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Antioxidants in health and disease
1. I S Young1,
2. J V Woodside2
1. 1Department of Clinical Biochemistry, Institute of Clinical Science, Grosvenor Road, Belfast, Northern Ireland, BT12 6BJ, UK
2. 2Department of Surgery, Royal Free and University College London Medical School, 67–73 Riding House Street, London, W1P 7LD, UK
1. Professor Young, Department of Clinical Biochemistry, Institute of Clinical Science, Royal Group of Hospitals, Grosvenor Road, Belfast BT12 6BJ, UK I.Young{at}qub.ac.uk

## Abstract

Free radical production occurs continuously in all cells as part of normal cellular function. However, excess free radical production originating from endogenous or exogenous sources might play a role in many diseases. Antioxidants prevent free radical induced tissue damage by preventing the formation of radicals, scavenging them, or by promoting their decomposition. This article reviews the basic chemistry of free radical formation in the body, the consequences of free radical induced tissue damage, and the function of antioxidant defence systems, with particular reference to the development of atherosclerosis.

• antioxidants
• oxidative stress
• coronary heart disease
• atherosclerosis

## Statistics from Altmetric.com

An antioxidant can be defined as: “any substance that, when present in low concentrations compared to that of an oxidisable substrate, significantly delays or inhibits the oxidation of that substrate”.1 The physiological role of antioxidants, as this definition suggests, is to prevent damage to cellular components arising as a consequence of chemical reactions involving free radicals. In recent years, a substantial body of evidence has developed supporting a key role for free radicals in many fundamental cellular reactions and suggesting that oxidative stress might be important in the pathophysiology of common diseases including atherosclerosis, chronic renal failure, and diabetes mellitus. The aim of this review is to consider mechanisms of free radical formation in the body, the consequences of free radical induced tissue damage, and the function of antioxidant defence systems in health and disease.

## Free radicals and their chemical reactions

A free radical can be defined as any molecular species capable of independent existence that contains an unpaired electron in an atomic orbital.2 The presence of an unpaired electron results in certain common properties that are shared by most radicals. Radicals are weakly attracted to a magnetic field and are said to be paramagnetic. Many radicals are highly reactive and can either donate an electron to or extract an electron from other molecules, therefore behaving as oxidants or reductants. As a result of this high reactivity, most radicals have a very short half life (10−6 seconds or less) in biological systems, although some species may survive for much longer.2 The most important free radicals in many disease states are oxygen derivatives, particularly superoxide and the hydroxyl radical. Radical formation in the body occurs by several mechanisms, involving both endogenous and environmental factors (fig 1).

Figure 1

Major sources of free radicals in the body and the consequences of free radical damage.

Superoxide (O2−.) is produced by the addition of a single electron to oxygen, and several mechanisms exist by which superoxide can be produced in vivo.3 Several molecules, including adrenaline, flavine nucleotides, thiol compounds, and glucose, can oxidise in the presence of oxygen to produce superoxide, and these reactions are greatly accelerated by the presence of transition metals such as iron or copper. The electron transport chain in the inner mitochondrial membrane performs the reduction of oxygen to water. During this process free radical intermediates are generated, which are generally tightly bound to the components of the transport chain. However, there is a constant leak of a few electrons into the mitochondrial matrix and this results in the formation of superoxide.4 The activity of several other enzymes, such as cytochrome p450 oxidase in the liver and enzymes involved in the synthesis of adrenal hormones, also results in the leakage of a few electrons into the surrounding cytoplasm and hence superoxide formation. There might also be continuous production of superoxide by vascular endothelium to neutralise nitric oxide,5, 6 production of superoxide by other cells to regulate cell growth and differentiation,7 and the production of superoxide by phagocytic cells during the respiratory burst.8

Any biological system generating superoxide will also produce hydrogen peroxide as a result of a spontaneous dismutation reaction. In addition, several enzymatic reactions, including those catalysed by glycolate oxidase and D-amino acid oxidase, might produce hydrogen peroxide directly.9 Hydrogen peroxide is not a free radical itself, but is usually included under the general heading of reactive oxygen species (ROS). It is a weak oxidising agent that might directly damage proteins and enzymes containing reactive thiol groups. However, its most vital property is the ability to cross cell membranes freely, which superoxide generally cannot do.10 Therefore, hydrogen peroxide formed in one location might diffuse a considerable distance before decomposing to yield the highly reactive hydroxyl radical, which is likely to mediate most of the toxic effects ascribed to hydrogen peroxide. Therefore, hydrogen peroxide acts as a conduit to transmit free radical induced damage across cell compartments and between cells. In the presence of hydrogen peroxide, myeloperoxidase will generate hypochlorous acid and singlet oxygen, a reaction that plays an important role in the killing of bacteria by phagocytes.11

The hydroxyl radical (OH.), or a closely related species, is probably the final mediator of most free radical induced tissue damage.12 All of the reactive oxygen species described above exert most of their pathological effects by giving rise to hydroxyl radical formation. The reason for this is that the hydroxyl radical reacts, with extremely high rate constants, with almost every type of molecule found in living cells including sugars, amino acids, lipids, and nucleotides. Although hydroxyl radical formation can occur in several ways, by far the most important mechanism in vivo is likely to be the transition metal catalysed decomposition of superoxide and hydrogen peroxide.13

All elements in the first row of the d-block of the periodic table are classified as transition metals. In general, they contain one or more unpaired electrons and are therefore themselves radicals when in the elemental state. However, their key property from the point of view of free radical biology is their variable valency, which allows them to undergo reactions involving the transfer of a single electron. The most important transition metals in human disease are iron and copper. These elements play a key role in the production of hydroxyl radicals in vivo.13 Hydrogen peroxide can react with iron II (or copper I) to generate the hydroxyl radical, a reaction first described by Fenton in 1894:$Math$

This reaction can occur in vivo, but the situation is complicated by the fact that superoxide (the major source of hydrogen peroxide in vivo) will normally also be present. Superoxide and hydrogen peroxide can react together directly to produce the hydroxyl radical, but the rate constant for this reaction in aqueous solution is virtually zero. However, if transition metal ions are present a reaction sequence is established that can proceed at a rapid rate:$Math$$Math$net result:$Math$

The net result of the reaction sequence illustrated above is known as the Haber-Weiss reaction. Although most iron and copper in the body are sequestered in forms that are not available to catalyse this reaction sequence, it is still of importance as a mechanism for the formation of the hydroxyl radical in vivo. The actual reactions, however, may be somewhat more complex than those described above and it is possible that other reactive intermediates such as the ferryl and perferryl radicals might also be formed.12

Approximately 4.5 g of iron can be found in the average adult man, most of which is contained in the haemoglobin molecule and other haem containing proteins. Dietary iron is absorbed preferentially from the proximal part of the small intestine in the divalent form and is transferred to the circulation in which it is carried by transferrin.14 Under most circumstances iron remains tightly bound to one of several proteins, including transferrin, lactoferrin, haem proteins, ferritin, or haemosiderin. In addition, however, it seems likely that a small iron pool will be maintained as complexes with a variety of small molecules, such as nucleotides and citrate within the cytoplasm and subcellular organelles.14 This pool is probably capable of catalysing an iron driven Fenton reaction in vivo. Certainly, these complexes can promote hydroxyl radical formation in vitro.15 Redox reactive iron can be measured using the bleomycin iron assay,16 although it remains unclear to what extent iron detected by this assay correlates with any discrete anatomical or physiological pool. In normal circumstances, no bleomycin reactive iron is detectable in plasma from healthy subjects, implying that transferrin or ferritin bound iron is not available to drive hydroxyl radical production.17 However, transferrin will release its iron at an acidic pH, particularly in the presence of small molecular weight chelating agents such as ADP, ATP, and citrate.15 Such conditions are found in areas of active inflammation and during ischaemia reperfusion injury,18 and it is therefore likely that hydroxyl radicals contribute to tissue damage in these settings. Iron is released from ferritin by reducing agents including ascorbate and superoxide itself,19, 20 and hydrogen peroxide can release iron from a range of haem proteins.21 Therefore, although the iron binding proteins effectively chelate iron and prevent any appreciable redox effects under normal physiological conditions, this protection can break down in disease states. The role of copper is analogous to that described above for iron.22, 23

Although free radical production occurs as a consequence of the endogenous reactions described above and plays an important role in normal cellular function, it is important to remember that exogenous environmental factors can also promote radical formation. Ultraviolet light will lead to the formation of singlet oxygen and other reactive oxygen species in the skin.24 Atmospheric pollutants such as ozone and nitrogen dioxide lead to radical formation and antioxidant depletion in the bronchoalveolar lining fluid, and this may exacerbate respiratory disease.2527 Cigarette smoke contains millimolar amounts of free radicals, along with other toxins.28

Various xenobiotics also cause tissue damage as a consequence of free radical generation, including paraquat,29 paracetamol,30 bleomycin,31 and anthracyclines.32

## Antioxidant defence systems

Because radicals have the capacity to react in an indiscriminate manner leading to damage to almost any cellular component, an extensive range of antioxidant defences, both endogenous and exogenous, are present to protect cellular components from free radical induced damage. These can be divided into three main groups: antioxidant enzymes, chain breaking antioxidants, and transition metal binding proteins2 (fig 2).

