Ligand-dependent tryptic inactivation of the ouabain sensitivity of ADP-ATP exchange catalyzed by canine renal Na+, K+-ATPase.

Phosphate transporter of bovine heart mitochondria was purified by solubilization of submitochondrial particles with octylglucoside and fractionation of the extract with ammonium sulfate. After reconstitution into liposomes the purified protein catalyzed phosphate transport which was sensitive to mersalyl and other SH reagents. Transport measured either as $\text{P}{}_{\mathrm{i}}\text{OH}$ or $\text{P}{}_{\mathrm{i}}\text{P}{}_{\mathrm{i}}$ exchange was proportional to protein concentration and time. The $\text{P}{}_{\mathrm{i}}\text{OH}$ but not the $\text{P}{}_{\mathrm{i}}\text{P}{}_{\mathrm{i}}$ exchange was stimulated several fold by valinomycin plus nigericin in the presence of K⁺. The reconstituted system provides a suitable assay during purification of the mitochondrial phosphate transporter.     

The permeability of the lysosomal membrane to small ions

The permeability of the lysosomal membrane to small anions and cations was studied at 37°C and pH 7.0 in a lysosomal-mitochondrial fraction isolated from the liver of untreated rats. The extent of osmotic lysis following ion influx was used as a measure of ion permeancy. In order to preserve electroneutrality, anion influx was coupled to an influx of K⁺ in the presence of valinomycin, and cation influx was coupled to an efflux of H⁺ using the protonophore $\text{3-tert-}\text{butyl-5,2′-dichloro-4′-nitrosalicilylanilide}$. Lysosomal lysis was monitored by observing the loss of latency of two lysosomal hydrolases.The order of permeability of the lysosomal membrane to anions was found to be $\text{SCN}{}^{\mathrm{?}}\text{> I}{}^{\mathrm{?}}\text{> CH}{}_3\text{COO}{}^{\mathrm{?}}\text{> Cl}{}^{\mathrm{?}}\text{≈ HCO}{}^{\mathrm{?}}{}_3\text{≈ P}{}_{\mathrm{i}}\text{> SO}{}_4{}^{\mathrm{2?}}$ and that to cations $\text{Cs}{}^{\mathrm{+}}\text{> K}{}^{\mathrm{+}}\text{> Na}{}^{\mathrm{+}}\text{> H}{}^{\mathrm{+}}$. These orders are largely in agreement with the lyotropic series of anions and cations.The implications of these findings for the mechanism by means of which a low intralysosomal pH is produced and maintained are discussed.     

Energetics of coupled Na+ and Cl− entry into epithelial cells of bullfrog small intestine

Na⁺, K⁺ and Cl^? concentrations ($\text{c}{}_{\mathrm{j}}{}^{\mathrm{<mtext>i</mtext>}}$) and activities ($\text{a}{}_{\mathrm{j}}{}^{\mathrm{<mtext>i</mtext>}}$), and mucosal membrane potentials ($\text{E}{}_{\mathrm{<mtext>m</mtext>}}$) were measured in epithelial cells of isolated bullfrog (Rana catesbeiana) small intestine. Segments of intestine were stripped of their external muscle layers, and bathed (at 25°C and pH 7.2) in oxygenated Ringer solutions containing 105 mM Na⁺ and Cl^? and 5.4 mM K⁺. Na⁺ and K⁺ concentrations were determined by atomic absorption spectrometry and Cl^? concentrations by conductometric titration following extraction of the dried tissue with 0.1 M HNO₃. ¹⁴C-labelled inulin was used to determine extracellular volume. $\text{E}{}_{\mathrm{<mtext>m</mtext>}}$ was measured with conventional open tip microelectrodes, $\text{a}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ with solid-state Cl^?-selective silver microelectrodes and $\text{a}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ and $\text{a}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ with Na⁺- and K⁺-selective liquid ion-exchanger microelectrodes. The average $\text{E}{}_{\mathrm{<mtext>m</mtext>}}$ recorded was ?34 mV. $\text{c}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$, $\text{c}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ and $\text{c}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ were 51, 105 and 52 mM. The corresponding values for $\text{a}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$, $\text{a}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ and $\text{a}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ were 18, 80 and 33 mM. These results suggest that a large fraction of the cytoplasmic Na⁺ is ‘bound’ or sequestered in an osmotically inactive form, that all, or virtually all the cytoplasmic K⁺ behaves as if in free solution, and that there is probably some binding of cytoplasmic Cl^?. $\text{a}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ significantly exceeds the level corresponding to electrochemical equilibrium across the mucosal and baso-lateral cell membranes. Earlier studies showed that coupled mucosal entry of Na⁺ and Cl^? is implicated in intracellular Cl^? accumulation in this tissue. This study permitted estimation of the steady-state transapical Na⁺ and Cl^? electrochemical potential differences (Δμ&#x0304;Na and Δμ&#x0304;Cl). Δμ&#x0304;Na (?7000 J · mol^?1; cell minus mucosal medium) was energetically more than sufficient to account for Δμ&#x0304;Cl (1000–2000 J · mol^?1).     

