The effect of the r a and r b loci on the lipid content of the seed of Pisum sativum

Summary The lipid content of seed from a set of isogenic lines for the R _a : r _a locus has been determined; the results show that this locus as well as affecting the starch, sugar and storage protein content and composition, also has a marked effect on the lipid content of the seed. Genotypes having different combinations of alleles at the r _a and r _b loci have also been examined; an r _a r _a r _b r _b , genotype had 5.57% purified total lipid in its seed — a more than 2-fold increase over that found in the round-seeded varieties (R _a R _a R _b R _b ) usually grown for the dry sed crop.     

Theoretical studies on the role of food exploitation for the competition of scaamble type

A model was made to clarify the basic processes of competition to occur among larvae by the exploitation as defined byBakker (1969). It was found that this model is applicable to the experimental results on the food exploitation among Droshophila larvae obtained byBakker (1961). In the model the preimaginal stage is divided into two periods;T_f which is the time that a group of larvae spends in exhausting the food after hatching, and T_s which is the duration of the starvation period after T_f.T_f and then W_l (larval body weight) just after the end of T_f are decided by F_s (amount of food supplied per larva at larval hatching) and F_c (amount of food consumed per larva).T_f affects on the onset of T_s as well as R_l (rate of decrease in the individual body weight during T_s).W_a (weight of emerging adults) is gotten by a subtraction of R_l from W_l just after the end of T_f,R_e is affected directly by these components of W_l and R_l. As a result, W_a and R_e are expressed by functions of F_s. This model confirmed that the food exploitation lead to the competition of scramble type. Finally it was suggested that there exist some strategies which prevent ill-effects owing to the food exploitation.     

Regulation of the activity of alcohol dehydrogenase isozymes during the development of the maize kernel

Summary The relative activities of alcohol dehydrogenase isozymes have been studied during the development of the endosperm and scutellum of heterozygous Adh ₁ ^F /Adh ₁ ^S maize kernels. The products of the Adh ₁ ^F allele are found earlier than the products of the Adh ₁ ^S allele in both the scutellum and the endosperm. A second gene (Adh _r )which controlsthe activity level of ADH is active in the scutellum only. The Adh _r ^N allele specifies increase in the relative activity of the Adh ₁ ^S products from 26 to 38 days after pollination. This increase is prevented by the Adh _r ^L allele which is dominant. These results ar discussed on the basis of the limited factor hypothesis proposed recently by Schwartz (1971) for the regulation of the Adh ₁gene in maize.     

Hypoxia tolerance of the mummichog: the role of access to the water surface

Low dissolved oxygen (DO) had a significant effect on specific growth rate (G_S), length increment (I_L) and haematocrit (Hct) of the mummichog Fundulus heteroclitus. Regardless of access to the water surface, F. heteroclitus maintained high growth rates (G_S and I_L) at DO concentrations as low as 3 mg O₂ l^?1. With access to the water surface, both G_S and I_L of F. heteroclitus decreased by c. 60% at 1·0 mg O₂ l^?1 compared to all higher DO treatments. When denied access to the water surface, a further decrease in G_S (c. 90%) and I_L (c. 75%) was observed at 1 mg O₂ l^?1. There was no effect of diel‐cycling DO (1–11 mg O₂ l^?1) with or without surface access on G_S, I_L or Hct of F. heteroclitus. Similar trends between G_S and faecal production across DO treatments suggest that decreased feeding contributed significantly to the observed decrease in growth rate. Haematocrit was significantly elevated at 1 mg O₂ l^?1 for fish with and without access to the water surface. Increased Hct, however, was not sufficient to maintain high G_S or I_L at severely low DO. When permitted to respire in the surface layer, however, F. heteroclitus was capable of maintaining moderate growth rates at DO concentrations of 1 mg O₂ l^?1 (c. 15% saturation). Although aquatic surface respiration (ASR) was not quantified in this study, F. heteroclitus routinely swam in contact with the water surface and performed ASR at DO concentrations ≤3 mg O₂ l^?1. No hypoxia‐related mortality was observed in any DO or surface access treatment for as long as 9 days. This study demonstrates that surface access, and thus potential for ASR, plays an important role in providing F. heteroclitus substantial independence of growth rate over a wide range of low DO conditions commonly encountered in shallow estuarine environments.     

