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Wednesday, March 18, 2015

Vitamin K


From Wikipedia, the free encyclopedia

Vitamin K
Drug class
Use Vitamin K deficiency, Warfarin overdose
Biological target Gamma-glutamyl carboxylase
ATC code B02BA
External links
MeSH D014812
AHFS/Drugs.com Medical Encyclopedia

Vitamin K1 (phylloquinone) - both forms of the vitamin contain a functional naphthoquinone ring and an aliphatic side chain. Phylloquinone has a phytyl side chain.

Vitamin K2 (menaquinone). In menaquinone, the side chain is composed of a varying number of isoprenoid residues. The most common number of these residues is four, since animal enzymes normally produce menaquinone-4 from plant phylloquinone.

A sample of phytomenadione for injection, also called phylloquinone.

Vitamin K refers to a group of structurally similar, fat-soluble vitamins the human body needs for complete synthesis of certain proteins that are required for blood coagulation, and also certain proteins that the body uses to manipulate binding of calcium in bone and other tissues. The vitamin K-related modification of the proteins allows them to bind calcium ions, which they cannot do otherwise. Without vitamin K, blood coagulation is seriously impaired, and uncontrolled bleeding occurs. Low levels of vitamin K also weaken bones and promote calcification of arteries and other soft tissues.

Chemically, the vitamin K family comprises 2-methyl-1,4-naphthoquinone (3-) derivatives. Vitamin K includes two natural vitamers: vitamin K1 and vitamin K2.[1] Vitamin K2, in turn, consists of a number of related chemical subtypes, with differing lengths of carbon side chains made of isoprenoid groups of atoms.

Vitamin K1, also known as phylloquinone, phytomenadione, or phytonadione, is synthesized by plants, and is found in highest amounts in green leafy vegetables because it is directly involved in photosynthesis. It may be thought of as the "plant" form of vitamin K. It is active as a vitamin in animals and performs the classic functions of vitamin K, including its activity in the production of blood-clotting proteins. Animals may also convert it to vitamin K2.

Vitamin K2, the main storage form in animals, has several subtypes, which differ in isoprenoid chain length. These vitamin K2 homologues are called menaquinones, and are characterized by the number of isoprenoid residues in their side chains. Menaquinones are abbreviated MK-n, where M stands for menaquinone, the K stands for vitamin K, and the n represents the number of isoprenoid side chain residues. For example, menaquinone-4 (abbreviated MK-4) has four isoprene residues in its side chain. Menaquinone-4 (also known as menatetrenone from its four isoprene residues) is the most common type of vitamin K2 in animal products since MK-4 is normally synthesized from vitamin K1 in certain animal tissues (arterial walls, pancreas, and testes) by replacement of the phytyl tail with an unsaturated geranylgeranyl tail containing four isoprene units, thus yielding menaquinone-4. This homolog of vitamin K2 may have enzyme functions distinct from those of vitamin K1.

Bacteria in the colon (large intestine) can also convert K1 into vitamin K2. In addition, bacteria typically lengthen the isoprenoid side chain of vitamin K2 to produce a range of vitamin K2 forms, most notably the MK-7 to MK-11 homologues of vitamin K2. All forms of K2 other than MK-4 can only be produced by bacteria, which use these forms in anaerobic respiration. The MK-7 and other bacterially derived forms of vitamin K2 exhibit vitamin K activity in animals, but MK-7's extra utility over MK-4, if any, is unclear and is a matter of investigation.

Three synthetic types of vitamin K are known: vitamins K3, K4, and K5. Although the natural K1 and all K2 homologues and synthetic K4 and K5 have proven nontoxic, the synthetic form K3 (menadione) has shown toxicity.[2]

Discovery of vitamin K1

Vitamin K1 was identified in 1929 by Danish scientist Henrik Dam when he investigated the role of cholesterol by feeding chickens a cholesterol-depleted diet.[3] After several weeks, the animals developed haemorrhages and started bleeding. These defects could not be restored by adding purified cholesterol to the diet. A second compound—together with the cholesterol—apparently had been extracted from the food, and this compound was called the coagulation vitamin. The new vitamin received the letter K because the initial discoveries were reported in a German journal, in which it was designated as Koagulationsvitamin.