Hydrolysis of a thiopeptide by cadmium carboxypeptidase A

Substitution of the active site zinc ion of carboxypeptidase A by cadmium yields an enzyme inactive towards ordinary peptide substrates. However, a substrate analog (BzGlyNHCH₂CSPheOH) containing a thioamide linkage at the scissile position is cleaved to the thioacid. The kinetic parameters and their pH dependencies are $\text{k}{}_{\mathrm{cat}}\text{K}{}_{\mathrm{m}}\text{= 5.04 × 10}{}^4\text{min}{}^{\mathrm{?1}}\text{M}{}^{\mathrm{?1}}$, decreasing with either acid or base (PK_E1 = 5.64, pK_E2 = 9.55), and k_cat = 1.02 × 10² min^?1, decreasing with acid (pK_ES = 6.61). The thiopeptide is less efficiently cleaved by native (zinc) carboxypeptidase A. This cadmium-sulfur synergism supports a mechanism wherein the substrate amide is activated by metal ion coordination to its (thio) carbonyl.     

Heterozygote frequencies in small subpopulations.

The mean fixation index within subpopulations (F_IS) has been defined as $\text{F}\text{̄}{}_{\mathrm{IS}}\text{= ∑w}{}_{\mathrm{i}}\text{F}{}_{\mathrm{ISi}}\text{or as}\text{F}\text{̂}{}_{\mathrm{IS}}\text{=}\text{∑w}{}_{\mathrm{i}}\text{p}{}_{\mathrm{i}}\text{q}{}_{\mathrm{i}}\text{F}{}_{\mathrm{ISi}}\text{∑w}{}_{\mathrm{i}}\text{p}{}_{\mathrm{i}}\text{q}{}_{\mathrm{i}}$. The latter definition is preferred because it can be obtained from the two other fixation indices, F_ST and F_IT and because it is unaffected by the mean gene frequency. The expected frequency of heterozygotes in small subpopulations of dioecious organisms will exceed Hardy-Weinberg expectations and this can be measured by $\text{F}\text{̂}{}_{\mathrm{IS}}$. In an isolated subpopulation of constant variance effective size $\text{N,}\text{F}\text{̂}{}_{\mathrm{IS}}$ rapidly tends to $\text{1 − 4N}{}^2\text{(N − 1 + [N}{}^2\text{+ 1]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^2$. In the Island model of population structure, $\text{F}\text{̂}{}_{\mathrm{IS}}$ is approximately $\text{−(1 − m)}\text{N}\text{where}\text{m}$ is the immigration rate.When a sample is drawn from a natural population, the observed F_IS will depend upon the genetic structure of the population. The values of F_IS expected in three different types of population structure are discussed.     

