Current noise generated by electrogenic ion pumps

Active ion transport by ATP-or light-driven pumps involves a sequence of elementary steps such as binding and release of ions, as well as conformational transitions of the pump protein. At the microscopic level the individual reaction steps occur at random intervals, and therefore the current generated by electrogenic pumps fluctuates around a mean value. In this paper, a theoretical treatment of the electrical noise associated with active ion transport is given. The analysis, which is based on the calculation of the correlation function, yields the spectral intensity S ₁ of current noise as a function of frequency, f. The shape of S _I(f) contains information on the rate constants as well as on the magnitude of the charge displacements occuring during single reaction steps. The contribution of electrogenic pumps to the total voltage noise of the cell may be estimated from S _I(f) and from the frequency-dependent impedance of the cell membrane.     

The mathematical model of concentration polarization coefficient in membrane transport and volume flows

In this paper, the authors investigate the membrane transport of aqueous non-electrolyte solutions in a single-membrane system with the membrane mounted horizontally. The purpose of the research is to analyze the influence of volume flows on the process of forming concentration boundary layers (CBLs). A mathematical model is provided to calculate dependences of a concentration polarization coefficient (ζ _s ) on a volume flux (J _vm ), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζ _s ?=?f(J _vm ) for J _vm ?>?0 and for J _vm ?≈?0 and property ζ _s ?=?f(ΔC ₁) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζ _s when J _vm ?=?0 and J _vm ?≠?0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζ _s and a concentration Rayleigh number (R _C ) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.     

Derivation of the equations that describe the effects of unstirred water layers on the kinetic parameters of active transport processes in the intestine

Unidirectional flux of solutes into the intestinal mucosal cells is determined by the rate of movement of these molecules across both an unstirred water layer and the microvillus membrane of the epithelial cell. Therefore, an equation is derived in this paper that describes the velocity of active transport as a function of the characteristics of both the transport carrier in the membrane and the resistance of the overlying unstirred water layer. Using this equation a series of curves are presented that depict the effect on the kinetics of active transport of varying the thickness (d) or surface area (S_w) of the unstirred water layer, the free diffusion coefficient (D) of the solute, the distribution of active transport sites along the villus ($\text{?}{}_{\mathrm{<mtext>n</mtext>}}$), the maximal transport velocity (J^m_d) and the true Michaelis constant (K_m). These theoretical curves illustrate the serious limitations inherent in interpretation of previously published data dealing with active transport processes in the intestine.     

Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions

Summary In the presence of the hydrophobic ion dipicrylamine, lipid bilayer membranes exhibit a characteristic type of noise spectrum which is different from other forms of noise described so far. The spectral density of current noise measured at zero voltage increases in proportion to the square of frequency at low frequencies and becomes constant at high frequencies. The observed form of the noise spectrum can be interpreted on the basis of a transport model for hydrophobic ions in which it is assumed that the ions are adsorbed in potential-energy minima at either membrane surface and are able to cross the central energy barrier by thermal activation. Accordingly, current-noise results from random fluctuations in the number of ions jumping over the barrier from right to left and from left to right. On the basis of this model the rate constantk _i for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentrationN _t of adsorbed ions may be caluculated from the observed spectral intensity of current noise. The values ofk _i obtained in this way closely agree with the results of previous relaxation experiments. A similar, although less quantitative, agreement is also found for the surface concentrationN _t .     