Conversion of vitamin K1 to vitamin K2 in animals

The MK-4 form of vitamin K2 is produced by conversion of vitamin K1 in the testes, pancreas, and arterial walls.[4]
While major questions still surround the biochemical pathway for this transformation, the conversion is not dependent on gut bacteria, as it occurs in germ-free rats[5][6] and in parenterally-administered K1 in rats.[7][8] In fact, tissues that accumulate high amounts of MK-4 have a remarkable capacity to convert up to 90% of the available K1 into MK-4.[9][10] There is evidence that the conversion proceeds by removal of the phytyl tail of K1 to produce menadione as an intermediate, which is then condensed with an activated geranylgeranyl moiety (see also prenylation) to produce vitamin K2 in the MK-4 (menatetrione) form.[11]

Subtypes of vitamin K2

Vitamin K2 (menaquinone) includes several subtypes. The two subtypes most studied are menaquinone-4 (menatetrenone, MK-4) and menaquinone-7 (MK-7).
Menaquinone-7 is different from MK-4 in that it is not produced by human tissue. MK-7 consumption has been shown to reduce the risk of bone fractures and cardiovascular disorders that are crucial health issues worldwide. Leading research teams from Australia, Japan, and Korea are broadening the understanding of MK-7 and its production. MK-7 may be converted from phylloquinone (K1) in the colon by E. coli bacteria.[12] However, bacterially derived menaquinones (MK-7) appear to contribute minimally to overall vitamin K status.[13][14] MK-4 and MK-7 are both found in the United States in dietary supplements for bone health.

The U.S. Food and Drug Administration (FDA) has not approved any form of vitamin K for the prevention or treatment of osteoporosis; however, MK-4 has been shown to decrease the incidence of fractures up to 87%.[15] MK-4 (45 mg daily) has been approved by the Ministry of Health in Japan since 1995 for the prevention and treatment of osteoporosis.[16]

Vitamin K2 as MK-4, but not as MK-7 (and also not vitamin K1) has also been shown to prevent bone loss and/or fractures in these circumstances:

Chemical structure

The three synthetic forms of vitamin K are vitamins K3, K4, and K5, which are used in many areas, including the pet food industry (vitamin K3) and to inhibit fungal growth (vitamin K5).[32]

Physiology

Vitamin K1, the precursor of most vitamin K in nature, is a steroisomer of phylloquinone, an important chemical in green plants, where it functions as an electron acceptor in photosystem I during photosynthesis. For this reason, vitamin K1 is found in large quantities in the photosynthetic tissues of plants (green leaves, and dark green leafy vegetables such as romaine lettuce, kale and spinach), but it occurs in far smaller quantities in other plant tissues (roots, fruits, etc.). Iceberg lettuce contains relatively little. The function of phylloquinone in plants appears to have no resemblance to its later metabolic and biochemical function (as "vitamin K") in animals, where it performs a completely different biochemical reaction.

Vitamin K (in animals) is involved in the carboxylation of certain glutamate residues in proteins to form gamma-carboxyglutamate (Gla) residues. The modified residues are often (but not always) situated within specific protein domains called Gla domains. Gla residues are usually involved in binding calcium, and are essential for the biological activity of all known Gla proteins.[33]

At this time, 16 human proteins with Gla domains have been discovered, and they play key roles in the regulation of three physiological processes:
Like other lipid-soluble vitamins (A, D, E), vitamin K is stored in the fat tissue of the human body.

Vitamin K absorption and dietary need

Previous theory held that dietary deficiency is extremely rare unless the intestine (small bowel) was heavily damaged, resulting in malabsorption of the molecule. Another at-risk group for deficiency were those subject to decreased production of K2 by normal intestinal microbiota, as seen in broad spectrum antibiotic use.[41] Taking broad-spectrum antibiotics can reduce vitamin K production in the gut by nearly 74% in people compared with those not taking these antibiotics.[42] Diets low in vitamin K also decrease the body's vitamin K concentration.[43]
Those with chronic kidney disease are at risk for vitamin K deficiency, as well as vitamin D deficiency, and particularly those with the apoE4 genotype.[44] Additionally, in the elderly there is a reduction in vitamin K2 production.[45]

Recent research results also demonstrate that the small intestine and large intestine (colon) seem to be inefficient at absorbing vitamin K supplements in rat populations low in Vitamin K.[46][47] These results are reinforced by human cohort studies, where a majority of the subjects showed inadequate vitamin K amounts in the body. This was revealed by the presence of large amounts of incomplete gamma-carboxylated proteins in the blood, an indirect test for vitamin K deficiency.[48][49][50] And in an animal model MK-4 was shown to prevent arterial calcifications, pointing to its potential role in prevention of such calcification.[51] In this study vitamin K1 was also tested, in an attempt to make connections between vitamin K1 intake and calcification reduction. Only vitamin K2 (as MK-4) was found to influence warfarin-induced calcification in this study.

