first hyperpolarizability (β ^F ). This comes from the centrosymmetry breaking of electron cloud. Two interesting rules are exhibited. (1) β ^F is anisotropic for different directional fields (F _i, i?=?X, Y, Z). (2) The field dependence of β ^F is a non-monotonic function, and an optimum external electric field causes the maximum value of β ^F . The largest first hyperpolarizability β ^F reaches the considerable level of 3.9?×?10⁵ a.u. under F _Y?=?330?×?10^?4 a.u. for benzene. The external electric field effects on non-centrosymmetric edge-modified graphene ribbon H₂N-(3,3)ZGNR-NO₂ was also studied in this work. The first hyperpolarizability reaches as much as 2.1?×?10⁷ a.u. under F _X?=?600?×?10^?4 a.u. for H₂N-(3,3)ZGNR-NO₂. We show that the external electric field can not only create a non-zero first hyperpolarizability for centrosymmetric molecule, but also remarkably enhance the first hyperpolarizability for a non-centrosymmetric molecule.     

Direct measurement of the melting temperature of supported DNA by electrochemical method

The development of biosensors based on DNA hybridization requires a more precise knowledge of the thermodynamics of the hybridization at a solid interface. In particular, the selectivity of hybridization can be affected by a lot of parameters such as the single-strand (ss)DNA density, the pH, the ionic strength or the temperature. The melting temperature, T_m, is in part a function of the ionic strength and of the temperature and therefore provides a useful variable in the control of the selectivity and sensitivity of a DNA chip. The electrochemical technique has been used to determine the T_m values when the probe is tethered by a DNA self-assembled monolayer (SAM). We have built a special thin layer cell, which allows the recording of the cyclic voltammogram under controlled temperature conditions. T_m has been determined by recording the thermogram (current versus temperature) of a redox indicator on a double-stranded hybrid (dsDNA) modified electrode and comparison with the corresponding ssDNA response. T_m of supported DNA varies linearly with the ionic strength. The stability of the SAMs has been considered and comparison between T_m in solution and on a solid support has been discussed.     

Effect of atoms evaporated from the anode on the structure of the vacuum arc space charge sheath

The structure of the anode space charge sheath of a vacuum arc is studied with allowance for the dependence of the negative anode fall on the ratio of the directed electron velocity v ₀ to the electron thermal velocity v _T for different values of the flux density of atoms evaporated from the anode. Poisson’s equation for the sheath potential is solved taking into account the electron space charge, fast cathode ions, and slow ions produced due to the ionization of atoms evaporated from the anode. The kinetic equation for atoms and slow anode ions is solved with allowance for ionization in the collision integral. Analytic solutions for the velocity distribution functions of atoms and slow ions and the density of slow ions are obtained. It is shown that the flux of slow ions substantially affects the spatial distribution of the electric field E(z) in the sheath. As the flux density increases, the nonmonotonic dependence E(z) transforms into a monotonic one and the sheath narrows. For a given flux of evaporated atoms Πa, the increase in the ratio of the directed electron velocity to the electron thermal velocity leads again to a nonmonotonic dependence E(z). As z increases, the electric field first increases, passes through the maximum, decreases, passes through the minimum E _min, and then again increases toward the anode. There is a limiting value of the ratio (v ₀/v _T )* at which E _min(z) vanishes. At v ₀/v _T > (v ₀/V _T )*, the condition for the existence of a steady-state sheath is violated and the profiles of the field and potential in the sheath become oscillating. The dependence of (v ₀/v _T )* on the flux density of evaporated atoms Π _a is obtained. It is shown that the domain of existence of steady-state solutions in the sheath broadens with increasing Π _a .     