Energetics of Active Transport Processes

Discussions of active transport usually assume stoichiometry between the rate of transport J₊ and the metabolic rate J_r. However, the observation of a linear relationship between J₊ and J_r does not imply a stoichiometric relationship, i.e., complete coupling. Since coupling may possibly be incomplete, we examine systems of an arbitrary degree of coupling q, regarding stoichiometry as a limiting case. We consider a sodium pump, with J₊ and J_r linear functions of the electrochemical potential difference, -X₊, and the chemical affinity of the metabolic driving reaction, A. The affinity is well defined even for various complex reaction pathways. Incorporation of a series barrier and a parallel leak does not affect the linearity of the composite observable system. The affinity of some region of the metabolic chain may be maintained constant, either by large pools of reactants or by regulation. If so, this affinity can be evaluated by two independent methods. Sodium transport is conveniently characterized by the open-circuit potential (Δψ)_I=0 and the natural limits, level flow (J₊)_X+=0, and static head X⁰₊ = (X₊)_J+=0. With high degrees of coupling -X⁰₊/F approaches the electromotive force E_Na (Ussing); -X⁰₊/F cannot be identified with ((RT/F) ln f)_X+=0, where f is the flux ratio. The efficiency η = -J₊X₊/J_rA is of significance only when appreciable energy is being converted from one form to another. When either J₊ or -X₊ is small η is low; the significant parameters are then the efficacies ε_J+ = J₊/J_rA and ε_X+ = -X₊/J_rA, respectively maximal at level flow and static head. Leak increases both J₊ and ε_J+ for isotonic saline reabsorption, but diminishes -X⁰₊ and ε_X♀. Electrical resistance reflects both passive parameters and metabolism. Various fundamental relations are preserved despite coupling of passive ion and water flows.     

Competitive blocking of apical sodium channels in epithelia

Apical sodium-selective channels in frog skin, when blocked by amiloride or triamterene, exhibit fluctuations in current, the spectra of which are Lorentzian. These effects have been modeled previously with two-state and three-state models by Lindemann and Van Driessche. A recent observation by Hoshiko and Van Driessche that corner frequencies are lowered by increasing the apical sodium concentration cannot be accounted for by these models. We explore the possibility that sodium (S) and amiloride (A) compete for a site at the mouth of the channel. A new three-state channel model (sodium-occupied, open/unoccupied, open/amiloride-blocked) is analyzed. Its corner frequency is of the form f_c = f_co[1 + (A/K_A)/(1 + S/K_S)], consistent with the observed sodium dependence of the corner frequency. The minimum frequency, f_co, and the inhibition constants, K_A and K_S, are expressed in terms of the rate constants of the model. To account for sodium self-inhibition, we postulate that two sodium ions in the channel may result in clogging — a fourth state. The two corner frequencies are calculated; so are the plateau values of the noise power. The noise power shows a maximum as a function of blocker concentration, as observed previously using triamterene. The four-state model predicts the observed suppression by small amounts of blocker of the low-frequency sodium (clogging) noise.     

A laser-temperature-jump method for the study of the rate of transfer of hydrophobic ions and carriers across the interface of thin lipid membranes

The first application of a laser-temperature-jump apparatus for the study of ion transport through planar (artificial) lipid membranes is described. The relaxation of the electric current is detected, either continuously at a constant applied voltage or discontinuously by a series of short voltage pulses. The second technique, a combined voltage- and temperature-jump method, is especially appropriate to investigate the kinetics of the adsorption/desorption process of hydrophobic ions and neutral carriers of cations at the membrane interface and to separate this phenomenon from the diffusion process through the unstirred aqueous layers adjacent to the membrane. The aim is to determine the rate-limiting step of transport. The permeation rate of the hydrophobic anion 2,4,6-trinitrophenolate is limited by the inner membrane barrier. For tetraphenylberate the rate constant of translocation across the inner barrier and that of desorption from the membrane into water are found to be of comparable magnitude. The membrane permeability of the neutral macrocyclic ion carrier enniatin B is strongly interface limited by its comparatively small rate of desorption into water. These results show that the frequently used a priori assumption of partition equilibrium at the membrane interfaces during transport is not justified.     

