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

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 in 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 constant ki for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentration Nt of adsorbed ions may be calculated from the observed spectral intensity of current noise. The values of ki 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 concentration Nt.     

The volumes of some compartment systems with sampling and loss from one compartment

If the concentrationc ₁(t)=∑ _i=1 ⁿ A _i exp (−α _i t) for one compartment, one presumes a linear catenaryn-compartment system without sinks and loss only from the same compartment, then the volumesV _i , rate constantsk _ij , and concentrationsc _i (t) in each compartment can be determined in terms of theA _i 's,A _i ′s, α _i ′s, the dose injectedD _o and the partition coefficientsr _ij =k _ij /k _ji . If the concentration would become uniform at equilibrium, then the total volume of distribution may be determined without knowledge ofr _ij or restriction to catenary configuration.     

Kinetic study on unzippering of polynucleotides and order-order transition in polypeptides

Solutions are presented for N + 1 sequential and reversible first-order reactions for which the magnitude of the reverse rate constant, k_b, for all steps except the last is identical. Also the magnitude of the forward rate constant, k_f, for all steps except the first and last is identical. The initial and final steps are nucleation reactions; therefore, the initial and final k_f are modified by the factors σ′ and γ respectively. The final k_b is modified by the factor γ σ. The ratio k_b/k_f is defined as s, which has the same meaning as s in the Zimm-Bragg theory. The mathematical model is intended to apply to polymeric molecules of N segments and allows the calculation of the mole fraction of molecules in state i at any time t, C_i(t). A molecule in state i has i unreacted segments and N – i reacted ones. Because the reactions are sequential, all reacted segments are contiguous. Our numerical results show that when σ′ is much less than unity and the forward reaction is favored, the relaxation curve is sigmoidal. If, however, the forward and reverse reactions are equally favored (i.e., s ? 1) the relaxation curve is a straight line. When s and σ′ are near unity, the curve is exponential for a considerably large fraction of the reaction. Further, in the exponential for a considerably large fraction of the reaction. Further, in the exponential phase of the reaction, the relaxation time is proportional to N² for highly cooperative systems (i.e., Nσ ? 1). As found by Pipkin and Gibbs, if N is sufficiently large and s is less than unity (e.g., N ? 50 and s ?0.9) the relaxation curve is largely linear with a slope inversely proportional to N. Applications are given for the unwinding of double-helical poly(A·U) and the order–order transition in poly-L -proline.     

Soil organic matter and the indigenous nitrogen supply of intensive irrigated rice systems in the tropics

Soil organic matter (SOM) has been proposed as an index of N supply in paddy soils although field validations are few. We evaluated the relationship between the indigenous N supply (N _i ) of the soil-floodwater system and soil organic carbon (SOC) or total N (N _t ) in surface soil of long-term fertility experiments (LTFEs) at 11 sites, in 42 farmer's fiels with similar soil type, and in the same field in ten consecutive rice (Oryza sativa L.) crops. The N _i was estimated by crop N uptake from plots without applied N (N _o plots) under otherwise favorable growth conditions. There was a tight linear correlation between yields and N uptake in N _o plots and tremendous variation in both parameters among LTFE sites, farmer's fields, and in the same field over time. Correlation between N _i and SOC or N _t explained little of this variation. Factors likely to contribute to the poor correlation were: (1) inputs of N from sources other than N mineralization of SOM in surface soil, (2) degree of congruence between soil N supply and crop demand, which is sensitive to soil drying, length of fallow, crop rotation, and residue management, and (3) differences in SOM quality related to intensive cropping in submerged soil. Better understanding of the processes governing the N _i of tropical lowland rice systems would contribute to the development of crop management practices that optimize utilization of indigenous N resources.     