Figure 2

Antioxidant defences against free radical attack. Antioxidant enzymes catalyse the breakdown of free radical species, usually in the intracellular environment. Transition metal binding proteins prevent the interaction of transition metals such as iron and copper with hydrogen peroxide and superoxide producing highly reactive hydroxyl radicals. Chain breaking antioxidants are powerful electron donors and react preferentially with free radicals before important target molecules are damaged. In doing so, the antioxidant is oxidised and must be regenerated or replaced. By definition, the antioxidant radical is relatively unreactive and unable to attack further molecules.

### THE ANTIOXIDANT ENZYMES

#### Catalase

Catalase was the first antioxidant enzyme to be characterised and catalyses the two stage conversion of hydrogen peroxide to water and oxygen:$Math$$Math$

Catalase consists of four protein subunits, each containing a haem group and a molecule of NADPH.33 The rate constant for the reactions described above is extremely high (∼107 M/sec), implying that it is virtually impossible to saturate the enzyme in vivo. Catalase is largely located within cells in peroxisomes, which also contain most of the enzymes capable of generating hydrogen peroxide. The amount of catalase in cytoplasm and other subcellular compartments remains unclear, because peroxisomes are easily ruptured during the manipulation of cells. The greatest activity is present in liver and erythrocytes but some catalase is found in all tissues.

#### Glutathione peroxidases and glutathione reductase

Glutathione peroxidases catalyse the oxidation of glutathione at the expense of a hydroperoxide, which might be hydrogen peroxide or another species such as a lipid hydroperoxide34:$Math$

Other peroxides, including lipid hydroperoxides, can also act as substrates for these enzymes, which might therefore play a role in repairing damage resulting from lipid peroxidation. Glutathione peroxidases require selenium at the active site, and deficiency might occur in the presence of severe selenium deficiency.35 Several glutathione peroxidase enzymes are encoded by discrete genes.36 The plasma form of glutathione peroxidase is believed to be synthesised mainly in the kidney.37 Within cells, the highest concentrations are found in liver although glutathione peroxidase is widely distributed in almost all tissues. The predominant subcellular distribution is in the cytosol and mitochondria, suggesting that glutathione peroxidase is the main scavenger of hydrogen peroxide in these subcellular compartments. The activity of the enzyme is dependent on the constant availability of reduced glutathione.38 The ratio of reduced to oxidised glutathione is usually kept very high as a result of the activity of the enzyme glutathione reductase:$Math$

The NADPH required by this enzyme to replenish the supply of reduced glutathione is provided by the pentose phosphate pathway. Any competing pathway that utilises NADPH (such as the aldose reductase pathway) might lead to a deficiency of reduced glutathione and hence impair the action of glutathione peroxidase. Glutathione reductase is a flavine nucleotide dependent enzyme and has a similar tissue distribution to glutathione peroxidase.39

#### Superoxide dismutase

The superoxide dismutases catalyse the dismutation of superoxide to hydrogen peroxide:$Math$

The hydrogen peroxide must then be removed by catalase or glutathione peroxidase, as described above. There are three forms of superoxide dismutase in mammalian tissues, each with a specific subcellular location and different tissue distribution.

1. Copper zinc superoxide dismutase (CuZnSOD): CuZnSOD is found in the cytoplasm and organelles of virtually all mammalian cells.40 It has a molecular mass of approximately 32 000 kDa and has two protein subunits, each containing a catalytically active copper and zinc atom.

2. Manganese superoxide dismutase (MnSOD): MnSOD is found in the mitochondria of almost all cells and has a molecular mass of 40 000 kDa.41 It consists of four protein subunits, each probably containing a single manganese atom. The amino acid sequence of MnSOD is entirely dissimilar to that of CuZnSOD and it is not inhibited by cyanide, allowing MnSOD activity to be distinguished from that of CuZnSOD in mixtures of the two enzymes.

3. Extracellular superoxide dismutase (EC-SOD): EC-SOD was described by Marklund in 198242 and is a secretory copper and zinc containing SOD distinct from the CuZnSOD described above. EC-SOD is synthesised by only a few cell types, including fibroblasts and endothelial cells, and is expressed on the cell surface where it is bound to heparan sulphates. EC-SOD is the major SOD detectable in extracellular fluids and is released into the circulation from the surface of vascular endothelium following the injection of heparin.43 EC-SOD might play a role in the regulation of vascular tone, because endothelial derived relaxing factor (nitric oxide or a closely related compound) is neutralised in the plasma by superoxide.44

### THE CHAIN BREAKING ANTIOXIDANTS

Whenever a free radical interacts with another molecule, secondary radicals may be generated that can then react with other targets to produce yet more radical species. The classic example of such a chain reaction is lipid peroxidation, and the reaction will continue to propagate until two radicals combine to form a stable product or the radicals are neutralised by a chain breaking antioxidant.45 Chain breaking antioxidants are small molecules that can receive an electron from a radical or donate an electron to a radical with the formation of stable byproducts.46 In general, the charge associated with the presence of an unpaired electron becomes dissociated over the scavenger and the resulting product will not readily accept an electron from or donate an electron to another molecule, preventing the further propagation of the chain reaction. Such antioxidants can be conveniently divided into aqueous phase and lipid phase antioxidants.

#### Lipid phase chain breaking antioxidants

These antioxidants scavenge radicals in membranes and lipoprotein particles and are crucial in preventing lipid peroxidation. The most important lipid phase antioxidant is probably vitamin E.47 Vitamin E occurs in nature in eight different forms, which differ greatly in their degree of biological activity. The tocopherols (α, β, γ, and δ) have a chromanol ring and a phytyl tail, and differ in the number and position of the methyl groups on the ring. The tocotrienols (α, β, γ, and δ) are structurally similar but have unsaturated tails. Both classes of compounds are lipid soluble and have pronounced antioxidant properties.48 They react more rapidly than polyunsaturated fatty acids with peroxyl radicals and hence act to break the chain reaction of lipid peroxidation. In addition to its antioxidant role, vitamin E might also have a structural role in stabilising membranes.49 Frank vitamin E deficiency is rare in humans, although it might cause haemolysis50 and might contribute to the peripheral neuropathy that occurs in abetalipoproteinaemia.51

The absorption, transport, and regulation of plasma concentrations of vitamin E in humans has been reviewed by Kayden and Traber,52 although in general the metabolism of vitamin E is not well described. In cell membranes and lipoproteins the essential antioxidant function of vitamin E is to trap peroxyl radicals and to break the chain reaction of lipid peroxidation.53 Vitamin E will not prevent the initial formation of carbon centred radicals in a lipid rich environment, but does minimise the formation of secondary radicals. α-Tocopherol is the most potent antioxidant of the tocopherols and is also the most abundant in humans. It quickly reacts with a peroxyl radical to form a relatively stable tocopheroxyl radical, with the excess charge associated with the extra electron being dispersed across the chromanol ring. This resonance stabilised radical might subsequently react in one of several ways. α-Tocopherol might be regenerated by reaction at the aqueous interface with ascorbate54 or another aqueous phase chain breaking antioxidant, such as reduced glutathione or urate.55 Alternatively, two α-tocopheroxyl radicals might combine to form a stable dimer, or the radical may be completely oxidised to form tocopherol quinone.

The carotenoids are a group of lipid soluble antioxidants based around an isoprenoid carbon skeleton.56 The most important of these is β-carotene, although at least 20 others may be present in membranes and lipoproteins. They are particularly efficient scavengers of singlet oxygen,57 but can also trap peroxyl radicals at low oxygen pressure with an efficiency at least as great as that of α-tocopherol. Because these conditions prevail in many biological tissues, the carotenoids might play a role in preventing in vivo lipid peroxidation.58 The other important role of certain carotenoids is as precursors of vitamin A (retinol). Vitamin A also has antioxidant properties,59 which do not, however, show any dependency on oxygen concentration.