Formation of Solid–Electrolyte Interfaces in Aqueous Electrolytes by Altering Cation‐Solvation Shell Structure

Aqueous lithium/sodium‐ion batteries (AIBs) have received increasing attention because of their intrinsic safety. However, the narrow electrochemical stability window (1.23 V) of the aqueous electrolyte significantly hinders the development of AIBs, especially the choice of electrode materials. Here, an aqueous electrolyte composed of LiClO₄, urea, and H₂O, which allows the electrochemical stability window to be expanded to 3.0 V, is developed. Novel [Li (H₂O)_x(organic)_y]⁺ primary solvation sheath structures are developed in this aqueous electrolyte, which contribute to the formation of solid–electrolyte interface layers on the surfaces of both the cathode and anode. The expanded electrochemical stability window enables the construction of full aqueous Li‐ion batteries with LiMn₂O₄ cathodes and Mo₆S₈ anodes, demonstrating an operating voltage of 2.1 V and stability over 2000 cycles. Furthermore, a symmetric aqueous Na‐ion battery using Na₃V₂(PO₄)₃ as both the cathode and anode exhibits operating voltage of 1.7 V and stability over 1000 cycles at a rate of 5 C.     

Membrane voltage as a dynamic platform for spatiotemporal signaling,physiological, and developmental regulation

Membrane voltage arises from the transport of ions through ion-translocating ATPases, ion-coupled transport of solutes, and ion channels, and is an integral part of the bioenergetic “currency” of the membrane. The dynamics of membrane voltage—so-called action, systemic, and variation potentials—have also led to a recognition of their contributions to signal transduction, both within cells and across tissues. Here, we review the origins of our understanding of membrane voltage and its place as a central element in regulating transport and signal transmission. We stress the importance of understanding voltage as a common intermediate that acts both as a driving force for transport—an electrical “substrate”—and as a product of charge flux across the membrane, thereby interconnecting all charge-carrying transport across the membrane. The voltage interconnection is vital to signaling via second messengers that rely on ion flux, including cytosolic free Ca²⁺, H⁺, and the synthesis of reactive oxygen species generated by integral membrane, respiratory burst oxidases. These characteristics inform on the ways in which long-distance voltage signals and voltage oscillations give rise to unique gene expression patterns and influence physiological, developmental, and adaptive responses such as systemic acquired resistance to pathogens and to insect herbivory.

Membrane voltage serves as a platform coordinating ion flux to transmit and transduce biological signals.

Advances

• The biophysics of transport that determine membrane voltage are well-described with quantitative flux equations.
• In the models of the guard cell and the giant algae Chara and Nitella these charge-transporting processes accurately describe and predict physiological behavior, including the coupling of membrane voltage oscillations with ion flux, [Ca²⁺]_i, pH, their consequences for cellular osmotic adjustments, and their spatial propagation.
• Unlike neuronal and other animal tissues, action potentials in plants are mediated by a temporal sequence of ion flux through Ca²⁺ and Cl^- channels with voltage recovery driven by ion flux through K⁺ channels. The interplay of channel-mediated ion flux and changes in H⁺-ATPase activity are likely responsible for the slower propagation of variation and systemic potentials.
• In terrestrial plants, membrane voltage transients may propagate along vascular traces, both through the parenchymal cells lining the xylem and through the phloem. Propagation of such voltage transients is associated with glutamate receptor-like channels that may contribute to plasma membrane Ca²⁺ flux and [Ca²⁺]_i elevations.
• Changes in [Ca²⁺]_i, pH, and reactive oxygen species are key mediators that translate voltage signals into physiological, developmental, and adaptive responses in plant tissues.

     

Supramolecular manganese(II) compounds influenced by conformational flexibility and rigidity of bis(4-pyridyl) containing bridging ligands

A covalent-bonded one-dimensional (1D) chain, [Mn(bpe)₂(SCN)₂]_n (1) [bpe=1,2-bis(4-pyridyl)ethane], and a hydrogen-bonded two-dimensional (2D) sheet, [Mn(tbp)₂(H₂O)₂(SCN)₂] (2) [tbp=trans-1,2-bis(4-pyridyl)ethylene], have been prepared. Complex 1 can be viewed as a purely coordinative-bonded 1D motif doubly bridged by the bpe ligand that is a gauche conformational isomer with a large dihedral angle of 73.9°. The two bridging bpe ligands feature a shape of square with a dimension of 10.064 Å × 9.776 Å. The compound 2 possesses non-covalent bonding forces of hydrogen bonds and π-π interactions responsible for the fabrication of the 2D architecture. Magnetic susceptibility data for 1 were fitted by employing the infinite chain model (H=−J∑S_i·S_i+1) to give parameters of J=−0.052 cm⁻¹ and g=2.00, indicating the presence of a weak anti-ferromagnetic coupling.     