Application of Polyelectrolyte Theory to the Study of the B-Z Transition in DNA (1)

Abstract

We have used the polyelectrolyte theory to study the ionic strength dependence of the B-Z equilibrium in DNA. A DNA molecule is molded as an infinitely long continuously charged cylinder of radius a with reduced linear charge density q. The parameters a and q for the B and Z forms were taken from X-ray data: a _B = 1nm, q _B = 4.2, a _z = 0.9 nm and q _z = 3.9. A simple theory shows that at low ionic strengths (when Debye screening length r _D>>a) the electrostatic free energy difference F ^el _Bz = F ^el _Z - F ^el _B increases with increasing ionic strength since q _B>q_z. At high ionic strengths (when r _D<<a) the F ^el _BZ would go on growing with increasing ionic strength if the inequality q _B/^a _B<q_z/a _z were valid. In the converse case when q _z/q _B<a_z/a _B the F ^el _BZ value decreases with increasing salt concentration at high ionic strength. Since X-ray data correspond to the latter case, theory predicts that the F ^el _BZ value reaches a maximum at an intermediate ionic strength of about 0.1 M (where r _D～a). We also performed rigorous calculations based on the Poisson-Boltzmann equation. These calculations have confirmed the above criterion of nonmonotonous behaviour of the F ^el _BZ value as a function of ionic strength. Different theoretical predictions for the B-Z transition in linear and superhelical molecules are discussed. Theory predicts specifically that at a very low ionic strength the Z form may prove to be more stable than the B form. Thus, one can observe the Z-B-Z transition with increasing ionic strength. In the light of our theoretical findings we discuss numerous experimental data on the B-Z transition in linear and superhelical DNA.     

松嫩平原苏打盐渍化旱田土壤表观电导率空间变异

在松嫩平原西部吉林省大安市乐胜乡,于2013年4月20日选择盐碱程度不均一的典型盐渍化旱田地块,面积为4.8 hm~2作为研究样地。利用EM38大地电导率仪测定结合田间定点采样,并通过经典统计和地统计相结合的方法研究了盐渍化旱田土壤表观电导率空间变异特征,分析了土壤表观电导率与土壤盐碱指标之间的关系。结果表明,盐渍化旱田土壤水平方向表观电导率(EC_h)经对数转换后具有强空间自相关,其变异特征主要是与地形地貌和水文状况等结构性因素有关。垂直方向表观电导率(EC_v)经对数转换后具有中等空间自相关性,其变异特征受结构性因素和随机因素共同作用。EC_h和EC_v半方差模拟的最优模型分别为球状模型和指数模型。Pearson分析表明土壤表观电导率(EC_h和EC_v)与土壤盐碱指标EC_(1∶5)、pH_(1∶5)、SAR、SC、Na~+、CO_3~(2-)、HCO_3~-呈正相关关系(P0.05),EC_h与土壤盐碱指标相关系数均大于EC_v。在实际应用中可以用EC_h来指示土壤的盐碱程度。回归分析表明土壤表观电导率(EC_h和EC_v)与土壤盐碱指标呈线性相关,且EC_h回归模型的决定系数均大于EC_v回归模型的决定系数,可用水平方向土壤表观电导率(EC_h)来计算土壤盐碱指标,进行土壤盐渍化的快速评估。     

Validation of the use of the lipophilic thiocyanate anion for the determination of membrane potential in Ehrlich ascites tumor cells

Summary The utility of the lipophilic anion thiocyanate (SCN⁺) as a probe for the indirect estimation of the cell membrane potential (V _m ) in Ehrlich ascites tumor cells has been evaluated by comparison to direct electrophysiological measurements. SCN accumulation is consisten with first-order uptake into a single kinetically-identifiable cellular compartement, achieving steadystate distribution in 20–30 min at 22°C. The steady-state distribution ratio ([SCN^–] _c /[SCN^–] _e ) in physiological saline is 0.44±0.02. Treatment of the cells with proparanolol (0.13 mM), an activator of Ca²⁺ dependent K⁺ channels, reduces the steady-state distribution ratio to 0.19±0.02. Conversely, treatmetn with BACl₂ (10 mM), an antagonist of the pathway, increases the SCN^– distribution ratio to 0.62±0.01. The equilibrium potentials (V _SCN ) calculated under these conditions are virtually identical to direct electrophysiological measurements of theV _m made under the same conditions. The effect of varing extracellular [K⁺]([K⁺] _e ) in the presence of constant [Na⁺] _e =100 mM has also been tested. In control cells, elevation of [K⁺] _e from 6 to 60 mM reducesV _SCN from –20.6±1.0 to –13.2±1.2 mV. Again, microelectrode measurements give excellent quantitative agreement. Propranolol increases the sensitivity of the cells to varying [K⁺] _e , so that a 10-fold elevation reducesV _SCN by approximately 31 mV. BaCl₂ greatly reduces this reponse: a 10-fold elevation in [K⁺] _e yielding only a 4-mV rediction inV _SCN . It is concluded that the membrane potential of Ehrlich cells can be estimated accurately from SCN^– distribution measurements.     