Flavonoids are a large group of polyphenolic antioxidants found in many fruits, vegetables, and beverages such as tea and wine.6062 Over 4000 flavonoids have been identified and they are divided into several groups according to their chemical structure, including flavonols (quercetin and kaempherol), flavanols (the catechins), flavones (apigenin), and isoflavones (genistein). Epidemiological studies suggest an inverse relation between flavonoid intake and incidence of chronic diseases such as coronary heart disease (CHD).6365 However, little is currently known about the absorption and metabolism of flavonoids and epidemiological associations might be a consequence of confounding by other factors. Available evidence suggests that the bioavailability of many flavonoids is poor,6668 and plasma values very low, although there is some evidence that augmenting the intake of flavonoids might improve biochemical indices of oxidative damage.68, 69 Apart from flavonoids, other dietary phenolic compounds might also make a small contribution to total antioxidant capacity.70

Ubiquinol-10, the reduced form of coenzyme Q10, is also an effective lipid soluble chain breaking antioxidant.71 Although present in lower concentrations than α-tocopherol, it can scavenge lipid peroxyl radicals with higher efficiency than either α-tocopherol or the carotenoids, and can also regenerate membrane bound α-tocopherol from the tocopheryl radical.72 Indeed, whenever plasma or isolated low density lipoprotein (LDL) cholesterol is exposed to radicals generated in the lipid phase, ubiquinol-10 is the first antioxidant to be consumed, suggesting that it might be of particular importance in preventing the propagation of lipid peroxidation.73 However, work to clarify further its role has been hampered by the ease with which ubinquinol-10 becomes oxidised during sample handling or analysis.

#### Aqueous phase chain breaking antioxidants

These antioxidants will directly scavenge radicals present in the aqueous compartment. Qualitatively the most important antioxidant of this type is vitamin C (ascorbate).74 In humans, ascorbate acts as an essential cofactor for several enzymes catalysing hydroxylation reactions. In most cases, it provides electrons for enzymes that require prosthetic metal ions in a reduced form to achieve full enzymatic activity. Its best known role is as a cofactor for prolyl and lysyl oxidases in the synthesis of collagen. However, in addition to these well defined actions, several other biochemical pathways depend upon the presence of ascorbate.75 In addition to its role as an enzyme cofactor, the other major function of ascorbate is as a key chain breaking antioxidant in the aqueous phase.76 Ascorbate has been shown to scavenge superoxide, hydrogen peroxide, the hydroxyl radical, hypochlorous acid, aqueous peroxyl radicals, and singlet oxygen. During its antioxidant action, ascorbate undergoes a two electron reduction, initially to the semidehydroascorbyl radical and subsequently to dehydroascorbate. The semidehydroascorbyl radical is relatively stable owing to dispersion of the charge associated with the presence of a single electron over the three oxygen atoms, and it can be readily detected by electron spin resonance in body fluids in the presence of increased free radical production.77 Dehydroascorbate is relatively unstable and hydrolyses readily to diketogulonic acid, which is subsequently broken down to oxalic acid. Two mechanisms have been described by which dehydroascorbate can be reduced back to ascorbate; one is mediated by the selenoenzyme thioredoxin reductase78 and the other is a non-enzyme mediated reaction that uses reduced glutathione.79 Dehydroascorbate in plasma is probably rapidly taken up by red blood cells before recycling, so that very little, if any, dehydroascorbate is present in plasma.80

Apart from ascorbate, other antioxidants are present in plasma in high concentrations. Uric acid efficiently scavenges radicals, being converted in the process to allantoin.81 Urate might be particularly important in providing protection against certain oxidising agents, such as ozone.82 Indeed, it has been suggested that the increase in life span that has occurred during human evolution might be partly explained by the protective action provided by uric acid in human plasma.83 Part of the antioxidant effect of urate might be attributable to the formation of stable non-reactive complexes with iron, but it is also a direct free radical scavenger. Albumin bound bilirubin is also an efficient radical scavenger,84 and it has been suggested that it might play a particularly crucial role in protecting the neonate from oxidative damage,85 because deficiency of other chain breaking antioxidants is common in the newborn.

The other major chain breaking antioxidants in plasma are the protein bound thiol groups. The sulphydryl groups present on plasma proteins can function as chain breaking antioxidants by donating an electron to neutralise a free radical, with the resultant formation of a protein thiyl radical. Albumin is the predominant plasma protein and makes the major contribution to plasma sulphydryl groups, although it also has several other antioxidant properties.86 Albumin contains 17 disulphide bridges and has a single remaining cysteine residue, and it is this residue that is responsible for the capacity of albumin to react with and neutralise peroxyl radicals.87 This property is important in view of the role albumin plays in transporting free fatty acids in the blood. In addition, albumin has the capacity to bind copper ions and will inhibit copper dependent lipid peroxidation and hydroxyl radical formation. It is also a powerful scavenger of the phagocytic product hypochlorous acid, and provides the main plasma defence against this oxidant.88

Because albumin itself is damaged when it acts as an antioxidant, it has been viewed as a sacrificial molecule that prevents damage occurring to more vital species.86 The high plasma concentration of albumin and a relatively short half life mean that any damage suffered is unlikely to be of biological importance. However, in vitro work has shown that protein thiyl radicals can themselves act as a potential source of reactive oxidants. The thiyl radical can abstract an electron from a polyunsaturated fatty acid to initiate the process of lipid peroxidation,89 a reaction that can be inhibited by ascorbate and retinol. The antioxidant effects of albumin and other proteins have been shown to decrease at high concentrations and it has been suggested that this is because thiyl radicals can oxidatively damage other molecules. The importance of these findings to the antioxidant role of albumin in vivo remains unclear.

Reduced glutathione (GSH) is a major source of thiol groups in the intracellular compartment but is of little importance in the extracellular space.90 GSH might function directly as an antioxidant, scavenging a variety of radical species, as well as acting as an essential factor for glutathione peroxidase (discussed above). Thioredoxin might also function as a key intracellular antioxidant, particularly in redox induced activation of transcription factors.91

### INTERACTIONS BETWEEN CHAIN BREAKING ANTIOXIDANTS

Although the actions of chain breaking antioxidants have been considered separately above, it is vital to remember that in vivo complex interactions between antioxidants are likely to occur. For instance, it is likely that ascorbate will recycle the tocopheryl radical at the aqueous–lipid interface, so regenerating tocopherol.54 This might be crucial in ensuring that tocopherol concentrations are maintained in lipoproteins and membranes. In a similar manner, glutathione can regenerate ascorbate from dehydroascorbate. A complex interplay is therefore likely to exist between antioxidants, making it difficult to predict how antioxidants will function in vivo. It therefore becomes meaningless to ask which antioxidant is most important: the answer will depend on the circumstances existing in a particular microenvironment at a specific time, and on the nature of the oxidant injury taking place.

A second important property of chain breaking antioxidants is their ability to act as pro-oxidants. In certain circumstances, the presence of an antioxidant might paradoxically lead to increased oxidative damage. For instance, it has been reported that the administration of vitamin C can sometimes lead to an increase in oxidative damage, particularly if iron is also administered.92 Similarly, it has been clearly shown in vitro that tocopherol might promote LDL oxidation in the absence of an aqueous phase antioxidant such as ascorbate.93 Whether these reactions are important in vivo is as yet unclear. However, the possibility that antioxidants may have pro-oxidant effects in vivo must be considered when designing and interpreting the results of clinical trials of antioxidant supplementation.

### THE TRANSITION METAL BINDING PROTEINS

As discussed above, transition metal binding proteins (ferritin, transferrin, lactoferrin, and caeruloplasmin) act as a crucial component of the antioxidant defence system by sequestering iron and copper so that they are not available to drive the formation of the hydroxyl radical. The main copper binding protein, caeruloplasmin, might also function as an antioxidant enzyme that can catalyse the oxidation of divalent iron.94$Math$

Fe2+ is the form of iron that drives the Fenton reaction and the rapid oxidation of Fe2+ to the less reactive Fe3+ form is therefore an antioxidant effect.

## Consequences of oxidative damage

Oxidative stress, arising as a result of an imbalance between free radical production and antioxidant defences, is associated with damage to a wide range of molecular species including lipids, proteins, and nucleic acids. Lipoprotein particles or membranes characteristically undergo the process of lipid peroxidation, giving rise to a variety of products including short chain aldehydes such as malondialdehyde or 4-hydroxynonenal, alkanes, and alkenes, conjugated dienes, and a variety of hydroxides and hydroperoxides.45 Many of these products can be measured as markers of lipid peroxidation. Detailed discussion of this complex issue is outside the scope of this review, but the measurement of isoprostanes by gas chromatography mass spectroscopy is probably the most specific marker of free radical damage to lipids.95 Oxidative damage to proteins and nucleic acids similarly gives rise to a variety of specific damage products as a result of modifications of amino acids or nucleotides.45 Such oxidative damage might also lead to cellular dysfunction, and it is this that might contribute to the pathophysiology of a wide variety of diseases.