Concentration Dependence of Permeability Coefficients to an Electrolyte Component across Bovine Lens Capsule In Vitro

Theoretical and experimental studies have been made on permeability coefficients to various kinds of electrolyte across lens capsules that are dissected from bovine eyes and that are found to be positively fixed charged membranes from our experiments of membrane potentials. The differential permeability coefficient, P_m, is defined as J_s = P_m(C₂ - C₁), where J_s is the flux of an electrolyte component in moles per sec across unit area of the lens capsule that separates two aqueous solutions of the same electrolyte at different concentrations, C₂ and C₁. Various types of strong electrolytes were studied; KCl, NaCl, Cacl₂, MgSO₄, MgCl₂ and LaCl₃. It was found that at C₂/C₁ = constant, P_m decreases to zero as C₂ decreases and P_m increases to a limiting value, (P_m)^∞, that is characteristic for the system of the salt used and the membrane as C₂ increases, despite of electrolytes. We assumed in theory that single ion activity coefficients of co-ion and gegen-ion are ideal, that the systems studied are in electric neutrality, that the fixed charge density of the membrane is independent of concentrations C₂, and that Donnan equilibrium holds between the bulk solution and membrane surface. Although the concentration-dependent changes of P_m were quantitatively different depending on the type of electrolyte used, general agreement between theory and experiment was obtained over a wide range of concentrations except for the case of very dilute solutions.     

Water-water cycle involved in dissipation of excess photon energy in phosphorus deficient rice leaves

The water-water cycle which may be helpful for dissipating the excitation pressure over electron transport chain and minimizing the risk of photoinhibition and photodamage was investigated in rice after 10-d P-deficient treatment. Net photosynthetic rate decreased under P-deficiency, thus the absorption of photon energy exceeded the energy required for CO₂ assimilation. A more sensitive response of effective quantum yield of photosystem 2 (Φ_PS2) to O₂ concentration was observed in plants that suffered P starvation, indicating that more electrons were transported to O₂ in the P-deficient leaves. The electron transport rate through photosystem 2 (PS 2) (J_f) was stable, and the fraction of electron transport rate required to sustain CO₂ assimilation and photorespiration (J_g/J_f) was significantly decreased accompanied by an increase in the alternative electron transport (J_a/J_f), indicating that a considerable electron amount had been transported to O₂ during the water-water cycle in the P-deficient leaves. However, the fraction of electron transport to photorespiration (J_o/J_f) was also increased in the P-deficient leaves and it was less sensitive than that of water-water cycle. Therefore, water-water cycle could serve as an efficient electron sink. The higher non-photochemical fluorescence quenching (q_N) in the P-deficient leaves depended on O₂ concentration, suggesting that the water-water cycle might also contribute to non-radiative energy dissipation. Hence, the enhanced activity of the water-water cycle is important for protecting photosynthetic apparatus under P-deficiency in rice.     

Random currents through nerve membranes

The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a onedimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits “1/f ^3/2 noise”. Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.     

Iterative linear integral isoconversional method: theory and application

In this work, the theory of the iterative linear integral isoconversional method was illustrated in detail. This method allows the dependence of the activation energy (E_α) on the conversion degree to be accurately determined in a short time. Moreover, the method can yield the term [A_αf(α)] (A_α: the frequency factor at conversion α, f(α): the reaction model). The obtained E_α and [A_αf(α)] values can be used to reconstruct the kinetic conversion data at experimental and extrapolated conditions. The suggested method was applied to the experimental data of combustion of biomass fast pyrolysis char, and the corresponding kinetic parameters were obtained.     