Recommended amounts

The U.S. Dietary Reference Intake (DRI) for an Adequate Intake (AI) of vitamin K for a 25-year old male is 120 micrograms (μg) per day. The AI for adult women is 90 μg/day, for infants is 10–20 μg/day, and for children and adolescents 15–100 μg/day. To get maximum carboxylation of osteocalcin, one may have to take up to 1000 μg of vitamin K1.[52]

Anticoagulant drug interactions

Phylloquinone (K1)[53][54] or menaquinone (K2) are capable of reversing the anticoagulant activity (incorrectly but colloquially referred to as "blood-thinning action") of the powerful anticoagulant warfarin (tradename Coumadin).
Warfarin works by blocking recycling of vitamin K, so that the body and tissues have lower levels of active vitamin K, and thus a deficiency of the active vitamin.

Supplemental vitamin K (for which oral dosing is often more active than injectable dosing in human adults) reverses the vitamin K deficiency caused by warfarin, and therefore modulates or totally reverses the intended anticoagulant action of warfarin and related drugs.[citation needed] Sometimes small amounts of vitamin K (one milligram per day) are given orally to patients taking Coumadin so that the action of the drug is more predictable.[citation needed] The proper anticoagulant action of the drug is a function of vitamin K intake and drug dose, and (due to differing absorption) must be individualized for each patient.[citation needed] The action of warfarin and vitamin K both require two to five days after dosing to have maximum effect, and neither Coumadin or vitamin K shows much effect in the first 24 hours after they are given.[citation needed]

In two separate studies in the rat model, after long term administration of Coumadin to induce calcification of arteries in the rodents, supplemental vitamin K was found to reverse or prevent some of the arterial calcification attendant on the long-term blockade of vitamin K.[55] A second study found that only vitamin K2 as MK-4, and not vitamin K1 was effective at preventing warfarin-induced arterial calcification in rats, suggesting differing roles for the two forms of the vitamin in some calcium-dependent processes.[56]

The newer anticoagulants dabigatran and rivaroxaban have different mechanisms of action that do not interact with vitamin K, and may be taken with supplemental vitamin K.[57][58]

Food sources

Vitamin K1

Food Serving size Vitamin K1[59] micrograms (μg) Food Serving size Vitamin K1[59] micrograms (μg)
Kale, cooked 1/2 cup 531 Parsley, raw 1/4 cup 246
Spinach, cooked 1/2 cup 444 Spinach, raw 1 cup 145
Collards, cooked 1/2 cup 418 Collards, raw 1 cup 184
Swiss chard, cooked 1/2 cup 287 Swiss chard, raw 1 cup 299
Mustard greens, cooked 1/2 cup 210 Mustard greens, raw 1 cup 279
Turnip greens, cooked 1/2 cup 265 Turnip greens, raw 1 cup 138
Broccoli, cooked 1 cup 220 Broccoli, raw 1 cup 89
Brussels sprouts, cooked 1 cup 219 Endive, raw 1 cup 116
Cabbage, cooked 1/2 cup 82 Green leaf lettuce 1 cup 71
Asparagus 4 spears 48 Romaine lettuce, raw 1 cup 57
Table from "Important information to know when you are taking: Warfarin (Coumadin) and Vitamin K", Clinical Center, National Institutes of Health Drug Nutrient Interaction Task Force.[60]

Vitamin K1 is found chiefly in leafy green vegetables such as dandelion greens (which contain 778.4 μg per 100 g, or 741% of the recommended daily amount), spinach, swiss chard, lettuce and Brassica (e.g. cabbage, kale, cauliflower, broccoli, and brussels sprouts) and often the absorption is greater when accompanied by fats such as butter or oils; some fruits, such as avocado, kiwifruit and grapes, are also high in vitamin K. By way of reference, two tablespoons of parsley contain 153% of the recommended daily amount of vitamin K.[61] Some vegetable oils, notably soybean, contain vitamin K, but at levels that would require relatively large calorific consumption to meet the USDA-recommended levels.[62] Colonic bacteria synthesize a significant portion of humans' vitamin K needs; newborns often receive a vitamin K shot at birth to tide them over until their colons become colonized at five to seven days of age from the consumption of their mother's milk.

Phylloquinone's tight binding to thylakoid membranes in chloroplasts makes it less bioavailable. For example, cooked spinach has a 5% bioavailability of phylloquinone, however, fat added to it increases bioavailability to 13% due to the increased solubility of vitamin K in fat.[63]

Vitamin K2

Food sources of vitamin K2 include fermented or aged cheeses, eggs, meats such as chicken and beef and their fat, livers, and organs, and in fermented vegetables, especially natto, as well as sauerkraut and kefir.[64]
 