## Oxidative stress and disease

A role for oxidative stress has been postulated in many conditions, including atherosclerosis, inflammatory conditions,96 certain cancers,97 and the process of aging.98 In many cases, this follows the observation of increased amounts of free radical damage products, particularly markers of lipid peroxidation, in body fluids. It is important to remember, however, that lipid peroxidation is an inevitable accompaniment of cell death from any cause. In most cases peroxidation is a secondary phenomenon, and this does not therefore directly indicate an important role for oxidative stress in the disease concerned. If a primary role for oxidative stress in a particular setting is to be sustained, there should be a plausible mechanism by which increased free radical production or a decrease in antioxidant defences might occur. In addition, evidence of oxidative stress should be detectable before the onset of tissue damage and augmentation of antioxidant status at an early stage should either prevent or greatly reduce tissue damage.

Atherosclerosis can be taken as an example of a process for which there is substantial evidence of a role for oxidative stress. Hypercholesterolaemia is universally accepted as a major risk factor for atherosclerosis. However, at any given concentration of plasma cholesterol, there is still great variability in the occurrence of cardiovascular events. One of the major breakthroughs in atherogenesis research has been the realisation that oxidative modification of LDL might be a crucially important step in the development of the atherosclerotic plaque.99, 100 The formation of foam cells from monocyte derived macrophages in early atherosclerotic lesions is not caused by native LDL but only after the modification of LDL by various chemical reactions such as oxidation. Oxidation of LDL is a process initiated and propagated by free radicals or by one of several enzymes,101 and is believed to occur mainly in the arterial wall in a microenvironment where antioxidants may become depleted. All the cells of the vessel wall—endothelial cells, smooth muscle cells, macrophages, and lymphocytes—can modify LDL in vitro.102104 Several mechanisms are likely to be involved, including transition metal ion mediated generation of hydroxyl radicals, the production of reactive oxygen species by enzymes such as myeloperoxidase and lipoxygenase, and direct modification by reactive nitrogen species. Because oxidation of LDL is primarily a free radical mediated process that is inhibited by antioxidants, antioxidant depletion might be a risk factor for cardiovascular disease (CVD).

Evidence for LDL oxidation in vivo is now well established. In immunocytochemical studies, antibodies against oxidised LDL stain atherosclerotic lesions but not normal arterial tissue.105 LDL extracted from animal and human lesions has been shown to be oxidised and is rapidly taken up by macrophage scavenger receptors.106 In young survivors of myocardial infarction (MI), an association has been demonstrated between increased susceptibility of LDL to oxidation and the degree of coronary atherosclerosis,107 whereas the presence of ceroid, a product of lipid peroxidation, has been shown in advanced atherosclerotic plaques.108

Oxidised LDL has several properties that promote atherogenesis, apart from its rapid uptake into macrophages via the scavenger receptor. Oxidised forms of LDL are chemotactic for circulating macrophages and smooth muscle cells and facilitate monocyte adhesion to the endothelium and entry into the subendothelial space.109 Oxidised LDL is also cytotoxic towards arterial endothelial cells110 and inhibits the release of nitric oxide and the resulting endothelium dependent vasodilation.111 Therefore, there is a potential role for oxidised LDL in altering vasomotor responses, perhaps contributing to vasospasm in diseased vessels. In addition, oxidised LDL is immunogenic; autoantibodies against various epitopes of oxidised LDL have been found in human serum.112, 113 and immunoglobulin (IgG) specific for epitopes of oxidised LDL can be found in lesions.114 Oxidised LDL can induce arterial wall cells to produce chemotactic factors, adhesion molecules, cytokines, and growth factors that have a role to play in the development of the plaque.115, 116

Apart from the atherogenic consequences of LDL oxidation, it is increasingly recognised that reactive oxygen and nitrogen species directly interact with signalling mechanisms in the arterial wall to regulate vascular function.117 The activities of oxidant generating enzymes in the arterial wall are regulated by both receptor activation and by non-receptor mediated pathways. The effects of antioxidants on these processes are complex but provide alternative mechanisms by which antioxidant supplementation might ameliorate vascular pathology, for instance by improving endothelial function.

Evidence that antioxidant micronutrients potentially reduce the risk of CHD comes from four major sources. First, studies of antioxidant supplementation in animal models of atherosclerosis have generally shown a reduction in disease.118, 119 Second, many studies have now shown that antioxidant supplementation in healthy subjects or patients with CHD can reduce levels of free radical damage products and protect LDL against oxidation.120, 121 Vitamin E appears to be the most effective antioxidant; both β-carotene and vitamin C have produced extensions in lag time to oxidation only in a few studies, although it remains possible that they might have a beneficial effect in individuals with poor baseline status. Third, large scale epidemiological studies generally show that low intakes of antioxidants are associated with increased cardiovascular risk after correcting for other risk factors.122125 The epidemiological evidence is strongest in the case of vitamin E. In particular, two large longitudinal studies in the USA examined the association between antioxidant intake and the risk of CHD. In a group of 39 910 male health professionals, men who took vitamin E supplements in doses of at least 100 IU/day for over two years had a 37% lower relative risk of CHD than those who did not take vitamin E supplements, after adjustment for age, coronary risk factors, and intake of vitamin C and β-carotene.126 In the nurses' health study of 87 245 female nurses, women who took vitamin E supplements for more than two years had a 41% lower relative risk of major coronary disease.127 This effect persisted after adjustment for age, smoking, obesity, exercise, blood pressure, cholesterol, and the use of postmenopausal oestrogen replacement, aspirin, vitamin C, and β-carotene. High vitamin E intakes from dietary sources were not associated with a significant decrease in risk, although even the highest dietary vitamin E intakes were far lower than intakes among supplement users.

The evidence linking the water soluble vitamin C with CVD is less strong than for vitamin E. In the physicians' follow-up study, a high intake of vitamin C was not associated with a lower risk of CHD in men, whereas in women from the nurses' health survey, an initial effect was attenuated after adjustment for multivitamin use. Only one prospective study involving 11 348 adults demonstrated an inverse relation between vitamin C intake and overall cardiovascular mortality.128 This effect resulted largely from the use of vitamin C in supplements and might have been caused by other antioxidant vitamins in multivitamin preparations. A prospective population study of 1605 healthy men aged 42, 48, 54, or 60 years in Finland has recently shown that men who had vitamin C deficiency had a relative risk of MI of 2.5 compared with men with higher plasma vitamin C concentrations, after adjustment for other risk factors.129 There is also some indication that increased dietary intake of β-carotene is associated with reduced risk of CHD, although again the evidence is less convincing than that for vitamin E. In the prospective nurses' health survey, consumption of vitamins A and β-carotene in food and supplements weakly predicted the incidence of CHD; Gaziano and Hennekens calculated a 22% risk reduction for women in the highest quintile of β-carotene compared with those in the lowest.130

Thus, there is a plausible case supported by experimental studies, animal experiments, and epidemiology linking oxidative stress and atherosclerosis. The key test of such a hypothesis is whether increased antioxidant intake can be shown to prevent the clinical manifestations of atherosclerosis in humans. Several published randomised studies have now considered this issue, and others are currently ongoing. Early results have not been encouraging.

The α-tocopherol, β-carotene cancer prevention trial (ATBC), conducted among 29 133 male heavy smokers in Finland, found no reduction in CHD morbidity or mortality during five to eight years of treatment with vitamin E (50 mg daily) or β-carotene (20 mg daily).131 Those assigned vitamin E had no significant decrease in deaths from ischaemic heart disease (IHD), but a 50% excess of deaths from cerebral haemorrhage, whereas those assigned to β-carotene experienced an 11% increase in deaths from IHD. In a further analysis, a subgroup of the original subjects who had suffered a previous MI were considered.132 The endpoint of this substudy was the first major coronary event after randomisation. The proportion of major coronary events did not decrease with either α-tocopherol or β-carotene supplements. In fact, β-carotene conferred an excess of fatal IHD (75% increase in risk). There was a beneficial effect of vitamin E on non-fatal MI with a risk reduction of 38%. By contrast, in the Chinese cancer prevention study conducted among 29 584 poorly nourished residents of Linxian, China, those randomised for 5.25 years to a combined regimen of 15 mg/day β-carotene, 30 mg/day vitamin E, and 50 μg/day selenium had a significant 9% reduction in total mortality, a significant 21% decrease in stomach cancer deaths, and a non-significant 10% decrease in cerebrovascular mortality.133 However, the wisdom of generalising these findings to well nourished populations remains uncertain.

