Analytic computation of the expectation of the linkage disequilibrium coefficient r2

The squared correlation coefficient r(2) (sometimes denoted Delta(2)) is a measure of linkage disequilibrium that is widely used, but computing its expectation E[r(2)] in the population has remained an intriguing open problem. The expectation E[r(2)] is often approximated by the standard linkage deviation sigma(d)(2), which is a ratio of two expectations amenable to analytic computation. In this paper, a method of computing the population-wide E[r(2)] is introduced for a model with recurrent mutation, genetic drift and recombination. The approach is algebraic and is based on the diffusion process approximation. In the limit as the population-scaled recombination rate rho approaches infinity, it is shown rigorously that the asymptotic behavior of E[r(2)] is given by 1/rho+O(rho(-2)), which, incidentally, is the same as that of sigma(d)(2). A computer software that computes E[r(2)] numerically is available upon request.     

The antioxidant functions of cytochrome c

Low (C(1/2) = 1.5 x 10(-7) M) concentrations of horse cytochrome c strongly inhibit H(2)O(2) production by rat heart mitochondria under conditions of reverse electron transfer from succinate to NAD(+). The effect is abolished by binding of cytochrome c with liposomes and is not prevented by SOD. Yeast cytochrome c is much less effective than the horse protein whereas acetylated horse cytochrome c is without effect. H(2)O(2) formation stimulated by antimycin A is resistant to added cytochrome c. In inside-out submitochondrial vesicles, H(2)O(2) production is suppressed by all three cytochrome c samples tested, but at higher concentrations (C(1/2) is about 5 x 10(-7) M). In vesicles, SOD abolishes the cytochrome c inhibition. We conclude that extramitochondrial cytochrome c is competent in down-regulation of the Complex I H(2)O(2) production linked to the reverse electron transfer. Such an effect is absent in the inside-out submitochondrial vesicles where another antioxidant cytochrome c function can be observed, i.e. the oxidation of O(2-*) to O(2). A possible role of cytochrome c in the antioxidant defence is discussed.     

Highly cytotoxic trithiophenolatodiruthenium complexes of the type [(η6-p-MeC6H4Pr i )2Ru2(SC6H4-p-X)3]+: synthesis, molecular structure, electrochemistry, cytotoxicity, and glutathione oxidation potential

A series of cationic dinuclear p-cymene ruthenium trithiophenolato complexes of the type [(η(6)-p-MeC(6)H(4)Pr(i))(2)Ru(2)(SC(6)H(4)-p-X)(3)](+) (1 X is H, 2 X is Me, 3 X is Ph, 4 X is Br, 5 X is OH, 6 X is NO(2), 7 X is OMe, 8 X is CF(3), 9 X is F, 10 X is Pr(i), 11 X is Bu(t)) have been synthesized from the reaction of [(η(6)-p-MeC(6)H(4)Pr(i))RuCl(2)](2) with the corresponding thiol, isolated as the chloride salts, and further studied for their electrochemical properties, cytotoxicity towards human ovarian cancer cells, and catalytic activity for glutathione (GSH) oxidation. Complex 1 was also compared with the benzene and hexamethylbenzene analogues [(η(6)-C(6)H(6))(2)Ru(2)(SC(6)H(5))(3)](+) (12) and [(η(6)-C(6)Me(6))(2)Ru(2)(SC(6)H(5))(3)](+) (13). The most active compound [11]Cl was structurally studied by single-crystal X-ray diffraction analysis. The concentrations corresponding to 50 % inhibition of cancer cell growth (IC(50) values) in the A2780 and A2780cisR cell lines of these complexes except for 6 were in the submicromolar range, complex 11 showing an IC(50) value of 0.03 μM in both cell lines. The high in vitro anticancer activity of these complexes may be at least partially due to their catalytic potential for the oxidation of GSH, although there is no clear correlation between the IC(50) values and the turnover frequencies at about 50 % conversion. However, the cytotoxicity is tentatively correlated to the physicochemical properties of the compounds determined by the electronic influence of the substituents X (Hammett constants σ(p)) and the lipophilicity of the thiols p-XC(6)H(4)SH (calculated log P parameters).     