Rate constants of acetylcholine receptor internalization and degradation in mouse muscles

The rate constants for internalization and subsequent extrusion of acetylcholine receptors (AChRs) during degradation in adult innervated and denervated mouse diaphragm muscles were determined using proteinase K (PK) digestion. This procedure separated ¹²⁵I-α-bungarotoxin (Bgt)-labeled AChRs into PK-sensitive and PK-resistant compartments. The time course of the residual radioactivity in these two compartments suggested that they represented surface membrane and internalized compartments, respectively. The data were compatible with a mathematical model based on the assumption that during degradation of AChRs a surface compartment, A, fed an internal compartment, B, with an internalization rate constant (k_i), and that B is drained from the cell with an extrusion rate constant (k_o). Using the mathematical model, we were able to determine that k_i and k_o were, respectively, 0.068 (t_1/2 ∼ 10.2 days) and 0.69–0.55 (t_1/2 ∼ 1.0– 1.25 days) for innervated muscle and were, respectively, 0.69 (t_1/2 ∼ 1.0 day) and 6.93 (t_1/2 ∼ 0.1day) for denervated muscle. Thus, the rate for internalization was about 8–10 times slower than that for extrusion from the cell for both the slowly degrading innervated (Rs) AChRs and for the rapidly degrading denervated (Rr) AChRs. This inequality betweeen k_i and k_o therefore allows the combined quantity of A(t) + B(t) , usually measured in AChR degradation studies, to approximate a single exponential. J. Cell. Physiol. 181:107–112, 1999. © 1999 Wiley-Liss, Inc.     

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

On the use of non-linear regression with the logistic equation for changes with time of percentage root length colonized by arbuscular mycorrhizal fungi

For the regression of sigmoid-shaped responses with time t of colonization C of roots by arbuscular mycorrhizal fungi, C=C _p/1+[e ^−k(t−ti) ] is the most useful form of the logistic equation. At the time of inflection t _i the slope is maximal and directly proportional to the product of the colonization plateau C _p and the abruptness k of the curve. Coefficient k has a high value when the curve rises abruptly following and preceding long shallow phases. The logistic equation has a curve that is symmetrical about t _i such that C=C _p/2 at inflection. Although the logistic equation can generate a good fit to many data sets for changes in colonization with time, there are cases that are not sigmoid and the logistic equation does not apply. For sigmoid curves, the lag in the development of colonization is directly related to both t _i and k but not to the plateau and not to the value of the maximum slope. Higher values of k or t _i reflect longer lag. When considered alone, t _i and k do not fully summarize the lag in colonization, and so a numerical method to combine them is presented here which allows lag to be compared between curves. In this method, the lag is evaluated by calculating the time during early colonization when the slope equals half of the value of the maximum slope. In summary, use of the logistic equation for regression of sigmoid curves of colonization with time allows numerical comparison between curves of the lag, the period of steep ascent, and the plateau. The logistic equation does not model directly the fundamental processes at work in the development of the mycorrhizae. Instead, it can be used as described here to gain insight into the colonization process by comparing the dynamics of that colonization for different species under various conditions. Accepted: 20 October 2000     

Simulations of Flexible Manifolds

Monte Carlo simulations of flexible two-dimensional model membranes embedded in three space dimensions are reported. We explain in detail the techniques how to simulate fluid open membranes and fluid closed membranes (vesicles). It is shown that polymerized open membranes are rough and flat. Accordingly, the two larger components of the inertia tensor are proportional to the number of monomers of the surface, λ₃ ≈ λ₂ ～ N, whereas the smallest λ₁ ～ N ^0.65. Polymerized vesicles are isotropic and their mean square radius of gyration is R ² ～ λ _k ～ N. In contrast, fluid membranes and vesicles exhibit crumpled shapes with λ _k ～ N ^0.8 for k = 1,2,3. A monomer on a fluid surface exhibits a time-dependent mean squared displacement of r ² (t) ～ t ^0.8.     

Intracellular ionic activities in frog skin

Summary Asymmetrical displacement currents are measured in the absence and in the presence of the lipophilic anion dipicrylamine (DPA) in the extracellular solution of nerve fibres of the frogRana esculenta. DPA (30nM-3 M) enhances the current by a component that has the properties expected for a translocation current of DPA ion across the lipid membrane. Analysis in terms of a single-barrier model yields the translocation rate constant (k), the total surface density of DPA absorbed to the membrane (N _t ), and the equidistribution voltage (). The value ofk of about 10⁴ s^–1 is similar to that for a solvent-free artificial bilayer formed by the Montal-Mueller method. The surface densityN _t varies with the DPA concentration as it does in the artificial bilayer, but is about tenfold smaller at all concentrations. The DPA ions sense an intrinsic electric field that is offset by a transmembrane voltage between 0 and 30 mV (inside positive). The part of the axolemma probed by the DPA ion appears as a thin (<2.5 nm), fluid bilayer of lipids. DPA ions seem, however, to be excluded from the major part of the axolemma as if this area is occupied by integral proteins or negative charges.     