The β-carotene and retinol efficacy trial (CARET), designed to test the effects of a combined supplement of 30 mg β-carotene and 25 000 IU retinol daily among 18 314 cigarette smokers and individuals with occupational asbestos exposure, was ended early when researchers recognised a raised risk of death from lung cancer in those receiving β-carotene and, again, no beneficial effect on CVD was found.134 For CVD mortality, there was a non-significant 26% increase in the treated group (p = 0.06).

The physicians' health study followed more than 22 000 US male doctors treated with 50 mg β-carotene or placebo every other day for an average of 12 years. The trial appears to have been conducted meticulously and its results seriously question any beneficial effect with such supplementation on CVD in well nourished populations. There were no significant effects on individual outcomes, or on a combined endpoint of non-fatal MI, non-fatal stroke, and cardiovascular death, for which the relative risk was 1.0 (95% confidence interval, 0.91 to 1.09).135 There was also no evidence of harm (or benefit) among the 11% of participants who were current smokers at baseline, although small effects could not be ruled out.

Greenberg et al studied the effect of β-carotene supplementation (50 mg/day) in 1720 male and female subjects for a median period of 4.3 years with a median follow up of 8.2 years.136 Subjects whose plasma values of β-carotene were in the highest quartile at the beginning of the study had the lowest risk of death from all causes compared with those in the lowest quartile. However, supplementation had no effect on either all cause or cardiovascular mortality. Thus for β-carotene supplementation, it would appear that there are no overall benefits among those individuals with a good nutritional status who are at low or average risk of developing CHD. The situation might be different, however, for those with a previous history of such disease.

Hodis et al have shown a reduction in CAD progression (as measured angiographically) in men given 100 IU vitamin E daily, although no benefit was found for vitamin C.137 Singh et al found that a combination of vitamins A, C, E, and β-carotene administered within a few hours after acute MI and continued for 28 days led to significantly fewer cardiac events and a lower incidence of angina pectoris in the supplemented group.138 The Cambridge heart antioxidant study (CHAOS), a trial of vitamin E supplementation on 2002 patients with angiographic evidence of coronary disease, was carried out with a mean treatment duration of 1.4 years.139 It was found that this short term supplementation with α-tocopherol (268 or 537 mg/day) reduced CHD morbidity in patients, in that patients had a significantly (77%) decreased risk of subsequent non-fatal MI. However, no benefit was found in terms of cardiovascular mortality, with a non-significant excess among vitamin E allocated participants.

The GISSI-P study randomised 11 324 men surviving a myocardial infarction to 300 mg vitamin E, 1 g n-3 polyunsaturated fatty acids (PUFAs), both, or neither in a randomised, placebo controlled trial.140 Results suggested a beneficial effect of n-3 PUFAs but no benefit with vitamin E (p = 0.07). However, further analysis of secondary endpoints suggested some beneficial effects of vitamin E. In addition, the effect of vitamin E might have been ameliorated by the Mediterranean diet of the subjects. Neither of these qualifications holds true for the HOPE study,141 which recruited over 9000 subjects likely to be eating a typical northern European diet, who were at high risk for cardiovascular events because they had CVD or diabetes in addition to one other risk factor. Subjects were randomly assigned according to a two by two factorial design to receive either 400 IU of vitamin E daily from natural sources or matching placebo, and either an angiotensin converting enzyme inhibitor (ramipril) or matching placebo for a mean of 4.5 years. Vitamin E supplementation had no effect on primary or secondary cardiovascular endpoints.

Thus, for vitamin E in Western populations, the only available trial data in primary prevention are from the ATBC trial, which show no effect. In secondary prevention, the accumulating trial data for vitamin E are less consistent, although not particularly encouraging. The CHAOS study was positive, although it suffers from design limitations. The GISSI-P study gave a borderline result, whereas the HOPE study was unequivocally negative.

How should we interpret the discordance between data from cohort studies and the results so far available from clinical trials? In general, it might be that the duration of clinical trials is too short to show a benefit, and that antioxidant intake over many years is required to prevent atherosclerosis. Thought needs to be given to trial design, with dose, duration of treatment and follow up period, initial antioxidant values and dietary intake, and extent and distribution of existing atherosclerosis being taken into consideration. Animal models have nearly always tested the effects of antioxidants on the early atherosclerotic lesions. Whether or not antioxidants have inhibitory effects on the later stages remains to be seen. In addition, the complex mixture of antioxidant micronutrients found in a diet high in fruit and vegetable intake might be more effective than large doses of a small number of antioxidant vitamins. It could be that several of these compounds work together but have no effect individually, or that other dietary components (such as trace elements) might be effectors of antioxidant action. The trial evidence available so far relates only to α-tocopherol and β-carotene. Although effective at protecting against lipid peroxidation, these antioxidants have little effect on arterial endothelial function. Ascorbate, in contrast, seems more effective in improving endothelial function, although there is less epidemiological support for a protective effect of ascorbate.

Alternatively, the significant results linking antioxidant intake with CHD risk observed in cohort studies might be the result of confounding with other lifestyle behaviours. Slattery et al examined dietary antioxidants and plasma lipids in the coronary artery risk development in young adults (CARDIA) study and found that a higher intake of antioxidants was associated with other lifestyle factors such as physical activity and non-smoking.142 Plasma concentrations of antioxidants are linked with social class, being higher in more affluent groups. Although these variables can be individually controlled for in analyses, it might be that a complex lifelong behaviour pattern needs to be studied before conclusions regarding antioxidants and CHD can be made. For example, passive smoking has recently been shown to have an atherogenic effect on LDL,143 yet exposure to smoke is a difficult lifestyle variable to control for in cohort analyses.

## Conclusions

There is overwhelming evidence that oxidative stress occurs in cells as a consequence of normal physiological processes and environmental interactions, and that the complex web of antioxidant defence systems plays a key role in protecting against oxidative damage. These processes appear to be disordered in many conditions, and a plausible hypothesis may be constructed implicating oxidative stress as a cause of tissue damage. However, as illustrated by the example of CHD, attempts to intervene therapeutically by using antioxidant supplements have so far been largely unsuccessful. A more complete understanding of the biochemical events occurring at a cellular level to influence oxidative damage is required to guide future therapeutic advances.

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16. ## Calculus 2

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17. ## Calculus 2

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18. ## English - oral

How to structure a 1 minute speech. I have to write it on an achievement i had. My one is a sports 1st place ribbon. PLEASE HELP!!!!

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What are intermediate sanctions , their purpose in the criminal justice process, and their function as a sentencing alternative?

20. ## math

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21. ## window server 2003

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23. ## social studies

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24. ## Thermodynamics

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A glass of water is placed on a very sensitive scale and several antacids tablets are dropped into the water. The weight of the glass and its contents is less after the tablets dissolve than before the tablets dissolved. Tell how matter is conserved ?

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Smokey the Bear celebrated his 65th birthday this year. Why has the message of the forest service that “only you can prevent forest fires” changed in recent years to allow more fires?

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30. ## Physics

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I am doing a 1000-1500 word contrast/comparision essay. This is what I have so far. Could you tell me if this is good enough. This is part of the body. My neighbours, Sharon and Shelley both have two children each. Sharon has two beautiful girls with long,

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Hi i was given the equation (y-2)^2 - x^2/4 =1. I need to find the center, vertices and asymptotes of this hyperbola. I found the center (0,2) and the vertices were tricky but I think they are (0,1) (0,3) but I'm having trouble finding the asymptotes. Can

35. ## 3rd grade math

Write an expression that equals 468 that includes a combination that adds up to 100

36. ## math

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37. ## trigonometry ?

A cottage under construction is to be 15.6m wide. The two sides of the roof are to be supported by equal rafters that meet at a 52 degree angle. Determine the length of the rafters to the nearest cm using a) the cosine law b) the sine law I am not

38. ## Calculus

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52. ## math

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Which test for iron(II) ions is conclusive?

54. ## algebra

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55. ## math

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60. ## Math 12

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61. ## math

What is the value of the y-coordinate of the solution to the system of equations x + 2y = 9 and x - y = 3?

62. ## 12th grade

Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.