Multiple forms of cyclic nucleotide phosphodiesterases in normal and goitrous rat thyroid

The stoichiometry of H⁺ ejection coupled to electron flow from succinate to ferricyanide in the electron transport chain of mitochondria from Ehrlich ascites tumor and AS30-D hepatoma cells was determined. Values close to 4.0 for the $\text{H}{}^{\mathrm{+}}\text{2e}{}^{\mathrm{?}}$ ejection ratio were found in both cell lines, with either Ca²⁺ or K⁺ (+ valinomycin) as charge-compensating permeant cation. The 4 H⁺ ejected were compensated by outward movement of two negative charges to reduce 2 Fe(CN)6^3? to 2 Fe(CN)6^4?, and the uptake of two positive charges in the form of the permeant cation. Experiments on (a) omission of rotenone (b) the effect of antimycin A and (c) depletion of endogenous NAD(P)-linked substrates showed that no significant endogenous electron flow or H⁺ ejection occurred, thus eliminating possible overestimation of the H⁺/2e^? ratio from endogenous substrates. These data on mitochondria from two tumor cell lines are fully consistent with earlier measurements of the H⁺/O stoichiometry for succinate and NADH oxidation in tumor mitochondria and with the $\text{H}{}^{\mathrm{+}}\text{2e}{}^{\mathrm{?}}$ stoichiometry for site 2 in normal rat liver mitochondria.     

Ouabain receptor interactions in (Na+ + K+)-ATPase preparations. II. Effect of cations and nucleotides on rate constants and dissociation constants

The action of ATP and its analogs as well as the effects of alkali ions were studied in their action on the ouabain receptor. One single ouabain receptor with a dissociation constant ($\text{K}{}_{\mathrm{<mtext>D</mtext>}}$) of 13 nM was found in the presence of ($\text{Mg}{}^{\mathrm{2+}}\text{+ P}{}_{\mathrm{i}}$) and ($\text{Na}{}^{\mathrm{+}}\text{+ Mg}{}^{\mathrm{2+}}\text{+ ATP}$). pH changes below pH 7.4 did not affect the ouabain receptor. Ouabain binding required Mg²⁺, where a curved line in the Scatchard plot appeared. The affinity of the receptor for ouabain was decreased by K⁺ and its congeners, by Na⁺ in the presence of ($\text{Mg}{}^{\mathrm{2+}}\text{+ P}{}_{\mathrm{i}}$), and by ATP analogs (ADP-C-P, ATP-OCH₃). Ca²⁺ antagonized the action of K⁺ on ouabain binding. It was concluded that the ouabain receptor exists in a low affinity (R_α) and a high affinity conformational state (R_β). The equilibrium between both states is influenced by ligands of $\text{(Na}{}^{\mathrm{+}}\text{+ K}{}^{\mathrm{+}}\text{)-ATPase}$. With 3 mM Mg²⁺ a mixture between both conformational states is assumed to exist (curved line in the Scatchard plot).     

The accumulation of superoxide radical during the aerobic action of xanthine oxidase A requiem for H2O4−

The action of xanthine oxidase upon acetaldehyde or xanthine at pH 10.2 has been shown to be accompanied by substantial accumulation of O₂^? during the first few minutes of the reaction. H₂O₂ decreases this accumulation of O₂^? presumably because of the Haber-Weiss reaction ($\text{H}{}_2\text{O}{}_2\text{+}\text{O}{}_2{}^{\mathrm{?}}\text{→}\text{OH}{}^{\mathrm{?}}\text{+}\text{OH}\text{+}\text{O}{}_2$) and very small amounts of superoxide dismutase eliminate it. This accumulation of O₂^? was demonstrated in terms of a burst of reduction of cytochrome $\text{c}$, seen when the latter compound was added after aerobic preincubation of xanthine oxidase with its substrate. The kinetic peculiarities of the luminescence seen in the presence of luminol, which previously led to the proposal of H₂O₄^?, can now be satisfactorily explained entirely on the basis of known radical intermediates.     