Food 100 grams (3.5 oz) portion Microgram (μg) Proportion of vitamin K2 Food 100 grams (3.5 oz) portion Microgram (μg) Proportion of vitamin K2
Natto, cooked 1,103.4 (90% MK-7, 10% other MK) Chicken Leg 8.5 (100% MK-4)
Goose liver pâté 369.0 (100% MK-4) Ground beef (medium fat) 8.1 (100% MK-4)
Hard cheeses (Dutch Gouda style), raw 76.3 (6% MK-4, 94% other MK) Chicken liver (braised) 6.7 (100% MK-4)
Soft cheeses (French Brie style) 56.5 (6.5 MK-4, 93.5% other MK) Hot dog 5.7 (100% MK-4)
Egg yolk, (Netherlands) 32.1 (98% MK-4, 2% other MK) Bacon 5.6 (100% MK-4)
Goose leg 31.0 (100% MK-4) Calf’s liver (pan-fried) 6.0 (100% MK-4)
Egg yolk (U.S.) 15.5 (100% MK-4) Sauerkraut 4.8 (100% MK-4)
Butter 15.0 (100% MK-4) Whole milk 1.0 (100% MK-4)
Chicken liver (raw) 14.1 (100% MK-4) Salmon (Alaska, Coho, Sockeye, Chum, and King wild (raw)) 0.5 (100% MK-4)
Chicken liver (pan-fried) 12.6 (100% MK-4) Cow’s liver (pan-fried) 0.4 (100% MK-4)
Cheddar cheese (U.S.) 10.2 (6% MK-4, 94% other MK) Egg white 0.4 (100% MK-4)
Meat franks 9.8 (100% MK-4) Skim milk 0.0
Chicken breast 8.9 (100% MK-4)
Table from Rhéaume-Bleue, pp. 66–67.

Vitamin K2 (menaquinone-4) is synthesized by animal tissues and is found in meat, eggs, and dairy products.[65] Menaquinone-7 is synthesized by bacteria during fermentation and is found in fermented soybeans (natto), and in most fermented cheeses.[66] In natto, none of the vitamin K is from menaquinone-4, and in cheese only 2–7% is.[67]

Deficiency

Average diets are usually not lacking in vitamin K, and primary deficiency is rare in healthy adults. Newborn infants are at an increased risk of deficiency. Other populations with an increased prevalence of vitamin K deficiency include those who suffer from liver damage or disease (e.g., alcoholics), cystic fibrosis, or inflammatory bowel diseases, or have recently had abdominal surgeries. Secondary vitamin K deficiency can occur in bulimics, those on stringent diets, and those taking anticoagulants. Other drugs associated with vitamin K deficiency include salicylates, barbiturates, and cefamandole, although the mechanisms are still unknown. Vitamin K1 deficiency can result in coagulopathy, a bleeding disorder.[68] Symptoms of K1 deficiency include anemia, bruising, and bleeding of the gums or nose in both sexes, and heavy menstrual bleeding in women.
Osteoporosis[69][70] and coronary heart disease[71][72] are strongly associated with lower levels of K2 (menaquinone). Vitamin K2 (MK-7) deficiency is also related to severe aortic calcification and all-cause mortality.[73] Menaquinone is not inhibited by salicylates as happens with K1, so menaquinone supplementation can alleviate the chronic vitamin K deficiency caused by long-term aspirin use.[citation needed]

Toxicity

Although allergic reaction from supplementation is possible, no known toxicity is associated with high doses of the phylloquinone (vitamin K1) or menaquinone (vitamin K2) forms of vitamin K, so no tolerable upper intake level (UL) has been set.[74]

Blood clotting (coagulation) studies in humans using 45 mg per day of vitamin K2 (as MK-4)[27] and even up to 135 mg/day (45 mg three times daily) of K2 (as MK-4),[75] showed no increase in blood clot risk. Even doses in rats as high as 250 mg/kg body weight did not alter the tendency for blood-clot formation to occur.[76]

Unlike the safe natural forms of vitamin K1 and vitamin K2 and their various isomers, a synthetic form of vitamin K, vitamin K3 (menadione), is demonstrably toxic. The U.S. FDA has banned this form from over-the-counter sale in the United States because large doses have been shown to cause allergic reactions, hemolytic anemia, and cytotoxicity in liver cells.[2]

Biochemistry

Function in animals



Vitamin K structures. MK-4 and MK-7 are both subtypes of K2.

The function of vitamin K2 in the animal cell is to add a carboxylic acid functional group to a glutamate amino acid residue in a protein, to form a gamma-carboxyglutamate (Gla) residue. This is a somewhat uncommon posttranslational modification of the protein, which is then known as a "Gla protein." The presence of two -COOH (carboxylate) groups on the same carbon in the gamma-carboxyglutamate residue allows it to chelate calcium ion. The binding of calcium ion in this way very often triggers the function or binding of Gla-protein enzymes, such as the so-called vitamin K dependent clotting factors discussed below.