63. ## Biology Research Paper

'We are currently in an energy crisis. After food, fossil fuels are humanity's most important source of energy. These resources take millions of years to make. We are currently using the fuels that were made more than 300 million years ago, before the time

64. ## calculus HELP URGENT

Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.

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67. ## science

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asked by Looking for someone to check my answer
75. ## apche,m

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77. ## apchem

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79. ## Algebra

Simplify the complex fraction m^-1+z^-1 _________ m^-1- z^-1

80. ## math

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83. ## english

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84. ## College Physics

During a rescue operation, a 5600-kg helicopter hovers above a fixed point. The helicopter blades send air downward with a speed of 69 m/s. What mass of air must pass through the blades every second to produce enough thrust for the helicopter to hover?

85. ## College Physics

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86. ## College Physics

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87. ## personal finance

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asked by Looking for someone to check my answer
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Determine the moles of ammonia in the following cobalt ammine complex: A sample of .1500 g of the cobalt ammine complex is places in a flask and 25.00mL of .200M HCL is added. a few drops of bromocresol green is added and the titration with .100M to NaOH

90. ## world history

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91. ## Chemistry

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92. ## algebra

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93. ## chemistry

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94. ## geometry

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95. ## statistics

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96. ## MATH

WHY DID THE TEACHER TEACH ADOLESSON

97. ## statistics

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asked by Looking for someone to check my answer
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99. ## math

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100. ## Math

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101. ## math

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102. ## computers

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103. ## Chemistry

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104. ## biology

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105. ## us history

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106. ## Algebra

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107. ## Probability/Math

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108. ## algebra

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109. ## math

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110. ## math

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200. ## Can anyone help me with a physics question?

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202. ## chemistry

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203. ## maths

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In a fit of pique, the Canadians fire a cannonball due south from vancouver (lat 49.2 degrees N) at a randomly picked city (39.4 degrees N). Assuming the cannonball takes 48 minutes to get there, by how far and in what direction will the cannonball miss?

205. ## math

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206. ## BIS 155 Data Analysis w/Spreadsheet

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207. ## English

1. She is good at dancing. 2. She is good at dance. (Which one is correct? Are both correct?) 3. I am a student at Class 1-1. 4. I am a student in Class1-1. 5. I am in Class 1-1. 6. I am a first year student in Class 1-1. 7. I am a first grader of Class

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209. ## math

one kilometer is how many meters

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If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a
(2) abc > 0
[Reveal] Spoiler: OA

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Last edited by Bunuel on 10 Aug 2012, 00:22, edited 1 time in total.
Edited the question.
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Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]

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10 Aug 2012, 01:15
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If a, b and c are integers such that b > a, is b+c > a ?

Question: is $$b+c > a$$ ? --> or: is $$b+c-a > 0$$?

(1) c > a. If $$a=1$$, $$b=2$$ and $$c=3$$, then the answer is clearly YES but if $$a=-3$$, $$b=-2$$ and $$c=-1$$, then the answer is NO. Not sufficient.

(2) abc > 0. Either all three unknowns are positive (answer YES) or two unknowns are negative and the third one is positive. Notice that in the second case one of the unknowns that is negative must be $$a$$ (because if $$a$$ is not negative, then $$b$$ is also not negative so we won't have two negative unknowns). To get a NO answer for the second case consider $$a=-3$$, $$b=1$$ and $$c=-4$$ and . Not sufficient.

(1)+(2) We have that $$b > a$$, $$c > a$$ ($$c-a>0$$) and that either all three unknowns are positive or $$a$$ and any from $$b$$ and $$c$$ is negative. Again for the first case the answer is obviously YES. As for the second case: say $$a$$ and $$c$$ are negative and $$b$$ is positive, then $$b+(c-a)=positive+positive>0$$ (you can apply the same reasoning if $$a$$ and $$b$$ are negative and $$c$$ is positive). So, we have that in both cases we have an YES answer. Sufficient.

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26 May 2009, 07:18
sondenso wrote:
If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0

E

a = -4 or 3
b = -3 or 4

The above satifies b>a, using - or + as examples.

(1) c>a
c = -2 or 4
Insuff
(2) abc>0
This means either 2 of the intergers are negative or all of the intergers are positive.
Insuff
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26 May 2009, 11:34
sondenso wrote:
If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0

b>a <==> 0>a-b <==> a-b is negative
Question:(b+c>a)?
Question:(c>a-b)?
Question:(c >= 0)?

(1) Insufficient, as a-b<0 could mean that a<0 or a>0, which means c<0 or c>=0.

(2) We have an even # of negatives, ie 0/2. If we have 0 negatives, then sufficient. Again if we have 2 insufficient.

I can see the pattern, the answer is E.

Here are the Yes/No cases:

Yes: 4 5 7
No: -9 3 -10

Final Answer, $$E$$.
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27 May 2009, 09:39
For me its straight A)
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27 May 2009, 11:27
why cant it be C?

1. b>a and c>a and abc>0:

If a<0, b can be less than or greater than 0.

If a<0, b<0 then c>0 (a=-6, b=-4, c=2) => b+c >a
If a<0, b>0, c<0 (a=-3, b=5, c=-1) => b+c >a

If all are positive, then also b+c >a.

Hence, C.

Are there any assumptions which do not satisfy both conditions simultaneously?

What is the OA?
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27 May 2009, 14:20

statement 1 does work for positives, but not for negatives. a= -2 b= -1 c= -1.

statement 2 doesnt work on its own because c could be way less than a, negating b,
a= -3 b=2 c= -5

however, both together mean that there can only be two negatives, and c must be larger than A.
for any value A, negative or not, two values that are greater than it with one positive are going to together be greater than A.
if A is positive = a=2, c=3, b=3, a=1 b=2 c=2
if A is negative = a= -3, c= -2, b=1, a= -2 b=-1 c=1

There is no solution with (1) and (2) true that doesn't end up with B + C > A

gmatprep is right
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27 May 2009, 14:22
Has anybody considered taking both the conditions 1 and 2 together? What is the OA for this? I still think its C.
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27 May 2009, 20:18
b>a
stmt 1 :

c>a so b+c>2a
we cannot tell whether b+c >a may or may not. So insufficient.

stmt 2 :
abc>0 and b >a
a = +ve b = +ve c =+ve so definetly b+c > a
a = -ve b = -ve c = +ve so definetly b+c > a. ( since c =+ve and b>a)
a = -ve b = +ve c = -ve ( here it is just the opposite u know b =+ve but do not know c>a).so u cant tell whether b+c > a

Combing : yes u know you have got what u wanted so C.

Thanks gmatprep09 and dk94588.
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27 May 2009, 21:02
I agree C is the answer.
If a,b and c and positive,it is possible.
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27 May 2009, 21:42
tkarthik wrote -
c>a so b+c>2a
we cannot tell whether b+c >a may or may not. So insufficient

If b+c>2a how in the world can it not be > a !!!! I m confused.Can you pls. elaborate or give example numbers.
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27 May 2009, 23:12
Hi mdfrahim

you need to take some negative value.

Say a,b,c are +ve then b+c > a and b+c>2a

say b = -2 c = -3 a =-4 ( c> a and b > a)

b + c = -5 which less than a but will be greater than 2a.

I meant to say this only. Hope i have made it clear.
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28 May 2009, 11:53

If you look at both together,

we have that b>a & c>a.

from (1) we get b+c>2a and we're almost sufficient, but only if 2a>a.
Well if a<0, no, but if a>0, yes.

(2) tells us that 0 or 2 are negative. If all 3 are positive, sufficient.
Now if 2 are negative, then a has to be negative as well. Suppose a were positive-- then b/c would be negative, and b>a & c>a would be false. Hence a has to be positive.

(C)

Very tricky
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Re: Property of Integers, Inequalities [#permalink]

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23 Oct 2009, 00:02
(1) because b and c both can be negative, thus (1) is insufficient

(2) insufficient for example, a = -2, b = 1, c = -4

Both are sufficient because either b or c is always greater than a.
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Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]

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09 Aug 2012, 23:40
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Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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If a, b and c are integers such that b > a, is b+c > a [#permalink]

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21 Oct 2014, 22:12
sondenso wrote:
If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a
(2) abc > 0

The question stem says that b > a. There are following possibilities for this
a. Both Positive Lets say $$b = 5 and a = 2$$

b. Both Negative, lets say $$b = -3 and a = -5$$

c. One positive one negative, lets say $$b = 3 and a = -1$$

d. Either of the two zero

1. c > a

C can be positive or negative and can fit in any of the above mentioned scenarios.

Insufficient

2. abc > 0

This means either all are positive or any two are negative. Since b > a, there are numerous possibilities for c.