On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

Drift variances of FSTand GST statistics obtained from a finite number of isolated populations

Approximate formulas for the mean and variance of the F_STor G_ST statistic in a finite number of isolated populations are developed under the effect of random genetic drift. Computer simulation has shown that the approximate formulas give a fairly accurate result unless the initial frequency of one of the alleles involved is close to 1 and t/2N is large, where N is the effective size of a subpopulation and t is the number of generations. It is shown that when the number of subpopulations (s) is small, the mean of F_STor G_ST depends on the initial gene frequencies as well as on s. When the initial frequencies of all alleles are nearly equal to each other and the number of subpopulations is large, the distribution of F_ST in the early generations is bell-shaped. In this case Lewontin and Krakauer's k parameter is approximately 2 or less. However, if one of the initial allele frequencies is close to 1, the distribution is skewed and leptokurtic, and the k parameter often becomes larger than 2 in later generations. Thus, even under pure random genetic drift, Lewontin and Krakauer's test of selective neutrality of polymorphic genes in terms of F_ST is not always valid. It is also shown that Jacquard's approximate formula for k generally gives an overestimate.     

The gas washout determination under a symmetry assumption

In an open circuit gas washout determination the output of test substance is shown to be of the form ∑ _i=0 ^∞ A _i λ _i ^k on thekth expiration whereA _i >0,i=1,2,... and 1 > λ₁ ≥ λ₂...≥ 0 provided the transition from inspiration to expiration has certain symmetry properties with the transition from expiration to inspiration. In general, no direct physical interpretation such as volume for theA _t ’s or fraction of retained gas on expiration for the λ _i is justified.     

Transport kinetics of hydrophobic ions in lipid bilayer membranes Charge-pulse relaxation studies

A modified version of the charge-pulse relaxation technique with improved time resolution was applied to the study of transport kinetics of hydrophobic ions (tetraphenylborate, dipicrylamine) through lipid bilayer membranes. Besides a better time resolution the charge-pulse method has the additional advantage that the perturbation of the membrane can be kept small (voltage amplitudes between 1 and 10 mV). The results of the analysis support the model proposed earlier, according to which the overall transport takes place in three consecutive steps, adsorption of the ion from water to the interface, translocation to the opposite interface, and desorption into the aqueous phase. The translocation rate constant K_i and the partition coefficient γ of the hydrophobic ion between water and the membrane were measured for lecithins with different mono-unsaturated fatty acid residues. Increasing the chain length of the fatty acid from C₁₆ to C₂₄ resulted in a decrease of k_i by a factor of about 9 in the case of tetraphenylborate and by a factor of about 17 in the case of dipicrylamine.     

Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors

Given independent multivariate random samples {X_ij: j = 1, …, n_i} from F_i, for i = 1,2, a test is desired for H₀: F₁ = F₂ against general alternatives. Consider the k · (n₁ + n₂) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let S_k be the proportion of these choices in which the point and neighbor are in the same sample. Schilling (1986) proposed S_k as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N Σ kS_k, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two-sample U-statistics of degrees (1, 2) and (2, 1). Simulation with multivariate normal data suggests that our test is generally more powerful than Schilling's test using k = 1, 2, or 3. We illustrate its use with Fisher's iris data.     