The paracellular channel for water secretion in the upper segment of the Malpighian Tubule of Rhodnius prolixus

Lumen to bath J ₁₂/C ₁ and bath to lumen J ₂₁/ C ₂ fluxes per unit concentration of 19 probes with diameters (d ^m) ranging from 3.0–30.0 Å (water, urea, erythritol, mannitol, sucrose, raffinose and 13 dextrans with d ^m 9.1–30.0 Å) were measured during volume secretion (J _v ) in the upper segment of the Malpighian Tubule of Rhodnius by perfusing lumen and bath with ¹⁴C or ³H-labeled probes. J _net=(J ₁₂/C ₁ – J ₂₁/C ₂) was studied as a function of J _v · J _v was varied by using different concentrations of 5-hydroxy tryptamine. J _net for ³H-water was not different from J _v We found: (i) A strong correlation between J _net and J _v for 8 probes d ^m =3.0–11.8 Å (group a probes), indicating that the convective component of J _net is more important than its diffusive component and than unstirred layers effects which are negligible. Therefore group a probes are solvent dragged as they cross the epithelium, (ii) There is no correlation between J _net and J _v for 11 probes with d ^m=11.8–30 Å (group b). Therefore these probes must cross the epithelium by diffusion and not by solvent drag, (iii) In a plot of J _net/J _v vs. d ^m group a probes show a steep linear relation with a slope = –0.111, while for group b probes the slope is –0.002. Thus there is a break between groups a and b in this plot. We tried to fit the data with models for restricted diffusion and convention through cylindrical or parallel slit pathways. We conclude that (i) group a probes are dragged by water through an 11.0 Å-wide slit, (ii) Most of J _v must follow an extracellular noncytosolic pathway, (iii) Group b probes must diffuse through a 42 Å-wide slit, (iv) A cylindrical pathway does not fit the data.E.G. is a Visiting Scientist at IVIC. It is a pleasure to thank Drs. A.E. Hill and Bruria Shachar-Hill for their suggestion of the use of dextrans, their instruction and help with the dextran separation technique, and their extensive discussions. Dr. R. Apitz, Mr H. Rojas and Mrs. Fulvia Bartoli were most helpful with suggestions during the course of the experimental work. Mr. Jose Mora was fundamental help with the equipment. Mrs. Lelis Ochoa and Mr. Luis F. Alvarez helped with some of the drawings. This work was partially supported by CONICIT, Fundación Polar and CDCH of UCV. It is a pleasure to thank Dr. H. Passow and Dr. K.J. Ullrich at the Max Planck Institut für Biophysik (Frankfurt/Main) where this work was initiated.     

Use of the harmonic mean to the determination of dissociation constants of stereoisomeric mixtures of biologically active compounds

Abstract

Herein we introduce the derivation of a mathematical expression to evaluate the dissociation constant of a mixture of stereoisomers in equal amounts (K_dMIX), when the corresponding dissociation constants (K_d) or medium response (MR₅₀) of the pure stereoisomers are known; the final equation takes the form of the harmonic mean. In order to validate the equation, we carried out a bibliographic search of experimental data of enantiomeric molecules with biological activity, considering the K_d’s or MR₅₀’s of the isolated enantiomers as well as that of the racemate. The comparisons between the experimental dissociation constants of the mixtures (K_dEXP or MR_50EXP) and the calculated values (K_dMIX or MR_50MIX) were consistent; the similarity between these values is supported through statistical analyses of group comparison and simple linear correlation. The equation we obtained, which corresponds to the harmonic mean, was used to predict the values of K_dMIX (or MR_50MIX) or K_d (or MR₅₀) in systems when only two of the experimental values are known: either the dissociation constants of both enantiomers or the K_d (or MR₅₀) of one of the enantiomers and dissociation constant of the racemate.     