阿拉善黄鼠的生命表及繁殖

将采自野生种群的阿拉善黄鼠(Spermophilus dauricus alaschanicus Buechner)( 下称黄鼠)样本划分为8个年龄间隔,然后编制生命表。结果表明,黄鼠的平均死亡率(qx)为0.7512(♂)和0．6222(♀),平均寿命为1.3311年(♂)和1.1073年(♀)。0-l岁龄黄鼠的期望寿命(ex)为0.8311年(♂)和1.1073年(♀)。世代净增殖率(R_o)每代为l.7327。种群内禀增长率(瞬时)(r_m)为0.1433,世代平均时间(T)为3.8346年,周限增长率(r)为1.1541/年。     

A simple parameter relating sequences with folding rates of small alpha helical proteins

It is found that the helix parameter (HP), which favors clustering of non-polar residues, is linearly correlated with the logarithms of rate constants of folding of small two-state alpha-helical proteins. The definition is HP = N(H)(-1) sigma [f(i)+ (f(i-1)+f(i+1))/2], where f(i)=1 or -1, if the i'th residue is hydrophobic or hydrophilic, respectively, N(H) is the number of hydrophobic residues and the summation is taken over the hydrophobic residues.     

The pyrophosphatase activity of pig kidney alkaline phosphatase and its inhibition by magnesium ions and excess of pyrophosphate

1. Pig kidney enzyme resembles other non-specific alkaline phosphatases in its ability to hydrolyse inorganic pyrophosphate (PP(i)). 2. Studies of enzyme velocity as a function of PP(i) concentration show that Michaelis-Menten kinetics are obeyed when a constant PP(i)/Mg(2+) concentration ratio is maintained, but velocity-substrate concentration curves are sigmoid when the concentration of PP(i) is increased but that of Mg(2+) is kept constant. The enzyme is inhibited when the total PP(i) concentration is greater than the total concentration of Mg(2+). Pyrophosphatase activity is activated by Mg(2+), but if the concentration of the metal ion is increased to a value in excess of the total PP(i) concentration Mg(2+) is then strongly inhibitory. 4. It appears that the enzyme is most active towards the complex ion MgPP(i) (2-). The enzyme probably hydrolyses PP(i) (4-) also, but this is a poorer substrate and its competition with MgPP(i) (2-) leads to inhibition. At high Mg(2+) concentrations Mg(2)PP(i) is formed. This complex appears to be a potent inhibitor. 5. Sigmoid plots of v against s and of v against i result from interactions occurring between Mg(2+) and PP(i) (4-) leading to MgPP(i) (2-) and Mg(2)PP(i), and are not indicative of allosteric behaviour.     

A stochastic-covariate failure model with an application to case-control analysis

A stochastic process X(t) is periodically stationary (and ergodic) if, for every k> or =1 and every (t(1),ellipsis,t(k)) in R(k), the sequence of random vectors (X(t(1)+n),ellipsis,X(t(k)+n))n=0,+1, ellipsis, is stationary (and ergodic). For such an ergodic process, let T be a positive random variable defined on the sample space of the process, representing a time of failure. The local failure-rate function is assumed to be of the form up(x),-infinity0 is a small number, tending to 0; and, for each u,T=T(u) is the corresponding failure-time. It is shown that X(T(u)) and uT(u) have, for u-->0, a limiting joint distribution and are, in fact, asymptotically independent. The marginal distributions are explicitly given. Let Y be a random variable whose distribution is the limit of that of X(T(u)). Under the hypothesis that p(x) is unknown or of known functional form but with unknown parameters, it is shown how p(x) can be estimated on the basis of independent copies of the random variable Y. The results are applied to the analysis of a case-control study featuring a 'marker' process X(t) and an 'event-time' T. The event in the study is considered to be particularly rare, and this is reflected in the assumption u-->0. The control-distribution is identified with the average marginal distribution of the (periodically stationary) marker process X(t), and the case-distribution is identified with that of Y. The particular application is a biomedical trial to determine the risk of stroke in terms of the level of an anticoagulant in the blood of the patient.     