THE KINETICS OF PENETRATION : I. EQUATIONS FOR THE ENTRANCE OF ELECTROLYTES

When the only solute present is a weak acid, HA, which penetrates as molecules only into a living cell according to a curve of the first order and eventually reaches a true equilibrium we may regard the rate of increase of molecules inside as See PDF for Equation where P_M is the permeability of the protoplasm to molecules, M_o, denotes the external and M_i the internal concentration of molecules, A_i denotes the internal concentration of the anion A^- and See PDF for Equation (It is assumed that the activity coefficients equal 1.) Putting P_MF_M = V_M, the apparent velocity constant of the process, we have See PDF for Equation where e denotes the concentration at equilibrium. Then See PDF for Equation where t is time. The corresponding equation when ions alone enter is See PDF for Equation. where K is the dissociation constant of HA, P_A is the permeability of the protoplasm to the ion pair H⁺ + A^-, and A_ie denotes the internal concentration of A_i at equilibrium. Putting P_AKF_M = V_A, the apparent velocity constant of the process, we have See PDF for Equation and See PDF for Equation When both ions and molecules of HA enter together we have See PDF for Equation where S_i = M_i + A_i and S_ie is the value of S_i at equilibrium. Then See PDF for Equation V_M, V_A, and V_MA depend on F_M and hence on the internal pH value but are independent of the external pH value except as it affects the internal pH value. When the ion pair Na⁺ + A^- penetrates and Na_i = BA_i, we have See PDF for Equation and See PDF for Equation where P _NaA is the permeability of the protoplasm to the ion pair Na⁺ + A^-, Na_o and Na_i are the external and internal concentrations of Na⁺, See PDF for Equation, and V _Na is the apparent velocity constant of the process. Equations are also given for the penetration of: (1) molecules of HA and the ion pair Na⁺ + A^-, (2) the ion pairs H⁺ + A^- and Na⁺ + A^-, (3) molecules of HA and the ion pairs Na⁺ + A^- and H⁺ + A^-. (4) The penetration of molecules of HA together with those of a weak base ZOH. (5) Exchange of ions of the same sign. When a weak electrolyte HA is the only solute present we cannot decide whether molecules alone or molecules and ions enter by comparing the velocity constants at different pH values, since in both cases they will behave alike, remaining constant if F_M is constant and falling off with increase of external pH value if F_M falls off. But if a salt (e.g., NaA) is the only substance penetrating the velocity constant will increase with increase of external pH value: if molecules of HA and the ions of a salt NaA. penetrate together the velocity constant may increase or decrease while the internal pH value rises. The initial rate See PDF for Equation (i.e., the rate when M_i = 0 and A_i = 0) falls off with increase of external pH value if HA alone is present and penetrates as molecules or as ions (or in both forms). But if a salt (e.g., NaA) penetrates the initial rate may in some cases decrease and then increase as the external pH value increases. At equilibrium the value of M_i equals that of M_o (no matter whether molecules alone penetrate, or ions alone, or both together). If the total external concentration (S_o = M_o + A_o) be kept constant a decrease in the external pH value will increase the value of M_o and make a corresponding increase in the rate of entrance and in the value at equilibrium no matter whether molecules alone penetrate, or ions alone, or both together. What is here said of weak acids holds with suitable modifications for weak bases and for amphoteric electrolytes and may also be applied to strong electrolytes.     

Regulation of the Activity of Lactate Dehydrogenases from Four Lactic Acid Bacteria

Despite high similarity in sequence and catalytic properties, the l-lactate dehydrogenases (LDHs) in lactic acid bacteria (LAB) display differences in their regulation that may arise from their adaptation to different habitats. We combined experimental and computational approaches to investigate the effects of fructose 1,6-bisphosphate (FBP), phosphate (P_i), and ionic strength (NaCl concentration) on six LDHs from four LABs studied at pH 6 and pH 7. We found that 1) the extent of activation by FBP (K_act) differs. Lactobacillus plantarum LDH is not regulated by FBP, but the other LDHs are activated with increasing sensitivity in the following order: Enterococcus faecalis LDH2 ≤ Lactococcus lactis LDH2 < E. faecalis LDH1 < L. lactis LDH1 ≤ Streptococcus pyogenes LDH. This trend reflects the electrostatic properties in the allosteric binding site of the LDH enzymes. 2) For L. plantarum, S. pyogenes, and E. faecalis, the effects of P_i are distinguishable from the effect of changing ionic strength by adding NaCl. 3) Addition of P_i inhibits E. faecalis LDH2, whereas in the absence of FBP, P_i is an activator of S. pyogenes LDH, E. faecalis LDH1, and L. lactis LDH1 and LDH2 at pH 6. These effects can be interpreted by considering the computed binding affinities of P_i to the catalytic and allosteric binding sites of the enzymes modeled in protonation states corresponding to pH 6 and pH 7. Overall, the results show a subtle interplay among the effects of P_i, FBP, and pH that results in different regulatory effects on the LDHs of different LABs.     

Simulation of the effect of an external GHz electric field on the potential energy profile of Ca2+ ions in the selectivity filter of the CaVAb channel

Ca_V channels are transmembrane proteins that mediate and regulate ion fluxes across cell membranes, and they are activated in response to action potentials to allow Ca²⁺ influx. Since ion channels are composed of charge or polar groups, an external alternating electric field may affect the ion‐selective membrane transport and the performance of the channel. In this article, we have investigated the effect of an external GHz electric field on the dynamics of calcium ions in the selectivity filter of the Ca_VAb channel. Molecular dynamics (MD) simulations and the potential of mean force (PMF) calculations were carried out, via the umbrella sampling method, to determine the free energy profile of Ca²⁺ ions in the Ca_VAb channels in presence and absence of an external field. Exposing Ca_VAb channel to 1, 2, 3, 4, and 5 GHz electric fields increases the depth of the potential energy well and this may result in an increase in the affinity and strength of Ca²⁺ ions to binding sites in the selectivity filter the channel. This increase of strength of Ca²⁺ ions binding in the selectivity filter may interrupt the mechanism of Ca²⁺ ion conduction, and leads to a reduction of Ca²⁺ ion permeation through the Ca_VAb channel.     