Tests of the carrier model for ion transport by nonactin and trinactin

The fluxes of K⁺ and NH₄⁺ carried by nonactin and trinactin across thin lipid membranes have been measured as functions of ion activity, electric potential and time. In agreement with the predictions of a version of the carrier model in common use, the shape of the initial current-voltage relation is independent of the activity of the electrolyte, $\text{a}{}_{\mathrm{<mtext>i</mtext>}}$ while the ratio of the initial conductance, $\text{G}{}_0$, to the steady-state conductance, $\text{G}{}_{\mathrm{\infty }}$, increases according to $\text{G}{}_0\text{/G}{}_{\mathrm{\infty }}\text{=}\text{const}{}_1\text{+ const}{}_2\text{× a}{}_{\mathrm{<mtext>i</mtext>}}$. For trinactin the data presented allow the estimation of the rate constants of the carrier process (in the limit of zero potential) in a manner which does not assume any particular variation with potential for the constants. Using empirically determined functions of potential, a complete set of values is also available for nonactin. The curve fitting which is necessary is described in the following paper. The data presently available for valinomycin are sufficient neither to test the model nor to determine a complete set of constants.     

Inhibition of chymotrypsin by alkyl phosphonates: a quantitative structure-activity analysis.

A quantitative structure-activity relationship has been formulated for 53 alkyl phosphonates [R₂OPO(CH₃)SR₃] inhibiting chymotrypsin: . In this so-called bilinear model, k_i is the bimolecular rate constant (m^?1 s^?1), β is a disposable parameter evaluated by a computerized iterative procedure, MR is the molar refractivity of a substituent, $\text{σ}{}_3{}^1$ is Taft's polar parameter, and I is an indicator variable for substituents containing a sulfonium group. The correlation coefficient for this equation is 0.985. This quantitative structure-activity relationship is compared with those previously formulated for the action of chymotrypsin on acylamino acid ester substrates.     

Active K+ transport in Mycoplasma mycoides var. Capri. Net and unidirectional K+ movements

Analysis of the cation composition of growing Mycoplasma mycoides var. Capri indicates that these organisms have a high intracellular K⁺ concentration ($\text{K}{}_{\mathrm{<mtext>i</mtext>}}\text{: 200–300}\text{mM}$) which greatly exceeds that of the growth medium, and a low Na⁺ concentration ($\text{Na}{}_{\mathrm{<mtext>i</mtext>}}{}^{\mathrm{+}}\text{: 20}\text{mM}$). Unlike $\text{Na}{}_{\mathrm{<mtext>i</mtext>}}{}^{\mathrm{+}}\text{, K}{}_{\mathrm{<mtext>i</mtext>}}{}^{\mathrm{+}}$ varies with cell aging.The K⁺ transport properties studied in washed organisms resuspended in buffered saline solution show that cells maintain a steady and large K⁺ concentration gradient across their membrane at the expense of metabolic energy mainly derived from glycolysis. In starved cells, $\text{K}{}_{\mathrm{<mtext>i</mtext>}}{}^{\mathrm{+}}$ decreases and is partially compensated by a gain in Na⁺. This substitution completely reverses when metabolic substrate is added (K⁺ reaccumulation process). Kinetic analysis of K⁺ movement in cells with steady K⁺ level shows that most of K⁺ influx is mediated by an autologous K⁺-K⁺ exchange mechanism. On the other hand, during K⁺ reaccumulation by K⁺-depleted cells, a different mechanism (a K⁺ uptake mechanism) with higher transport capacity and affinity drives the net K⁺ influx. Both mechanisms are energy-dependent.Ouabain and anoxia have no effect on K⁺ transport mechanisms; in contrast, both processes are completely blocked by dicyclohexylcarbodiimide, an inhibitor of the Mg²⁺-dependent ATPase activity.     

Mercaptide-anion as a trans-ligand in oxycytochrome P450

Oxygenation of heme-mercaptide as well as spectroscopic characteristics of the dioxygen complex formed have been studied. Absorption and magnetic circular dichroism spectra of the O₂ complex support the retention of mercaptide in the heme fifth position. A release of $\text{O}{}_2{}^{\mathrm{<mtext>?</mtext>}}$ in the decomposition of the oxygenated complex and an independent formation of the latter from hemine-dimercaptide and $\text{O}{}_2{}^{\mathrm{<mtext>?</mtext>}}$ together with electron paramagnetic resonance and Mössbauer data support the O₂ presence in the heme coordination sphere. The similarity of optical and magnetic circular dichroism spectra and the closeness of the ratio for oxy-heme-mercaptide and oxycytochrome P450 unequivocally confirm the presence of an axial cystein mercaptide ligand in oxycytochrome P450.     