常绿阔叶林8种乔灌木叶片氮含量及其分配与光合能力的关系

以浙江天童国家森林公园常绿阔叶林为研究对象,采用空间代替时间的方法,研究了5个不同演替阶段常见的4种乔木以及4种灌木叶片的光饱和速率(Pmax)、光合氮素利用效率(PNUE)及其与叶片氮含量(NL)、叶片氮素在细胞壁的分配比例(细胞壁N/叶片总N,NCW/NL)、氮素在光合酶中的分配比例(NR/NL)、单位面积叶干重(LMA)的相互关系。结果表明:(1)演替系列4种乔木和4种灌木各种间指标除NL外均表现出显著差异,前期种较后期种具有更高的NR/NL、PNUE、Pmax,而后期种LMA、NCW/NL、MCW/ML(细胞壁干重/叶片总干重)更大,NL在乔木各种间差异不明显,在灌木种间则差异显著;乔木种较灌木种具有更大的LMA、NCW/NL、MCW/ML,而NR/NL则较灌木小;8种植物的Pmax与NL以杨梅为最高,连蕊茶最低;苦槠具有最高的PNUE,而栲树最低。(2)随着演替的进行,前期种的NR/NL、PNUE、Pmax有减小趋势,而LMA、NCW/NL、MCW/ML逐渐增大,后期种则表现出相反的趋势。(3)NR/NL与Pmax、PNUE之间呈显著正相关关系,而LMA、NCW/NL、MCW/ML则与Pmax、PNUE、NR/NL显著负相关。研究认为,NR/NL与NCW/NL之间的负相关性及其对PNUE的影响可以在一定程度上解释树木在光合与维持两方面的权衡关系以及演替的生理机制。     

Response properties of FM-FM combination-sensitive neurons in the auditory cortex of the mustached bat

Summary For echolocation, the mustached bat,Pteronotus parnellii rubiginosus, emits orientation sounds (pulses) and listens to echoes. Each pulse is made up of 8 components, of which 4 are constant frequencies (CF_1–4) and 4 are frequency-modulated (FM_1–4). Target-range information, conveyed by the time delay of the echo FM from the pulse FM, is processed in this species by specialized neurons in a part of the auditory cortex known as the FM-FM area. These cortical neurons are responsive to pulse-echo pairs at specific echo delays (Fig. 1). The essential components in the sound pair include the pulse FM₁ followed by an echo FM_n (n=2, 3 or 4). Downward sweeping FM₁-FM_n sounds that are similar to those the animal naturally hears during echolocation are the most effective in evoking facilitative responses. Most FM-FM neurons, however, still exhibit facilitative responses to stimulus pairs consisting of upward sweeping FM sounds and/or pure tones at frequencies found in FM sweeps (Figs. 2 and 3). The magnitude of facilitation is altered by changes in echo rather than pulse amplitude (Figs. 5 and 6). Neurons characterized by shorter best delays (or echoes from closer targets) do not require larger best echo amplitudes for facilitation.Abbreviations CF constant frequency - FM frequency modulation - H _n CF — FM harmonics of the mustached bat biosonar signal - CF _n CF components of the harmonics - FM _n FM components of the harmonics - PCF _n pulse CF_n - ECF _n echo CF_n - PFM _n pulse FM_n - EFM _n echo FM_n - PH _n pulse H_n - EH _n echo H_n - BA best amplitude for facilitation - BD best delay for facilitation - PST peri-stimulus-time - PSTC peri-stimulus-time-cumulative - dB SPL dB re 20 Pa     

Kinetics of the effect of amiloride on the permeability of the apical membrane of rabbit descending colon to sodium

Summary The effects of the addition of graded concentrations of amiloride, (A) _m , to the mucosal bathing solution on the permeability of the apical membrane of rabbit descending colon to Na (P _Na ^m ) were determined when the Na activity in the mucosal bathing solution, (Na) _m , was 18, 32 or 100mm.P _Na ^m was obtained from current-voltage relations determined on tissues bathed with a high-K serosal solution before and after the addition of a maximally inhibitory concentration of amiloride to the mucosal solution as described by Turnheim et al. (Turnheim, K., Thompson, S.M., Schultz. S.G. 1983.J. Membrane Biol. 76:299–309).The results indicate that: (1) As demonstrated previously (Turnheim et al., 1983),P _Na ^m decreases with increasing (Na) _m . (2)P _Na ^m also decreases hyperbolically with increasing (A) _m . Kinetic analyses of the effect of amiloride onP _Na ^m are consistent with the conclusions that: (i) the stoichiometry between the interaction of amiloride with apical membrane receptors that results in a decrease inP _Na ^m is one-for-one; (ii) there is no evidence for cooperativity between amiloride and these binding sites; (iii) the value of (A) _m needed to halveP _Na ^m at a fixed (Na) _m is 0.6–1.0 m; and, (iv) this value is independent of (Na) _m over the fivefold range studied.These findings are consistent with the notion that the sites with which amiloride interacts to bring about closure of the channels through which Na crosses the apical membrane arekinetically distinct from the sites with which (Na) _m interacts to bring about closure (i.e., self-inhibition). In short, the effects of (Na) _m and (A) _m onP _Na ^m in this tissue appear to be independent and additive.     