The effect of amphotericin B on the water and nonelectrolyte permeability of thin lipid membranes

This paper reports the effects of amphotericin B, a polyene antibiotic, on the water and nonelectrolyte permeability of optically black, thin lipid membranes formed from sheep red blood cell lipids dissolved in decane. The permeability coefficients for the diffusion of water and nonelectrolytes (P_DDi) were estimated from unidirectional tracer fluxes when net water flow (J_w) was zero. Alternatively, an osmotic water permeability coefficient (P_f) was computed from J_w when the two aqueous phases contained unequal solute concentrations. In the absence of amphotericin B, when the membrane solutions contained equimolar amounts of cholesterol and phospholipid, P_f was 22.9 ± 4.6 µsec^-1 and P _DDHDH2O was 10.8 ± 2.4 µsec^-1. Furthermore, P_DDi was < 0.05 µsec^-1 for urea, glycerol, ribose, arabinose, glucose, and sucrose, and σ_i, the reflection coefficient of each of these solutes was one. When amphotericin B (10^-6 M) was present in the aqueous phases and the membrane solutions contained equimolar amounts of cholesterol and phospholipid, P _DDHDH2O was 18.1 ± 2.4 µsec^-1; P_f was 549 ± 143 µsec^-1 when glucose, sucrose, and raffinose were the aqueous solutes. Concomitantly, P_DDi varied inversely, and σ_i directly, with the effective hydrodynamic radii of the solutes tested. These polyene-dependent phenomena required the presence of cholesterol in the membrane solutions. These data were analyzed in terms of restricted diffusion and filtration through uniform right circular cylinders, and were compatible with the hypothesis that the interactions of amphotericin B with membrane-bound cholesterol result in the formation of pores whose equivalent radii are in the range 7 to 10.5 A.     

Phosphorus deprivation effects on water relations of <Emphasis Type="Italic">Nicotiana tabacum</Emphasis> plant via reducing plasma membrane permeability

Plants grown in phosphorus-deprived solutions often exhibit disruption of water transport due to reduction in root hydraulic conductivity (Lp_r). To uncover the relationship between root Lp_r and water permeability coefficient (P_f) of plasma membrane and the role of aquaporins, we evaluated P_f of plasma membrane and also PIP-type aquaporin gene expression in tobacco (Nicotiana tabacum L.) plant roots after seven days P-deprivation. The results showed significant reduction in sap flow rate (J_v) and osmotic root hydraulic conductivity (L_pr-o) in P-deprived roots. These effects were reversed 24 h after P-resupplying. Interestingly, the P_f of root protoplasts was 57% lower in P-deprived plants compared with P-sufficient ones. The expression of NtPIP1;1 and NtPIP2;1 aquaporins did not change significantly in P-deprived plants compared with P-sufficient ones, but the copy number of NtAQP1 increased significantly in P-deprived plants. P-deprivation did not change Lpr-o significantly in antisense NtAQP1 plants. Taken together, these findings suggest that P-deprivation may play an important role in modulation of root hydraulic conductivity by affecting P_f in transcellular pathway of water flow across roots and aquaporins. Finally, we concluded that dominant water transport pathway under P-deprivation was transcellular one.     

Topological control of the spin coupling in dinuclear copper(II) complexes with meta- and para-phenylenediamine bridging ligands