The elastic behavior of the urinary bladder for large deformations

The purpose of this paper is to investigate the theoretical basis for the pressure-distension behavior of the urinary bladder. A finite strain theory is developed for hollow spherical structures and it is shown that the Treloar model is a good prototype only for rubber balloons. The pressure-extension ratio relationship is inverted to lead a general form of strain energy function, and fitted by an empirical relation involving one exponential. The following form of strain energy function is derived: W(lambda, lambda, lambda -2) = C1 (P(1), a) + P(1)C2 (a, lambda)ea(lambda -1). Where C1(P(1), a) is a constant (N m-2), P(1) is the initial pressure, a is the rate of pressure increase and C2 (a, lambda) a third degree polynomial relation. P(1) and a are experimentally determined through volumetric pressure-distension data. It is verified that this type of energy function is also valid for uniaxial loading experiments by testing strips coming from the same bladder for which P(1) and a were computed. There is a good agreement between the experimental points and the theoretical stress-strain relation. Finally, the strain energy function is plotted as a function of the first strain invariant and appears to be of an exponential nature.     

Permeation of a beta-heptapeptide derivative across phospholipid bilayers

Based on a number of experiments it is concluded that the fluorescein labeled beta-heptapeptide fluoresceinyl-NH-CS-(S)-beta(3)hAla-(S)-beta(3)hArg-(R)-beta(3)hLeu-(S)-beta(3)hPhe-(S)-beta(3)hAla-(S)-beta(3)hAla-(S)-beta(3)hLys-OH translocates across lipid vesicle bilayers formed from DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine). The conclusion is based on the following observations: (i) addition of the peptide to the vicinity of micrometer-sized giant vesicles leads to an accumulation of the peptide inside the vesicles; (ii) if the peptide is injected inside individual giant vesicles, it is released from the vesicles in a time dependent manner; (iii) if the peptide is encapsulated within sub-micrometer-sized large unilamellar vesicles, it is released from the vesicles as a function of time; (iv) if the peptide is submitted to immobilized liposome chromatography, the peptide is retained by the immobilized DOPC vesicles. Furthermore, the addition of the peptide to calcein-containing DOPC vesicles does not lead to significant calcein leakage and vesicle fusion is not observed. The finding that derivatives of the beta-heptapeptide (S)-beta(3)hAla-(S)-beta(3)hArg-(R)-beta(3)hLeu-(S)-beta(3)hPhe-(S)-beta(3)hAla-(S)-beta(3)hAla-(S)-beta(3)hLys-OH can translocate across phospholipid bilayers is supported by independent measurements using Tb(3+)-containing large unilamellar vesicles prepared from egg phosphatidylcholine and wheat germ phosphatidylinositol (molar ratio of 9:1) and a corresponding peptide that is labeled with dipicolinic acid instead of fluorescein. The experiments show that this dipicolinic acid labeled beta-heptapeptide derivative also permeates across phospholipid bilayers. The possible mechanism of the translocation of the particular beta-heptapeptide derivatives across the membrane of phospholipid vesicles is discussed within the frame of the current understanding of the permeation of certain oligopeptides across simple phospholipid bilayers.     

Methods for estimation of radiation risk in epidemiological studies accounting for classical and Berkson errors in doses

With a binary response Y, the dose-response model under consideration is logistic in flavor with pr(Y=1 | D) = R (1+R)(-1), R = λ(0) + EAR D, where λ(0) is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as Dimes=fiQi(mes)/Mi(mes). Here, Qi(mes) is the measured content of radioiodine in the thyroid gland of person i at time t(mes), Mi(mes) is the estimate of the thyroid mass, and f(i) is the normalizing multiplier. The Q(i) and M(i) are measured with multiplicative errors Vi(Q) and ViM, so that Qi(mes)=Qi(tr)Vi(Q) (this is classical measurement error model) and Mi(tr)=Mi(mes)Vi(M) (this is Berkson measurement error model). Here, Qi(tr) is the true content of radioactivity in the thyroid gland, and Mi(tr) is the true value of the thyroid mass. The error in f(i) is much smaller than the errors in ( Qi(mes), Mi(mes)) and ignored in the analysis. By means of Parametric Full Maximum Likelihood and Regression Calibration (under the assumption that the data set of true doses has lognormal distribution), Nonparametric Full Maximum Likelihood, Nonparametric Regression Calibration, and by properly tuned SIMEX method we study the influence of measurement errors in thyroid dose on the estimates of λ(0) and EAR. The simulation study is presented based on a real sample from the epidemiological studies. The doses were reconstructed in the framework of the Ukrainian-American project on the investigation of Post-Chernobyl thyroid cancers in Ukraine, and the underlying subpolulation was artificially enlarged in order to increase the statistical power. The true risk parameters were given by the values to earlier epidemiological studies, and then the binary response was simulated according to the dose-response model.     