A modifier locus affecting the expression of the S-RNase gene could be the cause of breakdown of self-incompatibility in almond

Self-compatibility has become the primary objective of most almond (Prunus amygdalus Batsch) breeding programmes in order to avoid the problems related to the gametophytic self-incompatibility system present in almond. The progeny of the cross ‘Vivot’ (S ₂₃ S _fa) × ‘Blanquerna’ (S ₈ S _fi) was studied because both cultivars share the same S _f allele but have a different phenotypic expression: active (S _fa) in ‘Vivot’ and inactive (S _fi) in ‘Blanquerna’. In addition, the microscopic observation of pollen tube growth after self-pollination over several years showed an unexpected self-incompatible behaviour in most seedlings of this cross. The genotypes of this progeny showed that the S _fi pollen from ‘Blanquerna’ was not able to grow down the pistils of ‘Vivot’ harbouring the S _fa allele, confirming the active function of this allele against the inactive form of the same allele, S _fi. As self-compatibility was observed in some S ₈ S ₂₃ and S ₈ S _fa individuals of this progeny, the S _f haplotype may not always be linked to the expression and transmission of self-compatibility in almond, suggesting that a modifier locus may be involved in the mechanism of self-incompatibility in plants.     

Influence of rabbit cold adaptation on the depressor muscarinic cholinergic reaction of the arterial pressure of the hind limb vessels and the small intestine in situ and the systemic arterial pressure

Modification of the main parameters of cholinergic reactions in rabbits, i.e., of the specific sensitivity to agonists (EC ₅₀), maximal reaction values (P _m ) of arterial pressure in the hind limb vessels and small intestine in situ, and systemic arterial pressure after adaptation to cold for 1, 5, 10, and 30 days has been investigated. The depressor reaction to acetylcholine (muscarinic cholinergic receptors agonist) was established to correspond to the model p = (P _m A ⁿ )/(EC ₅₀ ⁿ + A ⁿ ) with n =1. In the control EC ₅₀ was equal to 0.85, 1.01, and 1.21 nmol/kg, while P _m equaled 100, 32.6, and 61.2 mm Hg for the hind limb vessels, small intestine in situ, and systemic arterial pressure, respectively.     

Limitations of the Eadie-Hofstee plot to estimate kinetic parameters of intestinal transport in the presence of an unstirred water layer

Summary In the presence of an intestinal unstirred water layer, the relationship between substrate concentration (C ₁) and unidirectional flux (J _d) is not described by the equation for a rectangular hyperbole. Accordingly, transformations of the Michaelis-Menten equation may not necessarily be linear and may lead to serious errors in the estimation of the affinity constant (K _m) and maximal transport rate (J _d ^m ) of carrier-mediated processes. An equation has previously been derived which describedJ _d under conditions of varying effective thickness or surface area of the unstirred water layer, the free diffusion coefficient of the probe molecule, and the distribution of transport sites along the villus. These theoretical curves have been analyzed by using the Eadie-Hofstee transformation (J _d vs. J_d/C₁) of the Michaelis-Menten equation. Use of this plot leads to serious discrepancies between the true and apparent affinity constants and between true and apparent maximal transport rates. These differences are further magnified by failure to correct for the contribution of passive permeation. The Eadie-Hofstee plot is of use, however, to infer certain qualitative characteristics of active transport processes, such as the variation in affinity constants and overlying resistance of the unstirred water layer at different sites along the villus and to predict the adequacy of the correction for the contribution of passive permeation.Abbreviations Used in the Text C ₁ Concentration of the probe molecule in the bulk phase - C ₂ Concentration of the probe molecule at the aqueous-membrane interface - d Effective thickness of UWL - D Free diffusion coefficient - d ⁿ d atn th segment of the villus - f _n Proportion of total carrier transport sites present on each segment of villus - J Unidirectional flux of probe molecule, uncorrected for surface area - J _d Unidirectional flux of probe molecule determined experimentally, corrected for surface area - J _d ^m Maximal transport rate, corrected for surface area - J _d ^m* Apparent maximal transport rate - J ^m Maximal transport rate, uncorrected for surface area - K _m Michaelis constant (true affinity constant) - K _m ^* Apparent affinity constant - K _m ⁿ K _m atnth segment of the villus - n The perpendicular height of the villus was divided into ten equal segments numberedn ₁ ton ₁₀ - p Passive permeability coefficient - S _m Functional surface area of the membrane - S _w Effective surface of UWL - S _w ⁿ S _w atnth segment of the villus - UWL Intestinal unstirred water layer     