A novel series of copper(II) complexes of formula [Cu(tren)(mpda)](ClO₄)₂ · 1/2H₂O (1), [Cu₂(tren)₂(mpda)](ClO₄)₄ · 2H₂O (2), and [Cu₂(tren)₂(ppda)](ClO₄)₄ · 2H₂O (3) containing the tetradentate tris(2-aminoethyl)amine (tren) terminal ligand and the potentially bridging 1,n-phenylenediamine [n = 3 (mpda) and 4 (ppda)] ligand have been prepared and spectroscopically characterized. X-ray diffraction on single crystals of 1 and 3 show the presence of mono- (1) and dinuclear (3) copper(II) units where the mpda (1) and ppda (3) ligands adopt terminal monodentate (1) and bridging bis(monodentate) (3) coordination modes toward [Cu(tren)]²⁺ cations with an overall non-planar, orthogonal disposition of the phenylene group and the N-Cu-N threefold axis of the trigonal bipyramid of each copper(II) ion [values of the Cu-N-C-C torsion angle (?) in the range of 50.8(3)-79.2(2) (1) and 80.9(2)-86.5(2)° (3)]. Variable-temperature magnetic susceptibility measurements on the dinuclear complexes 2 and 3 show the occurrence of moderate ferromagnetic (J = +8.3 cm⁻¹, 2) and strong antiferromagnetic (J = −51.4 cm⁻¹, 3) couplings between the two copper(II) ions across the meta- and para-phenylenediamine bridges, leading to S = 1 (2) and S = 0 (3) ground spin states [H = −JS₁ · S₂ with S₁ = S₂ = S_Cu = 1/2]. Density functional theory (DFT) calculations on the triplet (2) and broken-symmetry (BS) singlet (3) ground spin states, support the occurrence of a spin polarization mechanism for the propagation of the exchange interaction through the predominantly π-type orbital pathway of the 1,n-phenylenediamine bridge. Finally, a new magneto-structural correlation between the magnitude of the magnetic coupling (J) and the Cu-N-C-C torsion angle (?) has been found which reveals the role of σ- versus π-type orbital pathways in the modulation of the magnetic coupling for m- and p-phenylenediamine-bridged dicopper(II) complexes.     

A comparison of the effects of ouabain and 2-deoxy-d-glucose on the thermodynamic variables of the frog skin

Previous studies support the validity of a linear thermodynamic formalism relating the rates of active Na⁺ transport and oxygen consumption J_r to the electrical potential difference ΔΨ an the affinity α (negative free energy) of the metabolic driving reaction. The formulation was further tested in paired control and experimental hemiskins by the use of two inhibitors of Na⁺ transport. Ouabain, a specific inhibitor of the Na⁺ pump, might be expected to diminish the dependence of J_r on ΔΨ without affecting α, whereas 2-deoxy-d-glucose, a competitive inhibitor of glucose metabolism, should be expected to diminish α. Both inhibitors were used at concentrations adequate to depress Na⁺ transport (i.e. short-circuit current J_o) to some 50°_o of control level. Measurements were made of I_o and $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$, and the apparent value of the affinity α_app was calculated according to the thermodynamic formulation. Ouabain depressed $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$ without affecting α_app whereas 2-deoxy-d-glucose depressed α_app without affecting $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(αΨ)}$. The demonstration of these effects indicates the utility of the formalism.     

Partitioning of taxifolin-iron ions complexes in octanol-water system

The composition of taxifolin-iron ions complexes in an octanol-water biphasic system was studied using the method of absorption spectrophotometry. It was found that at pH 5.0 in an aqueous biphasic system the complex of [Tf · Fe₂(OH) _k (H₂O)_{8 ? k} ] is present, but at pH 7.0 and 9.0 the complexes of [Tf₂ · Fe(OH) _k (H₂O)_{2 ? k} ] and [Tf · Fe(OH) _k (H₂O)_{4 ? k} ] are predominantly observed. The formation of a stable [Tf₃ · Fe] complex occurred in octanol phase. The charged iron ion of this complex is surrounded by taxifolin molecules, which shield the iron ion from lipophilic solvent. During transition from water to octanol phase the changes of the composition of complexes are accompanied by reciprocal changes in portion of taxifolin and iron ions in these phases. It was shown that the portion of taxifolin in aqueous solution in the presence of iron ions is increased at high pH values, and the portion of iron ions is minimal at pH 7.0. In addition, the parameters of solubility limits of taxifoliniron ions complexes in an aqueous solution were determined. The data obtained gain a better understanding of the role of complexation of polyphenol with metal of variable valency in passive transport of flavonoids and metal ions across lipid membranes.     

Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential,Soma Membrane Current and Single-Neuron Contribution to the EEG

Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.