Determination of the optimum operating time for batch isothermal performance of enzyme-catalyzed multisubstrate reactions

This communication consists of a mathematical analysis encompassing the maximization of the average rate of monomer production in a batch reactor performing an enzymatic reaction in a system consisting of a multiplicity of polymeric substrates which compete with one another for the active site of a soluble enzyme, under the assumption that the form of the rate expression is consistent with the Michaelis-Menten mechanism. The general form for the functional dependence of the various substrate concentrations on time is obtained in dimensionless form using matrix terminology; the optimum batch time is found for a simpler situation and the effect of various process and system variables thereon is discussed. The reasoning developed here emphasizes, in a quantitative fashion, the fact that the commonly used lumped substrate approaches lead to nonconservative decisions in industrial practice, and hence should be avoided when searching for trustworthy estimates of optimum operation.List of Symbols O 1/s row vector of zeros - a 1/s row vector of rate constants k _i(i = 2,...,N) - A 1/s matrix of rate constants k _i and k_–i (i=2,...,N) - b 1/s row vector of rate constant k ₂ and zeros - C mol/m³ molar concentration of S - C mol/m³ vector of molar concentrations of C _i (i=0, 1, 2, ..., N) - C ₀ mol/m³ column vector of initial molar concentrations of C _i(i=0, 1, 2,.., N) - C _–01 mol/m³ column vector of initial molar concentrations of C _i(i=2,..., N) - C _{E, tot} mol/m³ total molar concentration of enzyme molecules - C _i mol/m³ molar concentration of S _i (i=0,1,2,...,N) - C _{i, o} mol/m³ initial molar concentration of S _i(i=0, 1, 2, ..., N) - E enzyme molecule - I identity matrix - K 1/s matrix of lumped rate constants - k _i 1/s pseudo-first order lumped rate constant associated with the formation of S _i -1 (i=1, 2, ...,N) - k _{cat, i} 1/s first order rate constant associated with the formation of S _i-1 (i=1, 2, ..., N) - K _m mol/m³ Michaelis-Menten constant - L number of distinct eigenvalues - M _i multiplicity of the i-th eigenvalue - N maximum number of monomer residues in a single polymeric molecule - r ₁ mol/m³ s rate of formation of S ₀ - r _i mol/m³ s rate of release of S _i -1 - r _opt maximum average dimensionless rate of production of monomer S₀ - S lumped, pseudo substrate - S₁ inert moiety - S _i substrate containing i monomer residues, each labile to detachment as - S₀ by enzymatic action (i=1,2,...,N) - t s time elapsed since startup of batch reaction - t _lag s time interval required for cleaning, loading, and unloading the batch reactor - t _opt s time interval leading to the maximum average rate of monomer production - v _ij s^1-j eigenvectors associated with eigenvalue imi (i=1, 2, ..., L; j =1, 2, ..., M_i) Greek Symbols _ij mol/m³ arbitrary constant associated with eigenvalue _i (i=1, 2, ..., L; j=1, 2, ..., M _i ) - 1/s generic eigenvalue - _i 1/s i-th eigenvalue     

The role of interphase nitrogen transport in the dynamic measurement of the overall volumetric mass transfer cefficient in air-sparged systems

It has been shown both theoretically and experimentally that interphase nitrogen transport may have a significant influence on the rate of interphase oxygen transport, and thereby also on the value of the volumetric mass transfer coefficient of oxygen, k_la, determined in mechanically agitated bubble fermentors using the variants of dynamic method presented in the literature. The experiments were carried out in 1M KCI solution at five stirrer frequencies and two gas inlet levels. The gas interchanges were performed either without interrupting the aeration and agitation of the charge (A) or with the aeration and agitation of the charge turned on at the same time (B). The applied variants of the interchange were N₂→ O₂→, O₂→ N₂, N₂→ air, air→ N₂, O→ O₂, and O→ air. In the two last variants the oxygen dissolved in the charge was removed by reacting with sulfite ions. The k_la values calculated by allowing for the nitrogen transport for procedure A were approximately equal to the values obtained by disregarding the nitrogen transport, whereas those for procedure B were higher (up to 40%), than the values obtained disregarding the nitrogen transport.     