Within the cell, vitamin K undergoes electron reduction to a reduced form called vitamin K hydroquinone by the enzyme vitamin K epoxide reductase (VKOR).[77] Another enzyme then oxidizes vitamin K hydroquinone to allow carboxylation of Glu to Gla; this enzyme is called the gamma-glutamyl carboxylase[78][79] or the vitamin K-dependent carboxylase. The carboxylation reaction only proceeds if the carboxylase enzyme is able to oxidize vitamin K hydroquinone to vitamin K epoxide at the same time. The carboxylation and epoxidation reactions are said to be coupled. Vitamin K epoxide is then reconverted to vitamin K by VKOR. The reduction and subsequent reoxidation of vitamin K coupled with carboxylation of Glu is called the vitamin K cycle.[80] Humans are rarely deficient in vitamin K1 because, in part, vitamin K 1 is continuously recycled in cells.[81]

Warfarin and other 4-hydroxycoumarins block the action of the VKOR.[82] This results in decreased concentrations of vitamin K and vitamin K hydroquinone in the tissues, such that the carboxylation reaction catalyzed by the glutamyl carboxylase is inefficient. This results in the production of clotting factors with inadequate Gla. Without Gla on the amino termini of these factors, they no longer bind stably to the blood vessel endothelium and cannot activate clotting to allow formation of a clot during tissue injury. As it is impossible to predict what dose of warfarin will give the desired degree of clotting suppression, warfarin treatment must be carefully monitored to avoid overdose.

Gamma-carboxyglutamate proteins

The following human Gla-containing proteins ("gla proteins") have been characterized to the level of primary structure: the blood coagulation factors II (prothrombin), VII, IX, and X, the anticoagulant proteins C and S, and the factor X-targeting protein Z. The bone Gla protein osteocalcin, the calcification-inhibiting matrix Gla protein (MGP), the cell growth regulating growth arrest specific gene 6 protein (Gas6), and the four transmembrane Gla proteins (TMGPs), the function of which is at present unknown. Gas6 can function as a growth factor to activate the Axl receptor tyrosine kinase and stimulate cell proliferation or prevent apoptosis in some cells. In all cases in which their function was known, the presence of the Gla residues in these proteins turned out to be essential for functional activity.
Gla proteins are known to occur in a wide variety of vertebrates: mammals, birds, reptiles, and fish. The venom of a number of Australian snakes acts by activating the human blood-clotting system. In some cases, activation is accomplished by snake Gla-containing enzymes that bind to the endothelium of human blood vessels and catalyze the conversion of procoagulant clotting factors into activated ones, leading to unwanted and potentially deadly clotting.

Another interesting class of invertebrate Gla-containing proteins is synthesized by the fish-hunting snail Conus geographus.[83] These snails produce a venom containing hundreds of neuroactive peptides, or conotoxins, which is sufficiently toxic to kill an adult human. Several of the conotoxins contain two to five Gla residues.[84]

Methods of assessment

Vitamin K status can be assessed by:
  • The prothrombin time (PT) test measures the time required for blood to clot. A blood sample is mixed with citric acid and put in a fibrometer; delayed clot formation indicates a deficiency. This test is insensitive to mild deficiency, as the values do not change until the concentration of prothrombin in the blood has declined by at least 50%.[85]
  • Undercarboxylated prothrombin (PIVKA-II), in a study of 53 newborns, found "PT (prothrombin time) is a less sensitive marker than PIVKA II",[86] and as indicated above, PT is unable to detect subclinical deficiencies that can be detected with PIVKA-II testing.
  • Plasma phylloquinone was found to be positively correlated with phylloquinone intake in elderly British women, but not men,[87]
but an article by Schurgers et al. reported no correlation between FFQ and plasma phylloquinone.[88]
  • Urinary γ-carboxyglutamic acid responds to changes in dietary vitamin K intake. Several days are required before any change can be observed. In a study by Booth et al., increases of phylloquinone intakes from 100 μg to between 377 and 417 μg for five days did not induce a significant change. Response may be age-specific.[89]
  • Undercarboxylated osteocalcin (UcOc) levels have been inversely correlated with stores of vitamin K[90] and bone strength in developing rat tibiae. Another study following 78 postmenopausal Korean women found a supplement regimen of vitamins K and D, and calcium, but not a regimen of vitamin D and calcium, was inversely correlated with reduced UcOc levels.[91]

Function in bacteria

Many bacteria, such as Escherichia coli found in the large intestine, can synthesize vitamin K2 (menaquinone-7 or MK-7, up to MK-11),[92] but not vitamin K1 (phylloquinone). In these bacteria, menaquinone transfers two electrons between two different small molecules, during oxygen-independent metabolic energy production processes (anaerobic respiration).[93] For example, a small molecule with an excess of electrons (also called an electron donor) such as lactate, formate, or NADH, with the help of an enzyme, passes two electrons to a menaquinone. The menaquinone, with the help of another enzyme, then transfers these two electrons to a suitable oxidant, such fumarate or nitrate (also called an electron acceptor). Adding two electrons to fumarate or nitrate converts the molecule to succinate or nitrite + water, respectively.