The interaction of ions with phosphatidylcholine bilayers

The interaction of lanthanides and other cations with phosphatidylcholine bilayers present as single bilayer vesicles in ²H₂O has been investigated in terms of stoichiometry, apparent binding constants and environmental conditions.Lanthanides are shown to form 2 : 1 (molar ratio) phosphatidylcholine to metal ion complexes.The apparent binding constant $\text{K}{}_{\mathrm{<mtext>b</mtext>}}$ varies as a function of the quantity of metal ion bound and as a function of the Cl^? concentration. The apparent binding constant at “zero loading” is $\text{K}{}_0\text{= 1.25 · 10}{}^4\text{L}{}^2\text{·}\text{M}{}^{\mathrm{?}}\text{at}\text{0.15}\text{M KCl}$. It decreases exponentially with increased “loading” expressed as the molar ratio of metal ion bound to effective phosphatidylcholine concentration and increases exponential with Cl^? concentration.The interaction of lanthanides and divalent cations such as Ca²⁺ and Mg²⁺ is independent of pH in the pH range 3–7⁺ and 3–10 respectively, but is sensitive to the nature of the anion. The presence of anions enhances the interaction with polyvalent cations, the chaotropic anions showing the largest effect. The order of enhancement is $\text{Cl}{}^{\mathrm{?}}\text{< Br}{}^{\mathrm{?}}\text{< NO}{}_3{}^{\mathrm{?}}\text{< SCN}{}^{\mathrm{?}}\text{< I}{}^{\mathrm{?}}\text{< ClO}{}_4{}^{\mathrm{?}}$. The nature of the monovalent counterion (cation) has little effect on the enhanced binding of lanthanides in the presence of the above anions.The affinity of other polyvalent cations for phosphatidylcholine bilayers has been determined by competition with lanthanides. The physiologically important divalent cations Ca²⁺ and Mg²⁺ both bind less strongly (by about an order of magnitude) to the lipid surface. The order of binding of cations reflects direct binding to the phosphodiester group, with UO₂²⁺ showing the highest affinity.     

Bacillus subtilis aminopeptidase: specificity toward amino acyl-beta-naphthylamides.

The kinetic parameters for the hydrolyses of different l-α-amino acid-β-naphthylamides by Bacillus subtilis aminopeptidase have been measured for the native enzyme and for the enzyme activated in 5 mm Co(NO₃)₂. In most cases Co²⁺ activation decreased K_m(app) values and increased k_cat values, in other cases k_m(app) and k_cat values were increased; for the remainder of the substrates tested k_m(app) values and k_cat values were decreased. In all cases tested the ratios of $\text{(}\text{k}\text{cat}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)</mtext>}}\text{)}\text{CO}{}^{\mathrm{2+}}\text{/(}\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)nativ</mtext>}}\text{)}$ were increased (2- to 108-fold). For the native enzyme the order of specificity toward the l-amino acid-β-naphthylamides was Arg > Met > Trp > Lys > Leu and for the Co²⁺ activated enzyme the order of specificity was Lys > Arg > Met > Trp > Leu. The native enzyme hydrolyzed Pro-β-naphthylamide, but not α-Glu-β-naphthylamide; Co²⁺ activation of the enzyme affected an appreciable rate of hydrolysis of the latter substrate.     

The characterization of energized and partially de-energized (respiration-independent) β-galactoside transport into escherichia coli