Electron leakage mechanism in a plasma-filled magnetically insulated transmission line

It is shown that relativistic electron current can propagate across the magnetic field B ₀ over a distance d much larger than the electron gyroradius, r ₀ ? m _e v _z c/(eB ₀) ? d. This current is driven by the Hall electric field, which is generated on a spatial scale equal to the magnetic Debye radius r _B = B ₀/(4πen _e) and causes the electrons to drift in crossed electric and magnetic fields. For a plane equilibrium current configuration, analytic profiles of the electron velocity and electron density are calculated and the electric and magnetic fields are determined. The results obtained are used to explain electron leakages in magnetically insulated transmission lines filled with a plasma expanding from the electrodes. Equations describing an equilibrium configuration of the ions and electrons that drift simultaneously across a strong magnetic field are derived.     

The rate of Qx→Qy relaxation in bacteriochlorophylls of reaction centers from Rhodobacter sphaeroides determined by kinetics of the ultrafast carotenoid bandshift

Transient absorption changes induced by excitation of isolated reaction centers (RCs) from Rhodobacter sphaeroides with 600 nm laser pulses of 20 fs (full width at half maximum) were monitored in the wavelength region of 420–560 nm. The spectral features of the spectrum obtained are characteristic for an electrochromic band shift of the single carotenoid (Car) molecule spheroidene, which is an integral constituent of these RCs. This effect is assigned to an electrochromic bandshift of Car due to the local electric field of the dipole moment formed by electronic excitation of bacteriochlorophyll (BChl) molecule(s) in the neighborhood of Car. Based on the known distances between the pigments, the monomeric BChl (B_B) in the inactive B-branch is inferred to dominate this effect. The excitation of B_B at 600 nm leads to a transition into the S₂ state (Q_x band), which is followed by rapid internal conversion to the S₁ state (Q_y band), thus leading to a change of strength and orientation of the dipole moment, i.e., of the electric field acting on the Car molecule. Therefore, the time course of the electrochromic bandshift reflects the rate of the internal conversion from S₂ to S₁ of B_B. The evaluation of the kinetics leads to a value of 30 fs for this relaxation process. This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: from Natural to Artificial.     

Selectivity sequences in a model calcium channel: role of electrostatic field strength

The energetics that give rise to selectivity sequences of ionic binding selectivity of Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺ in a model of a calcium channel are considered. This work generalizes Eisenman’s classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres). The selectivity filter of the model calcium channel allows the carboxyl terminal groups of glutamate and aspartate side chains to directly interact with and coordinate the permeating ions. Ion dehydration effects are represented with a Born energy between the dielectric coefficients of the selectivity filter and the bath. High oxygen concentration creates a high field strength site that prefers small ions, as in Eisenman’s model. On the other hand, a low filter dielectric constant also creates a high field strength site, but this site prefers large ions, contrary to Eisenman’s model. These results indicate that field strength does not have a unique effect on ionic binding selectivity sequences once entropic, electrostatic, and dehydration forces are included in the model. Thus, Eisenman’s classic relationship between field strength and selectivity sequences must be supplemented with additional information about selectivity filters such as the calcium channel that has amino acid side chains mixing with ions to make a crowded permeation pathway.     

On the theory of interfacial double-layer potential differences and periaxonal accumulation of potassium in squid giant axons

The steady state potassium conductance as a function of measured membrane potential difference (p.d.) ? of the squid giant axon is corrected for the effect of accumulation of potassium in the periaxonal space. This correction is made on the assumption that several mathematical models of the axon are valid. These are (i) the McIlroy (1975), McIlroy-Hahn (1978) model of membrane conductanceg _i(i=K, Na) which is a detailed model of passive transport of ions across the axonal membrane with the aid of mobile, negatively-charged carriers, (ii) the Adelmanet al. (1973) compartmental model of the periaxonal and external bathing-solution spaces, (iii) the enzymatic theory of nervous conduction due to McIlroy (1970 a, b, c), (iv) the Wien dissociative effect of the axolemmic electric field on the weak membrane buffer proposed by Bass and Moore (1968) as a trigger mechanism in nervous excitation and (v) the model (McIlroy, 1979) of the interfacial double-layer p.d.s. which are assumed to exist at the membrane’s surfaces because of the presence of a fixed surface charge. From the correctedg _k (?) curves the values of the double-layer p.d.s. of model (v) are deduced and these are shown to lead to a consistent, physically reasonable solution for the distance (approx. 6.8Å) between the fixed surface charges and for the dissociation constants of these sites in their interactions with the ions of the extra-membrane electrolytes. Assuming that the selectivity coefficint of the potassium conducting system for the squid giant axon is approx. 52 it is deduced that the potassium permeability,P _ks , of the periaxonal barrier ≈1.37(±0.5)×10^?4 cm sec^?1 and the thickness of the periaxonal space ≈451±159Å.     