Some of these reactions generate a cellular energy source, ATP, in a manner similar to eukaryotic cell aerobic respiration, except the final electron acceptor is not molecular oxygen, but fumarate or nitrate. In aerobic respiration, the final oxidant is molecular oxygen (O2), which accepts four electrons from an electron donor such as NADH to be converted to water. E. coli, as facultative anaerobes, can carry out both aerobic respiration and menaquinone-mediated anaerobic respiration.

Vitamin K injection in newborns

The blood clotting factors of newborn babies are roughly 30 to 60% that of adult values; this may be due to the reduced synthesis of precursor proteins and the sterility of their guts. Human milk contains 1–4 μg/L of vitamin K1, while formula-derived milk can contain up to 100 μg/L in supplemented formulas. Vitamin K2 concentrations in human milk appear to be much lower than those of vitamin K1. Occurrence of vitamin K deficiency bleeding in the first week of the infant's life is estimated at 0.25 to 1.7%, with a prevalence of two to 10 cases per 100,000 births.[94] Premature babies have even lower levels of the vitamin, so they are at a higher risk from this deficiency.

Bleeding in infants due to vitamin K deficiency can be severe, leading to hospitalization, blood transfusions, brain damage, and death. Supplementation can prevent most cases of vitamin K deficiency bleeding in the newborn. Intramuscular administration is more effective in preventing late vitamin K deficiency bleeding than oral administration.[95][96]

USA

As a result of the occurrences of vitamin K deficiency bleeding, the Committee on Nutrition of the American Academy of Pediatrics has recommended 0.5 to 1.0 mg vitamin K1 be administered to all newborns shortly after birth.[96]

UK

In the UK vitamin K supplementation is recommended for all newborns within the first 24 hours.[97] This is usually given as a single intramuscular injection of 1 mg shortly after birth but as a second-line option can be given by three oral doses over the first month.[98]

Controversy

Controversy arose in the early 1990s regarding this practice, when two studies suggested a relationship between parenteral administration of vitamin K and childhood cancer,[99] however, poor methods and small sample sizes led to the discrediting of these studies, and a review of the evidence published in 2000 by Ross and Davies found no link between the two.[100] Doctors reported emerging concerns in 2013,[101] after treating children for serious bleeding problems. They cited lack-of newborn Vitamin K administration, as the reason that the problems occurred, and recommended that breast-fed babies could have an increased risk unless they receive a preventative dose.

Vitamin K and bone health

There is no good evidence that vitamin K supplementation helps prevent osteoporosis or fractures in postmenopausal women.[102]

45 mg daily MK-4 has been approved by the Ministry of Health in Japan since 1995 for the prevention and treatment of osteoporosis.[16]

MK-4 (but not MK-7 or vitamin K1) prevented bone loss and/or fractures in the following circumstances:

Vitamin K2 (MK-7) and bone health

Menaquinone-7 (MK-7), which is abundant in fermented soybeans (natto), has been demonstrated to stimulate osteoblastic bone formation and to inhibit osteoclastic bone resorption.[104] In another study, use of MK-7 caused significant elevations of serum Y-carboxylated osteocalcin concentration, a biomarker of bone formation. MK-7 also completely inhibited a decrease in the calcium content of bone tissue by inhibiting the bone-resorbing factors parathyroid hormone and prostaglandin E2.[105] On 19 February 2011, HSA (Singapore) approved a health supplement that contains vitamin K2 (MK-7) and vitamin D3 for increasing bone mineral density.[citation needed]

Vitamin K and vascular calcification

The potential benefit of vitamin k in reducing cardiovascular disease (CVD) risk is due to its function as a cofactor in the post-translational modification of matrix gla protein (MGP) in vascular smooth muscle cells (VSMC).
Increased calcification of blood vessels is a risk factor for CVD as it lends to the hardening of arteries and/or to the development of hard atherosclerotic plaque. MGP may play a role in preventing ectopic calcification in the arteries. Although the mechanism of MGP on arterial calcification is not fully understood, it is known that MGP must be in its active form to have a beneficial effect in the blood vessel. MGP becomes activated by carboxylation, which requires vitamin k as a cofactor. Because it is thought that phylloquinones exerts its actions mainly in the liver, it is speculated that menaquinones may have a more significant influence in the extra-hepatic regions of the body, such as VSMCs, where they are known to travel to by LDL.[106] In addition, menaquinones have been demonstrated to have a longer half-life in circulation compared to phylloquinone.[106] Menaquinones may therefore be important for preventing vascular calcification (VC) and thus reducing risk for CVD.