Unidirectional fluxes of [¹⁴C]lactose by whole cells of Escherichia coli under highly energized and partially de-energized (in the presence of CN^?) conditions are analyzed kinetically.When the cells are energized, the value for $\text{V}$ influx is $\text{0.45 ± 0.01}\text{mM}$ internal concentration increment/s and $\text{K}{}_{\mathrm{t}}$ is $\text{0.26 ± 0.03}\text{mM}$. At an external concentration of 0.61 mM the steady-state internal concentration is 0.25 M, reached after about 1h. The maximum steady-state concentration ratio is $\text{2 · 10}{}^3$.The efflux process under these conditions is non-saturable, being linearly dependent upon internal concentration over the range 25–250 mM with a first-order rate constant of $\text{8.8 ± 0.2 · 10}{}^{\mathrm{?4}}\text{s}{}^{\mathrm{?1}}$.The transport in the presence of CN^? is active, with a maximum concentration ratio (internal concentration/external concentration) of 104, and the uptake is mimicked by anoxia (< 70 ppm O₂).The effects of CN^? are to lower the $\text{V}$ for influx and to change the efflux from a non-saturable to a saturable process with a value for $\text{K}{}_{\mathrm{t}}$ (60 mM) intermediate between that for energized efflux ($\text{> 250}\text{mM}$) and influxe (0.3–0.6 mM), the latter value not changing appreciably. Partial de-energization thus affects both the influx and efflux processes.     

Flash-induced photophosphorylation in chloroplasts with activated ATPase

Chloroplasts which were rapidly isolated from illuminated leaves showed activity of ATP hydrolysis at a level much higher than that of the dark control. Under the high-intensity illumination or under repetitive flash excitation, the activated chloroplasts synthesized more ATP than those with a low ATP hydrolysis activity. formed under repetitive flashes was smaller in the activated chloroplasts than in the inactive chloroplasts. The inhibition of ATP yield per flash by valinomycin or nigericin in the presence of K⁺ was stronger in the inactive chloroplasts than in the activated chloroplast. ATP synthesis in the activated chloroplasts seems to have a lower threshold.     

Respiration-driven proton translocation with nitrite and nitrous oxide in Paracoccus denitrificans

(1) $\text{H}$⁺/electron acceptor ratios have been determined with the oxidant pulse method for cells of denitrifying Paracoccus denitrificans oxidizing endogenous substrates during reduction of O₂, NO^?₂ or N₂O. Under optimal H⁺-translocation conditions, the ratios $\text{H}{}^{\mathrm{+}}\text{O}$, $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were 6.0–6.3, 4.02, 5.79 and 3.37, respectively. (2) With ascorbate/N,N,N′,N′-tetramethyl-p-phenylenediamine as exogenous substrate, addition of NO^?₂ or N₂O to an anaerobic cell suspension resulted in rapid alkalinization of the outer bulk medium. $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were ?0.84, ?2.33 and ?1.90, respectively. (3) The $\text{H}{}^{\mathrm{+}}\text{oxidant}$ ratios, mentioned in item 2, were not altered in the presence of $\text{valinomycin}\text{K}{}^{\mathrm{+}}$ and the triphenylmethylphosphonium cation. (4) A simplified scheme of electron transport to O₂, NO^?₂ and N₂O is presented which shows a periplasmic orientation of the nitrite reductase as well as the nitrous oxide reductase. Electrons destined for NO^?₂, N₂O or O₂ pass two H⁺-translocating sites. The $\text{H}{}^{\mathrm{+}}\text{electron}$ acceptor ratios predicted by this scheme are in good agreement with the experimental values.     

The covariance of relatives derived from a random mating population.

Attention is drawn to errors common in the derivation of forms for the genotypic covariance of noninbred relatives from a Hardy-Weinberg population of diploids. A synthesis of Fisher's least-squares method of partitioning the genotypic variance and Malécot's probability method of expressing kinship, yields a general form. For one locus, the form is $\text{(P}{}_{\mathrm{ss}}\text{+ P}{}_{\mathrm{sd}}\text{+ P}{}_{\mathrm{ds}}\text{+ P}{}_{\mathrm{dd}}\text{)}\text{1}\text{2}\text{σ}{}_{\mathrm{a}}{}^2\text{+ (P}{}_{\mathrm{ss}}\text{P}{}_{\mathrm{dd}}\text{+ P}{}_{\mathrm{sd}}\text{P}{}_{\mathrm{ds}}\text{) σa}{}_{\mathrm{d}}{}^2$, where σ_a² is the additive genetic variance, α_d² is the variance of dominance deviations, p_ij is the probability that parental gamete i is identical by descent to parental gamete j, i = s, d indexes the parents of one relative, and j = s, d indexes those of the other. The form provides a framework for obtaining the covariance of relatives from an equilibrium population with linkage.