On the Analysis and Synthesis of a Four-Field-Table

The real four-field-table measure k is calculable as follows: K₁ for V(a, b, c, d) with k₁ = (arc K₁)/100, K₁₁ for V(a, b, 0, 0) with k₁₁ = (arc K₁₁)/100, K₁₂ for V(c, d, 0, 0) with k₁₂ = (arc K₁₂)/100 and K₁₂₁ for V(0, 0, c, d) with k₁₂₁ = – k₁₂. The equation k₁ = k₁₁ – k₁₂ holds good. It is possible to calculate the probability of error of a four-field-table with small frequencies, indirectly from component values. Two examples are given.     

Resolution of parameters in the equivalent electrical circuit of the sodium transport mechanism across toad skin

Summary In amphibian epithelia, amiloride reduces net sodium transport by hindering the entry of sodium to the active transport mechanism, that is, by increasing the series resistance (R _ser ). Theoretically, therefore, analysis of amiloride-induced changes in potential differences and short-circuit current should yield numerical estimates of all the parameters in the equivalent electrical circuit of the sodium transport mechanism.The concept has been explored by analysis of such changes in toad skins (Xenopus laevis) bathed in hypotonic sulphate Ringer's, after exposure to varying doses of amiloride, or to amphotericin, dinitrophenol or Pitressin.The estimated values ofR _ser , of the electromotive force of the sodium pump (E _Na), and of the shunt resistance (R _sh ) were independent of the dose of amiloride employed. Skins bathed in hypotonic sulphate Ringer's exhibited a progressive rise inE _Na. Amphotericin produced a fall inR _ser , while dinitrophenol caused a fall inE _Na; washout of the drugs reversed these effects. Pitressin produced a fall in bothR _ser andR _sh , with a rise inE _Na. These results are in accord with earlier suggestions regarding the site(s) of action of these agents.     

Limiting similarity and the form of the competition coefficient

The question of whether there is a limit to the similarity of competing species has previously been investigated by a number of authors. These studies have all used the Lotka-Volterra model of competition, and have assumed that the competition coefficient α_ij may be calculated using the expression, α_ij = ∝ U_i(R) U_j(R) dR/∝ (U_i(R))² dR. In this paper, the generality of this formula is questioned and two alternative expressions for α_ij are proposed. When these expressions are used in an analysis of limiting similarity, qualitatively different conclusions emerge regarding the existence and nature of this limit, using either deterministic or stochastic models. The relevance of these findings to theories of character convergence and similarity barriers is discussed. The available field evidence does not strongly support the validity of the formula for α_ij used in previous studies. Since a given method of calculating α_ij must be derived from a higher level model, it is suggested that the Lotka-Volterra model is not sufficient in an investigation of limiting similarity.     

A theory on the effect of low molecular salts on the dissociation of linear polyacids

A theoretical analysis is given on the effect of low molecular salts on the titration behavior of partially neutralized linear polyacids or polybases. On the basis of the additivity law experimentally and theoretically established on the activity of counterions in polyelectrolyte solutions containing salts, the chemical potential of alkali added for neutralization of polyacids is derived as a function of the salt concentration. The relation between the pH and the salt, concentration at constant degree of neutralization is expressed by pH(c_s) ? pH(0) = ({[? (γ_pC_a)/?C_a]/γ_os} ? 1) ln [1 + (γ_osC_s/γ_pC_A)] where C_a is the concentration of alkali, C₈, the concentration of salts, γ_p is the activity coefficient of counterions in the absence of salts and γ_os is that in the absence of polyelectrolytes. This relation is found to be in good agreement with experimental data obtained in synthetic linear polyelectrolytes as well as in rodlike charged proteins. Therefore, it is concluded that the titration behavior of linear polyions can be understood from the special feature of the integrated coulomb interaction between linear polyions and small ions which was essential for the additivity law. In addition, the screening effect of salts on the electric potential around the polyion is discussed.