Previous research conducted on MGP knockout mice demonstrated the importance of MGP on inhibiting VC. Luo, Ducy, McKee, Pinero, Loyer, Behringer, and Karsenty (1997) found that the aorta of MGP knockout mice became severely calcified within the first two months of life, leading to rupture of the artery and finally death of the mice due to internal hemorrhaging.[107] This study became a basis for many future studies to further explore the influence of MGP on VC since it was hypothesized that if a human had low levels of MGP they could develop VC more quickly than those with optimal levels of MGP. It became a question as to whether MGP could help to reduce the risk of CVD development. However, because MGP undergoes different post-translational modifications, several forms of MGP can exist in the human body, so which form of MGP is most effective at preventing VC? Schurgers, Spronk, Soute, Schiffers, DeMay, andVermeer (2007) found that the carboxylated form of MGP was responsible for reducing VC in rats.[108] In the study, rats were subjected to a dose of warfarin to induce VC. Warfarin is a commonly prescribed drug given to humans to help prevent heart disease and stroke by reducing the development of blood clots in the blood vessels. Warfarin acts to inhibit the vitamin k cycle; thereby preventing activation of essential blood clotting factors. In the aforementioned study, VC was significantly decreased in the rats inflicted with VC via warfarin, when supplemented for 6 weeks with a high dose of either menaquinone or phylloquinone.[108] Both menaquinone and phylloquinone supplementation in concentrations of 100 μg/g (supplied in the rat food), were able to inflict a significant reduction in VC in the rats.[108] When examining the different MGP forms in the rats, it was found that the high menaquinone and phylloquinone supplement groups had greater levels of carboxylated MGP compared to the control, rats receiving warfarin, and rats receiving a normal phylloquinone dose.[108] Furthermore, levels of uncarboxylated MGP were higher in the rats receiving warfarin and in the rats receiving a normal phylloquinone dose.[108] This study demonstrated a benefit of both menaquinone and phylloquinone on VC but did not determine the mechanism by which carboxylated MGP was able to reduce VC. In 2008, Wallin, Schurgers, and Wajih set out to help establish this mechanism. The researchers evaluated uncarboxylated MGP and carboxylated MGP by experimenting with the glutamic acid and gamma-carboxyglutamic acid residues of MGP.[109] It was found that the gamma-carboxyglutamic acid residues were capable of inhibiting a protein called bone morphogenic protein-2 (BMP-2), that may play a role in differentiation of vascular smooth muscle cells (VSMCs) into bone-like cells.[109] On the other hand, the glutamic acid residues were unable to inhibit BMP-2, which confirmed that MGP must be carboxylated to be active in VC inhibition.[109]

Intervention studies with menaquinones in humans have become more frequently published in recent years. In a randomized, double blind, placebo controlled human trial, menaquinone-7 supplementation was studied in healthy adults for its influence on circulating forms of MGP. In the twelve-week study, sixty adults were divided into three supplement groups: placebo, 180 μg menaquinone-7/day, and 360 μg menaquinone-7/day and circulating forms of MGP were analyzed from blood and urine samples that were collected at weeks 1, 4, and 12.[110] The researchers found that after only 4 weeks of menaquinone-7 supplementation, the total level of dephosphorylated-uncarboxylated MGP was decreased compared to baseline and that the effect was dose dependent with 360 μg menaquinone-7/day having a greater effect than 180 μg menaquinone-7/day.[110] Furthermore, no change in dephosphorylated-uncarboxylated MGP was evident in the placebo group.[110] In another study examining the relationship between menaquinone-7 supplementation and circulating dephosphorylated-uncarboxylated MGP levels, 165 patients undergoing chronic hemodialysis were divided into three menaquinone-7 supplementation groups: 360 μg/day, 720 μg/day, or 1080 μg/day for a total of 8 weeks.[111] At baseline, it was determined through 3-day food diaries that there was a significant inverse relationship between menaquinone intake and dephosphorylated-uncarboxylated MGP levels, whereas phylloquinone intake had no association.[111] After 8 weeks of menaquinone-7 supplementation, the researchers found that circulating dephosphorylated-uncarboxylated MGP levels had significantly decreased, and that the effect was dose dependent.[111] Unfortunately, other forms of MGP were not measured. In both of these aforementioned studies, neither examined the relationship of dephosphorylated-uncarboxylated MGP levels to VC or CVD. However, a recent cohort study investigating vitamin k insufficiency and CVD found that low circulating dephosphorylated-uncarboxylated MGP levels (less than 400 pmol/L) were significantly associated with increased risk of fatal and non-fatal CVD in 577 healthy men and women aged 55 – 65 years.[112]

If VC can be prevented or reduced by menaquinones then the risk for CVD may also be reduced. Future strategies to reduce the risk of CVD may one day encourage increasing one’s intake of dietary menaquinone.