So, Insufficient.

c > a and abc > 0

This would mean that either all are positive - b + c > a

or two negatives and one one positive - a has to be negative, either of b and c has to be negative and the other one positive. This would also mean that c + b > a

Ans - C
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Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]

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07 Mar 2016, 14:51
Bunuel wrote:
If a, b and c are integers such that b > a, is b+c > a ?

Question: is $$b+c > a$$ ? --> or: is $$b+c-a > 0$$?

(1) c > a. If $$a=1$$, $$b=2$$ and $$c=3$$, then the answer is clearly YES but if $$a=-3$$, $$b=-2$$ and $$c=-1$$, then the answer is NO. Not sufficient.

(2) abc > 0. Either all three unknowns are positive (answer YES) or two unknowns are negative and the third one is positive. Notice that in the second case one of the unknowns that is negative must be $$a$$ (because if $$a$$ is not negative, then $$b$$ is also not negative so we won't have two negative unknowns). To get a NO answer for the second case consider $$a=-3$$, $$b=1$$ and $$c=-4$$ and . Not sufficient.

(1)+(2) We have that $$b > a$$, $$c > a$$ ($$c-a>0$$) and that either all three unknowns are positive or $$a$$ and any from $$b$$ and $$c$$ is negative. Again for the first case the answer is obviously YES. As for the second case: say $$a$$ and $$c$$ are negative and $$b$$ is positive, then $$b+(c-a)=positive+positive>0$$ (you can apply the same reasoning if $$a$$ and $$b$$ are negative and $$c$$ is positive). So, we have that in both cases we have an YES answer. Sufficient.

Bunuel could you please explain how you can solve the problem with the approach above in 2 min?

It took me almost 3,5...

Thanks!
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If a, b and c are integers such that b > a, is b+c > a [#permalink]

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16 Mar 2016, 22:41
If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a
(2) abc > 0
Either two are negative and one positive or all are positive.

Individually both the statements are not sufficient.
Combining 1 and 2 Sufficient.

Hence C.
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Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]

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18 Mar 2016, 08:08
Bunuel

In this problem can we subtract the following inequalities?

b>a
b+c>a

and arrive at 'is c>0??'
Re: If a, b and c are integers such that b > a, is b+c > a   [#permalink] 18 Mar 2016, 08:08

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text:
# Green–Tao theorem

In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004,[1] states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words there exist arithmetic progressions of primes, with k terms, where k can be any natural number. The proof is an extension of Szemerédi's theorem.

In 2006, Terence Tao and Tamar Ziegler extended the result to cover polynomial progressions.[2] More precisely, given any integer-valued polynomials P1,..., Pk in one unknown m all with constant term 0, there are infinitely many integers x, m such that x + P1(m), ..., x + Pk(m) are simultaneously prime. The special case when the polynomials are m, 2m, ..., km implies the previous result that there are length k arithmetic progressions of primes.

## Statement

Let $\pi(N)$ denote the number of primes less than or equal to $N$. If $A$ is a subset of the prime numbers such that

$\limsup_{N\rightarrow\infty} \dfrac{|A\cap [1,N]|}{\pi(N)}>0$,

then for all positive integers $k$, the set $A$ contains infinitely many arithmetic progressions of length $k$. In particular, the entire set of prime numbers contains arbitrarily long arithmetic progressions.

## Overview of the proof

Green and Tao's proof has three main components:

1. Szemerédi's theorem, which asserts that subsets of the integers with positive upper density have arbitrarily long arithmetic progressions. It does not a priori apply to the primes because the primes have density zero in the integers.
2. A transference principle that extends Szemerédi's theorem to subsets of the integers which are pseudorandom in a suitable sense. Such a result is now called a relative Szemerédi theorem.
3. A pseudorandom subset of the integers containing the primes as a dense subset. To construct this set, Green and Tao used ideas from Goldston, Pintz, and Yıldırım's work on prime gaps.[3] Once the pseudorandomness of the set is established, the transference principle may be applied, completing the proof.

Numerous simplifications to the argument in the original paper[1] have been found. Conlon, Fox & Zhao (2014) provide a modern exposition of the proof.

## Numerical work

The proof of the Green–Tao does not show how to find the progressions of primes; it merely proves they exist. There has been separate computational work to find large arithmetic progressions in the primes. On January 18, 2007, Jarosław Wróblewski found the first known case of 24 primes in arithmetic progression:[4]

468,395,662,504,823 + 205,619 · 223,092,870 · n, for n = 0 to 23.

The constant 223092870 here is the product of the prime numbers up to 23 (see primorial).

On May 17, 2008, Wróblewski and Raanan Chermoni found the first known case of 25 primes:

6,171,054,912,832,631 + 366,384 · 223,092,870 · n, for n = 0 to 24.

On April 12, 2010, Benoãt Perichon with software by Wróblewski and Geoff Reynolds in a distributed PrimeGrid project found the first known case of 26 primes (sequence A204189 in OEIS):

43,142,746,595,714,191 + 23,681,770 · 223,092,870 · n, for n = 0 to 25.


text:
# In a fluorescent lamp choke (a small transformer)

Question:

In a fluorescent lamp choke (a small transformer) $100 \mathrm{~V}$ of reverse voltage is produced when the choke current changes uniformly from $0.25$ A to 0 in a duration of $0.025$ ms. The self-inductance of the choke (in $\mathrm{mH}$ ) is estimated to be

Solution:

(10) Given $d I=0.25-0=0.25 \mathrm{~A}$

$d t=0.025 \mathrm{~ms}$

Induced voltage

$E_{\text {ind }}=100 \mathrm{v}$

Self-inductance, $L=$ ?

Using, $E_{\text {ind }}=\frac{\Delta \phi}{\Delta t}$

$\Rightarrow 100=\frac{L(0.25-0)}{.025 \times 10^{-3}}$

$\Rightarrow \mathrm{L}=10^{-3} \mathrm{H}=10 \mathrm{mH}$


text:
# Product rule for Differentiation

Covid-19 has led the world to go through a phenomenal transition .

E-learning is the future today.

Stay Home , Stay Safe and keep learning!!!

The product rule for differentiation of two functions 'f' and 'g' in which both the functions should be differentiable. Moreover, the derivative of is the first function times the derivative of the second, plus the second function times the derivative of the first.

$\frac{\text{d}}{\text{d}x}[f(x)g(x)] =g(x) \frac{\text{d}}{\text{d}x}f(x) + f(x)\frac{\text{d}}{\text{d}x}g(x)$

$\frac{\text{d}}{\text{d}x}[f(x)g(x)] = f(x)g'(x)| + g(x)f'(x)$

$\frac{\text{d}}{\text{d}x}[u.v] = v.\frac{\text{d}u}{\text{d}x} + u.\frac{\text{d}v}{\text{d}x}$

$\frac{\text{d}}{\text{d}x}[u.v] = v.u ' + u.v '$

Note : Order of the function does not matter as addition is a commutative property.

Prove that : $\frac{\text{d}}{\text{d}x}[f(x)g(x)] =g(x) \frac{\text{d}}{\text{d}x}f(x) + f(x)\frac{\text{d}}{\text{d}x}g(x)$

Proof : $\frac{\text{d}}{\text{d}x}[f(x)g(x)] =\lim_{\triangle x \rightarrow 0} \frac{f(x + \triangle x)g(x +\triangle x)- f(x)g(x)}{\triangle x}$

Add and subtract $f(x +\triangle x)g(x)$

${ =\lim_{\triangle x \rightarrow 0} \frac{f(x + \triangle x)g(x +\triangle x)\color{red}{-f(x +\triangle x)g(x) +f(x +\triangle x)g(x)}- f(x)g(x)}{\triangle x}}$

=$\lim_{\triangle x \rightarrow 0}[f(x +\triangle x)\frac{g(x + \triangle x) -g(x)}{\triangle x}+ g(x)\frac{f(x + \triangle x) - f(x)}{\triangle x}]$

=$\lim_{\triangle x \rightarrow 0}[f(x +\triangle x)\frac{g(x + \triangle x) -g(x)}{\triangle x}]+ \lim_{\triangle x \rightarrow 0}[ g(x)\frac{f(x + \triangle x) - f(x)}{\triangle x}]$

=$\lim_{\triangle x \rightarrow 0}[f(x +\triangle x)\lim_{\triangle x \rightarrow 0}\frac{g(x + \triangle x) -g(x)}{\triangle x}]+ \lim_{\triangle x \rightarrow 0}g(x)\lim_{\triangle x \rightarrow 0}[\frac{f(x + \triangle x) - f(x)}{\triangle x}]$

By the definition of derivative and $\lim_{\triangle x \rightarrow 0}[f(x +\triangle x)$ = f(x)
$\frac{\text{d}}{\text{d}x}[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)$

If there are are more than two functions then product rule can be extended.