Unusually high standard redox potential of acrylyl-CoA/propionyl-CoA couple among enoyl-CoA/acyl-CoA couples: a reason for the distinct metabolic pathway of propionyl-CoA from longer acyl-CoAs.

The standard redox potential of acrylyl-CoA/propionyl-CoA couple (C(3)) was determined to be 69 mV (vs. standard hydrogen electrode) at pH 7 and 25 degrees C. This value implies that the 2, 3-dehydrogenation of propionyl-CoA is thermodynamically much more unfavorable than that of longer acyl-CoAs because the standard redox potentials of crotonyl-CoA/butyryl-CoA (C(4)), octenoyl-CoA/octanoyl-CoA (C(8)), and hexadecenoyl-CoA/palmitoyl-CoA (C(16)) are all about -10 mV. The unusually high standard redox potential of the acrylyl-CoA/propionyl-CoA couple is thought to be one of the reasons that in mammals propionyl-CoA is not metabolized by beta-oxidation as in the case of longer acyl-CoAs, but by a methylmalonyl-CoA pathway. The obvious structural difference between C(3) and C(4) (and longer) is whether an H or the C(4) atom is connected to -C(3)H=C(2)H-C(1)O-S-CoA. The molecular orbital calculations (MOPAC) for the enoyl and acyl forms of C(3) and C(4) revealed that this structural feature is the main cause for the higher standard redox potential of the C(3) couple. That is, the C(4)-C(3) bond is stabilized by the dehydrogenation to a greater degree than the H-C(3) bond.     

Steroid-binding specificity of human sex hormone-binding globulin is influenced by occupancy of a zinc-binding site

One calcium-binding site (site I) and a second poorly defined metal-binding site (site II) have been observed previously within the amino-terminal laminin G-like domain (G domain) of human sex hormone-binding globulin (SHBG). By soaking crystals of this structure in 2.5 mm ZnCl(2), site II and a new metal-binding site (site III) were found to bind Zn(2+). Site II is located close to the steroid-binding site, and Zn(2+) is coordinated by the side chains of His(83) and His(136) and the carboxylate group of Asp(65). In this site, Zn(2+) prevents Asp(65) from interacting with the steroid 17beta-hydroxy group and alters the conformations of His(83) and His(136), as well as a disordered region over the steroid-binding site. Site III is formed by the side chains of His(101) and the carboxylate group of Asp(117), and the distance between them (2.7 A) is increased to 3.7 A in the presence of Zn(2+). The affinity of SHBG for estradiol is reduced in the presence of 0. 1-1 mm Zn(2+), whereas its affinity for androgens is unchanged, and chemically-related metal ions (Cd(2+) and Hg(2+)) have similar but less pronounced effects. This is not observed when Zn(2+) coordination at site II is modified by substituting Gln for His(136). An alteration in the steroid-binding specificity of human SHBG by Zn(2+) occupancy of site II may be relevant in male reproductive tissues where zinc concentrations are very high.     

The regulation of extramitochondrial free calcium ion concentration by rat liver mitochondria