Complexes of vitamin B6. XVI. Kinetics and reaction mechanism of iron(III) complexes with pyridoxal-5′-phosphate

The stopped flow technique has been used to study the kinetics of complex formation of iron(III) with pyridoxal-5-phosphate (PLP) in the pH range 1.00–2.50, and in the temperature range 18 °C– 30 °C, at an ionic strength of. 0.50 M (NaCl). From the initial concentration dependence of PLP (T_PLP,) of the reaction rate it can be shown that two kinetic steps can be represented as: k_obs′ = m_i + m_i′_PLP where m_i and m_i′ are pH-dependent parameters. The calculated activation data are δE* = 23.2 ± 1.8 kcal mol^?1 and 10.98 ± 0.53 kcal mol^?1 for the first and second kinetic steps, respectively and δS* are ?20.50 ± 5.96 e.u. and 24.62 ± 1.81 e.u., respeetively.     

Identification of Amino Acid Residues in the α, β, and γ Subunits of the Epithelial Sodium Channel (ENaC) Involved in Amiloride Block and Ion Permeation

The amiloride-sensitive epithelial Nachannel (ENaC) is a heteromultimeric channel made of three αβγ subunits. The structures involved in the ion permeation pathway have only been partially identified, and the respective contributions of each subunit in the formation of the conduction pore has not yet been established. Using a site-directed mutagenesis approach, we have identified in a short segment preceding the second membrane-spanning domain (the pre-M2 segment) amino acid residues involved in ion permeation and critical for channel block by amiloride. Cys substitutions of Gly residues in β and γ subunits at position βG525 and γG537 increased the apparent inhibitory constant (K _i) for amiloride by >1,000-fold and decreased channel unitary current without affecting ion selectivity. The corresponding mutation S583 to C in the α subunit increased amiloride K _i by 20-fold, without changing channel conducting properties. Coexpression of these mutated αβγ subunits resulted in a nonconducting channel expressed at the cell surface. Finally, these Cys substitutions increased channel affinity for block by externalZn²⁺ ions, in particular the αS583C mutant showing a K _i for Zn²⁺of 29 μM. Mutations of residues αW582L or βG522D also increased amiloride K _i, the later mutation generating a Ca²⁺blocking site located 15% within the membrane electric field. These experiments provide strong evidence that αβγ ENaCs are pore-forming subunits involved in ion permeation through the channel. The pre-M2 segment of αβγ subunits may form a pore loop structure at the extracellular face of the channel, where amiloride binds within the channel lumen. We propose that amiloride interacts with Na⁺ions at an external Na⁺binding site preventing ion permeation through the channel pore.     

Study of Electromagnetic Electron Cyclotron Waves for Kappa Distribution with AC Field in the Magnetosphere of Saturn

Parallel propagating electromagnetic electron cyclotron (EMEC) waves in the extended plasma sheet (~12R_S) and in the outer magnetosphere (~18R_S) of Saturn have been studied. A dispersion relation for parallel propagating relativistic EMEC waves has been applied to the magnetosphere of Saturn, and comparisons have been made with the data of Voyager 1 at these radial distances. The detailed investigations for EMEC waves have been done in the presence of the perpendicular AC electric field, using the kappa distribution function. The relativistic temporal growth rate is calculated by the method of characteristic solution with the data provided by Voyager 1. The effect of the suprathermal electron density, temperature anisotropy, frequency of AC electric field, thermal energy of ions, and relativistic factor on the temporal growth rate of EMEC wave emission has been studied. The simulation results show that the growth of parallel propagating EMEC waves is significantly affected by variations in the temperature anisotropy, electron density, ion thermal energy, and relativistic factor in both the extended plasma sheet and the outer magnetosphere of Saturn. The temperature anisotropy (T⊥/T_║), ion thermal energy (K_BT_║i), and electron density (n₀) have been found to be a major source of free energy for parallel propagating EMEC waves in both regions.