Adsorption Mechanism of Cr(VI) onto Coir Pith

Reductive adsorption of Cr(VI) on coir pith (hereafter CP) was examined as a function of pH, ionic strength, and temperature. The CP contains 1.33 meq g^{? 1} phenolic, 0.43 meq g^{? 1} of lactonic, and 0.35 meq g^{? 1} carboxylic sites. Thus the CP surface is enriched with electron-donating oxygen functionalities. As evidenced by infrared (IR) spectroscopy, the Cr(VI) → Cr(III) conversion is facilitated by CP sites that are enriched with O─ O functional groups. The adsorption of reduced Cr(VI) was found to occur via C─ O─ functional groups first forming innersphere complexes with the CP surface, yielding keto (> C═ O) groups on the CP surface. The reductive adsorption of Cr(VI) was almost completed within 3 to 4 h, and it was dependent on pH and background ionic strength, yielding the highest monolayer coverage (9.56E-7 mol m^{? 2}) at pH 3.7 in 0.1 M NaNO₃. The Γ_Cr(III) followed the order with respect to the ionic strength: Γ_{0.1 M} > Γ_{0.01 M} > Γ_{0.001 M}. The initial rate constant, k _i , increased with temperature as k _i ^{313 K} > k _i ^{303 K} > k _i ^{293 K} > k _i ^{283 K}.     

Effect of monovalent ion adsorption on the electric charge of phosphatidylcholine - decylamine liposomal membranes

We examined the effect of adsorbed monovalent ions on the surface charge of phosphatidylcholine (PC) – decylamine (DA) liposomal membranes. Surface charge density values were determined from electrophoretic mobility measurements of lipid vesicles performed at various pH levels. The interaction between solution ions and the PC-DA liposomal surface was described by a six component equilibrium model. The previously determined association constants of the -PO^(-) and –N⁽⁺⁾(CH₃)₃ groups of PC with H⁺, OH^-, Na⁺ and Cl^- ions (K _A1H, K _B1OH, K _A1Na, K _B1C1) were used to calculate K _B2OH, and K _B2C1, the association constants of the –N⁽⁺⁾H₃ group of DA with OH^- and Cl^- ions, providing an experimental verification for the proposed model.     

Asymptotic theory for analyzing dose-response survival data with application to the low-dose extrapolation problem

A model of the form P(t, d)=1−;exp{-(t)σ^K_i=0q_idⁱ}, q_i 0, is proposed for analyzing dose-response survival data with right censoring. The q_i's in the dose polynomial are estimated by maximizing the Cox partial likelihood, and given these estimates. Λ(t) is estimated nonparametrically by an estimator proposed by Breslow. Large-sample properties of these estimators are established. Estimates and related large-sample properties are provided for the “virtually safe dose” and other parameters for assessing low-dose carcinogenic risk as a function of age, using data from animal carcinogenesis experiments.     

Gas Exchange,Leaf Structure,and Hydraulic Features in Relation to Sex,Shoot Form,and Leaf Form in An Evergreen Shrub Sabina vulgaris in the Semi-Arid Mu Us Sandland in China

We examined differences in net photosynthetic rate (P _N), transpiration rate (E), water use efficiency (WUE), ratio of substomatal to atmospheric CO₂ concentration (C _i/C _a), cuticle thickness (CT), epidermis cell size (ECS), mesophyll cell size (MCS), vascular bundle size (VBS), tissue density (TD), and coefficient of water loss (k) in Sabina vulgaris as related to sex, shoot form, and leaf form. P _N, E, WUE, C _i/C _a, MCS, VBS, and k varied with sex, whereas CT, ECS, and TD did not. These differences in physiology and anatomy between the female and male plants may be closely related with their reproduction behaviour. P _N, E, C _i/C _a, CT, ECS, MCS, and VBS were significantly smaller in the erect shoots than in the prostrate shoots, WUE was just opposite; TD and k did not vary with shoot form. These changes in physiology with shoot form indicate that erect shoots may be more tolerant of water stress than prostrate shoots. P _N, E, C _i/C _a, TD, and k were significantly greater in the spine leaves than in the scale leaves, whereas WUE, CT, ECS, MCS, and VBS followed the opposite trends. The changes in physiology and anatomy with leaf form suggest that scale leaves have higher drought-resistant and water-holding capacities than spine leaves. Measurements of field gas exchange showed that three-year-old seedlings had lower drought-resistance and higher water loss than five-year-old seedlings, which provides some evidence that seedling survival decreases with decreasing plant age.