The mechanism whereby rat liver mitochondria regulate the extramitochondrial concentration of free Ca(2+) was investigated. At 30 degrees C and pH7.0, mitochondria can maintain a steady-state pCa(2+) (0) (the negative logarithm of the free extramitochondrial Ca(2+) concentration) of 6.1 (0.8mum). This represents a true steady state, as slight displacements in pCa(2+) (0) away from 6.1 result in net Ca(2+) uptake or efflux in order to restore pCa(2+) (0) to its original value. In the absence of added permeant weak acid, the steady-state pCa(2+) (0) is virtually independent of the Ca(2+) accumulated in the matrix until 60nmol of Ca(2+)/mg of protein has been taken up. The steady-state pCa(2+) (0) is also independent of the membrane potential, as long as the latter parameter is above a critical value. When the membrane potential is below this value, pCa(2+) (0) is variable and appears to be governed by thermodynamic equilibration of Ca(2+) across a Ca(2+) uniport. Permeant weak acids increase, and N-ethylmaleimide decreases, the capacity of mitochondria to buffer pCa(2+) (0) in the region of 6 (1mum-free Ca(2+)) while accumulating Ca(2+). Permeant acids delay the build-up of the transmembrane pH gradient as Ca(2+) is accumulated, and consequently delay the fall in membrane potential to values insufficient to maintain a pCa(2+) (0) of 6. The steady-state pCa(2+) (0) is affected by temperature, incubation pH and Mg(2+). The activity of the Ca(2+) uniport, rather than that of the respiratory chain, is rate-limiting when pCa(2+) (0) is greater than 5.3 (free Ca(2+) less than 5mum). When the Ca(2+) electrochemical gradient is in excess, the activity of the uniport decreases by 2-fold for every 0.12 increase in pCa(2+) (0) (fall in free Ca(2+)). At pCa(2+) (0) 6.1, the activity of the Ca(2+) uniport is kinetically limited to 5nmol of Ca(2+)/min per mg of protein, even when the Ca(2+) electrochemical gradient is large. A steady-state cycling of Ca(2+) through independent influx and efflux pathways provides a model which is kinetically and thermodynamically consistent with the present observations, and which predicts an extremely precise regulation of pCa(2+) (0) by liver mitochondria in vivo.     

Is N2O3 the main nitrosating intermediate in aerated nitric oxide (NO) solutions in vivo? If so,where, when,and which one?

The widespread opinion that N(2)O(3) as a product of NO oxidation is the only nitros(yl)ating agent under aerobic conditions is based on experiments in homogeneous buffered water solutions. In vivo NO is oxidized in heterogeneous media and this opinion is not correct. The equilibrium in the system being dependent on temperature and DeltaG((sol)) for NO, NO(2), isomers of both N(2)O(3), and N(2)O(4). For polar solvents including water, DeltaG((sol)) for N(2)O(3) is high enough, and a stationary concentration of N(2)O(3) in the mixture with other oxides is sufficient to guarantee the hydrolysis of N(2)O(3) to nitrite. In heterogeneous media, the mixture contains solvates NO(2(sol)), N(2)O(3(sol)), and N(2)O(4(sol)) at stationary nonequilibrium concentrations. As far as DeltaG((sol)) is decreased in heterogeneous mixtures with low polar solvents and/or at increased temperatures, the equilibrium in such a system shifts to NO(2). Although NO(2) is a reactive free radical, it almost does not react with water. In contrast, the reaction with most functional protein groups efficiently proceeds by a radical type with the formation of nitrite and new radicals (X) further stabilized in various forms. Therefore, the ratio of the nitrosylated and nitrated products yields depends on actual concentrations of all NO(x).     

How might spatial nonuniformity of dose in a homogeneous biological system affect its total response?

The total response of a homogeneous biological system to a fixed total dose of a biological agent is modeled by dividing the system into N cubical voxels, each of which can be associated with an individual dose D(n) and an individual response R(n) =F(D(n)). Among the results shown are the following: A. (Voxel Theorem). Let the average dose D(avg) be held fixed as the dose distribution is shifted from uniform u to arbitrary a. Then, if F' > or = 0 over [D(min), D(max)] and R = summation operator (n = 1)(N) R(n), a sufficient condition that NF(D(avg)) = R(u) < or = R(a) is that F be a concave-upwards function of dose; that is, F" > or = 0 over [D(min), D(max)]. B.If F' is constant over [D(min), D(max)], then R(a) = R(u). That is, the total response is a function of D(avg) only. The applications of these (and other) results are illustrated by examples from bioelectromagnetics.     

Transient kinetic analysis of the 130-kDa myosin I (MYR-1 gene product) from rat liver. A myosin I designed for maintenance of tension?