$\frac{\text{d}}{\text{d}x}[f(x)g(x)h(x)] = f(x).h(x)g'(x) + g(x)h(x)f'(x) + f(x)g(x)h'(x)$

## Examples on product rule for differentiation

1) Find the derivative of f(x)= $x^{3}$cos(x)
Solution : f(x)= $x^{3}$cos(x)
Using the product rule,

$\frac{\text{d}}{\text{d}x}[f(x)g(x)] =g(x) \frac{\text{d}}{\text{d}x}f(x) + f(x)\frac{\text{d}}{\text{d}x}g(x)$

f(x) = $x^{3}$ and g(x) = cos(x)

$\frac{\text{d}}{\text{d}x}[x^{3} cos(x)] =cos(x) \frac{\text{d}}{\text{d}x}x^{3} + x^{3}\frac{\text{d}}{\text{d}x}cos(x)$

= $cos(x).3x^{2} + x^{3}(-sin(x))$ [ using the power rule and derivative of trigonometric function]

$\frac{\text{d}}{\text{d}x}[x^{3} cos(x)] = 3cos(x).x^{2} - x^{3}sin(x)$

2) Find the derivative of f(x)= $\sqrt{x}tan(x)$
Solution : f(x)= $\sqrt{x}tan(x)$
Using the product rule,

$\frac{\text{d}}{\text{d}x}[f(x)g(x)] =g(x) \frac{\text{d}}{\text{d}x}f(x) + f(x)\frac{\text{d}}{\text{d}x}g(x)$

f(x) = $\sqrt{x}$ and g(x) = tan(x)

$\frac{\text{d}}{\text{d}x}[\sqrt{x}tan(x)] =tan(x) \frac{\text{d}}{\text{d}x}\sqrt{x} + \sqrt{x}\frac{\text{d}}{\text{d}x}tan(x)$

= $tan(x).\frac{1}{2}(x)^{\frac{-1}{2}} + \sqrt{x}sec{2}x$ [ using the power rule and derivative of trigonometric function]

=$tan(x).\frac{1}{2\sqrt{x}}+\sqrt{x}sec{2}x$

$\frac{\text{d}}{\text{d}x}[\sqrt{x}.tan(x)] = tan(x).\frac{1}{2\sqrt{x}}+\sqrt{x}.sec^{2}x$

3) Find the derivative of f(x) = x.cos(x) and find f'(c) at c= $\frac{\pi}{4}$

Solution : f(x) = x.cos(x)
Using the product rule,

$\frac{\text{d}}{\text{d}x}[f(x)g(x)] =g(x) \frac{\text{d}}{\text{d}x}f(x) + f(x)\frac{\text{d}}{\text{d}x}g(x)$

f(x) = x and g(x) = cos(x)

$\frac{\text{d}}{\text{d}x}[x. cos(x)] =cos(x). \frac{\text{d}}{\text{d}x}x + x.\frac{\text{d}}{\text{d}x}cos(x)$

= cos(x).(1) + x.(-sin(x)) [ using the power rule and derivative of trigonometric function]

f '(x) = cos(x) - x.sin(x)

f '(c) = cos(c) - c.sin(c)

When c = $\frac{\pi}{4}$

$f'(\frac{\pi}{4}) = cos(\frac{\pi}{4}) -\frac{\pi}{4}.sin(\frac{\pi}{4})$

$f'(\frac{\pi}{4}) = cos(\frac{\sqrt{2}}{2}) -\frac{\pi}{4}.sin(\frac{\sqrt{2}}{2})$


text:
## Text as a resource for network population?

You say elsewhere that you want to avoid bias - that you want to work basically form experimental measurements as much as possible. This has some merit, but it also seems like there must be quite a lot of value out there in the space of biased knowledge.. Some of that bias will be real signal. Would be great to execute an experiment to empirically test the impact of bringing in prior knowledge (e.g. via text mining techniques for relation extraction). Does it make it better or worse at the task at hand?

Daniel Himmelstein Researcher

there must be quite a lot of value out there in the space of biased knowledge

You are correct. In our current proposal, we do use text mining for the symptom-disease edges and tissue-disease edges. We also rely on literature curation for compound-target binding and protein interactions.

Would be great to execute an experiment to empirically test the impact of bringing in prior knowledge

I agree, we should fit a model that excludes all knowledge-biased domains. I reckon this model's performance on known indications will be drastically inferior. The worry with predicting known indications with known biology is that your testing performance becomes nearly perfect. However, your novel predictions are not interesting — they would be readily apparent to a pharmacologist.

The more text mining data you include the larger your gap between testing performance and generative performance (see our discussion on evaluation). Therefore, I like the following workflow:

1. Start with high-throughput resources that are not affected by knowledge bias (a.k.a. study bias)
2. If the algorithm performs significantly better than random, explore the top predictions.
3. If performance is mediocre, add a biased resource that provides orthogonal information (information not already included from a systematic resource)
4. Repeat.

One final note to help explain the insidiousness of the knowledge bias. In CTD [1], curators may read that compound_X treats disease_X and also targets gene_X and therefore add interactions between all three entities to their knowledgebase. In reality the study hasn't proven that gene_X is associated with disease_X but this relationship was still extracted. This happens on a macro-scale across the entire compendium of published literature: specific network vicinities become well studied and the resulting disease-gene-compound triangles are more a result of attention rather than noteworthy biology.

Daniel Himmelstein Researcher

# Knowledge biased and unbiased edges

Thanks to @b_good's suggestion for text mining and curated databases, we have incorporated several edges that are subject to knowledge bias.

Text mining edges include:

Literature curation edges include:

And we have several edges from systematic technologies that are not subject to knowledge biases.

• Disease — expression — Anatomy edges from Bgee and TISSUES
• Disease — up/down-regulation — Gene edges from STARGEO
• Gene — membership — Perturbation Gene Set edges from MSigDB
• Gene — interaction — Gene edges from Y2H experiments
• Gene — evolution — Gene edges from evolutionary rate covariation
• Gene — knowdown up/down-reglulation — Gene edges from LINCS L1000
• Compound — up/down-regulation — Gene from LINCS L1000

Thus, for each edge we will create an unbiased attribute which takes a True or False value. Using our network masking feature, we can easily switch between using the whole network or only the knowledge-unbiased portion.

Some metaedges will contain a mix of biased and unbiased edges. For example, protein interactions based on their source database. When both a biased and unbiased source contribute an edge, we will give precedence to the unbiased designation.

• Benjamin Good: I'm wondering about your relation ontology here. Can you really distinguish a causal relation from co-occurrence information? Do the names on these edges actually matter based on how you are using the network ? If the meaning of the relations is really important, I think there are other text-mining approaches that you should look into. If not, the co-occurrence stuff should be fine. Really curious about this experiment.. Would also like to see how the result of other text-ming approaches would influence the outcome. e.g. would it change things if you swapped in the relations from semmedDB ?

Daniel Himmelstein Researcher

Do the names on these edges actually matter based on how you are using the network?

@b_good, for predicting the probability of efficacy of a compound–disease pair, the metaedge names do not matter. The algorithm only considers the structure of the network. The names are used to assist with interpretability. For example, the CtGad feature (capturing when a compound targets genes that are associated with the disease) may be predictive. In this case, we would conclude that disease-associated genes are informative for repurposing. If what we call an 'association' is actually some other type of relationship, then the interpretation that associations are influential will be unfounded.

When we have multiple metaedges between the same metanodes, we hope there is a difference in the type of information encoded. Otherwise, we would be better off having only a single metaedge. For example, we included binding and target edges between compounds and genes. It is unclear whether merging these edges would be beneficial, because it's difficult to know how they differ. Therefore, a good understanding what information each metaedge captures will assist with metagraph design. Accurate metaedge names can help with understanding edge content and therefore network design decisions.

Would also like to see how the result of other text-ming approaches would influence the outcome. e.g. would it change things if you swapped in the relations from semmedDB?

Currently, I am happy with the quality of our MEDLINE topic cooccurrence approach. I assume that you highlight SemMedDB [1] because it has the ability to extract the type of relationship. I agree this could be a valuable addition. However, in the interest of time, this will most likely have to wait till a successive project.

Status: Accepted
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Benjamin Good, Daniel Himmelstein (2015) Text as a resource for network population?. Thinklab. doi:10.15363/thinklab.d48