The 130-kDa myosin I (MI(130)), product of the myr-1 gene, is one member of the mammalian class I myosins, a group of small, calmodulin-binding mechanochemical molecules of the myosin superfamily that translocate actin filaments. Roles for MI(130) are unknown. Our hypothesis is that, as with all myosins, MI(130) is designed for a particular function and hence possesses specific biochemical attributes. To test this hypothesis we have characterized the enzymatic properties of MI(130) using steady-state and stopped-flow kinetic analyses. Our results indicate that: (i) the Mg(2+)-ATPase activity is activated in proportion to actin concentration in the absence of Ca(2+); (ii) the ATP-induced dissociation of actin-MI(130) is much slower for MI(130) than has been observed for other myosins (-Ca(2+), second order rate constant of ATP binding, 1.7 x 10(4) M(-1) s(-1); maximal rate constant, 32 s(-1)); (iii) ADP binds to actin-MI(130) with an affinity of approximately 10 microM and competes with ATP-induced dissociation of actin-MI(130); the rate constant of ADP release from actin-MI(130) is 2 s(-1); (iv) the rates of the ATP-induced dissociation of actin-MI and ADP release are 2-3 times greater in the presence of CaCl(2), indicating a sensitivity of motor activity to Ca(2+); and (v) the affinity of MI(130) for actin (15 nM) is typical of that observed for other myosins. Together, these results indicate that although MI(130) shares some characteristics with other myosins, it is well adapted for maintenance of cortical tension.     

Hairpin-Tail: A Case of Post-Reductional Gene Action in the Mouse Egg?

Hairpin-tail (T(hp)) is a new allele of brachyury on chromosome 17 (linkage group IX) of the mouse. The morphological effects in the heterozygote are on the notochord and the tail. The homozygous abnormal is unknown. T(hp) is unique in that the phenotype of the heterozygote seems to depend on the source of the T(hp) gene. If it is inherited via the egg the phenotype is extreme and death follows in utero. Embryos derived from a T(hp) sperm and a+egg are less abnormal and viable. This is not a simple maternal effect, as T(hp)xT(hp) matings produce two distinct types of heterozygous embryos.     

Kinetics and mechanisms of the oxidation of myoglobin by Fe(III) and Cu(II) complexes

Two distinct mechanisms by which sperm whale myoglobin reduces, respectively, complexes of Fe(III) and Cu(II) and, in turn, is oxidized to metmyoglobin have been characterized. For both mechanisms, deoxymyoglobin is the active reductant. An outer sphere electron transfer, probably at the edge of the heme, is involved for Fe(III)NTA (NTA is nitrilotriacetic acid). This pathway does not involve ionic binding of the Fe(III) complex to the protein. The most reactive species of Fe(III)NTA is uncharged. No inhibition is observed with Ni(II) or Zn(II). An outer sphere site specific electron transfer is operative for reduction of Cu(II) complexes. The site has been characterized using NMR spectroscopy and involves one or more histidines. There is an initial binding of the Cu(II) chelate. The ternary complex of chelator-Cu(II)-deoxymyoglobin is a mandatory intermediate. Ni(II) and Zn(II) compete with Cu(II) for the binding site. A scheme for the participation of either or both of these mechanisms in reduction reactions of heme proteins is proposed. Both the overall redox potential, delta E0, and the stability constant for the ternary complex, K, govern the pathway and the reaction rate.     

A role for apolipoprotein(a) in protection of the low-density lipoprotein component of lipoprotein(a) from copper-mediated oxidation

Low-density lipoprotein (LDL) oxidation is stimulated by copper. Addition of a recombinant form of apolipoprotein(a) (apo(a); the distinguishing protein component of lipoprotein(a)) containing 17 plasminogen kringle IV-like domains (17K r-apo(a)) protects LDL against oxidation by copper. Protection is specific to apo(a) and is not achieved by plasminogen or serum albumin. When Cu(2+) is added to 17K r-apo(a), its intrinsic fluorescence is quenched in a concentration-dependent and saturable manner. Quenching is unchanged whether performed aerobically or anaerobically and is reversible by ethylenediaminetetraacetate, suggesting that it is due to equilibrium binding of Cu(2+) and not to oxidative destruction of tryptophan residues. The fluorescence change exhibits a sigmoid dependence on copper concentration, and time courses of quenching are complex. At copper concentrations below 10 microM there is little quenching, whereas above 10 microM quenching proceeds immediately as a double-exponential decay. The affinity and kinetics of copper binding to 17K r-apo(a) are diminished in the presence of the lysine analogue epsilon -aminocaproic acid. We propose that copper binding to the kringle domains of 17K is mediated by a His-X-His sequence that is located about 5A from the closest tryptophan residue of the lysine binding pocket. Copper binding may account for the natural resistance to copper-mediated oxidation of lipoprotein(a) relative to LDL that has been previously reported and for the protection afforded by apo(a) from copper-mediated oxidation of LDL that we describe in the present study.