Vitamin K2 (MK-7) and coronary heart disease

A study by Gast et al. (2009),[72] reports "an inverse association between vitamin K2 and risk of CHD with a Hazard Ratio (HR) of 0.91 [95% CI 0.85–1.00] per 10 μg/d vitamin K2 intake. This association was mainly due to vitamin K2 subtypes MK-7, MK-8 and MK-9. Vitamin K1 intake was not significantly related to CHD. The authors conclude that "a high intake of menoquinones, especially MK-7, MK-8 and MK-9, could protect against CHD.
However, more research is necessary to define optimal intake levels of vitamin K intake for the prevention of CHD."

Vitamin K and Alzheimer's disease

Research into the antioxidant properties of vitamin K indicates that the concentration of vitamin K is lower in the circulation of carriers of the APOE4 gene, and recent studies have shown its ability to inhibit nerve cell death due to oxidative stress. It has been hypothesized that vitamin K may reduce neuronal damage and that supplementation may hold benefits to treating Alzheimer's disease, although more research is necessary in this area.[113]

Vitamin K used topically

Vitamin K may be applied topically, typically as a 5% cream, to diminish postoperative bruising from cosmetic surgery and injections, to treat broken capillaries (spider veins), to treat rosacea, and to aid in the fading of hyperpigmentation and dark under-eye circles.[114][115]

Vitamin K and cancer

While researchers in Japan were studying the role of vitamin K2 as the menaquinone-4 (MK-4) form in the prevention of bone loss in females with liver disease, they discovered another possible effect. This two-year study that involved 21 women with viral liver cirrhosis found that women in the supplement group were 90% less likely to develop liver cancer.[116][117] A German study performed on men with prostate cancer found a significant inverse relationship between vitamin K2 consumption and the risk of advanced prostate cancer.[118]

In 2006, a clinical trial showed that K2 as the menaquinone-4 (MK-4) (called menatetrenone in the study) might be able to reduce recurrence of liver cancer after surgery. It should be noted that this was a small pilot study and other similar studies did not show much effect. MK-4 is now being tested along with other drugs to reduce liver cancer and has shown promising early results.[119]

Vitamin K and diabetes in the elderly

A research shows that total diabetes risk of individual who have highest circulating levels of vitamin K1 were 51% lower than those with the lowest levels. The researchers conclude that dietary phylloquinone intake is associated with reduced risk of type 2 diabetes.[120]

Vitamin K and non-Hodgkin lymphoma

A research shows that the risk of developing non-Hodgkin lymphoma was decreased by 45 percent for the study participants who had the highest vitamin K levels compared to participants with the lowest levels of the vitamin.[121]

Vitamin K as antidote for poisoning by 4-hydroxycoumarin drugs

Vitamin K is part of the suggested treatment regime for poisoning by rodenticide.[122]

Vitamin K antagonists are substances that reduce blood clotting by reducing the active form of vitamin K. They are used as rat poisons and as medications to prevent thrombosis. Examples include 4-hydroxycoumarins such as the pharmaceutical warfarin, and also anticoagulant-mechanism poisons such as bromadiolone, which are commonly found in rodenticides.[citation needed]

4-Hydroxycoumarin drugs possess anticoagulatory and rodenticidal properties because they inhibit recycling of vitamin K and thus cause simple deficiency of active vitamin K. This deficiency results in decreased vitamin K-dependent synthesis of some clotting factors by the liver. Death is usually a result of internal hemorrhage. Treatment for rodenticide poisoning usually consists of repeated intravenous doses of vitamin K, followed by doses in pill form for a period of at least two weeks, though possibly up to 2 months, after poisoning (this is necessary for the more potent 4-hydoxycoumarins used as rodenticides, which act by being fat-soluble and thus having a longer residence time in the body). If caught early, prognosis is good even when great amounts of the drug or poison are ingested, as these drugs are not true vitamin K antagonists, so the same amount of fresh vitamin K administered each day is sufficient for any dose of poison (although as noted, this must be continued for a longer time with more potent poisons). No matter how large the dose of these agents, they can do no more than prevent vitamin K from being recycled, and this metabolic problem may always be simply reversed by giving sufficient vitamin K (often 5 mg per day) to ensure that enough fresh vitamin K resides in the tissues to carry out its normal functions, even when efficient use of it by the body is prevented by the poison.[medical citation needed]

Vitamin K and brain sulfatides

A recent study has shown that rats who are fed excess amounts of vitamin K had greater amounts of brain sulfatide concentrations.[123] This study indicates that vitamin K has more uses than originally thought, thus furthering the importance of daily vitamin K intake. The same study showed that a diet with insufficient vitamin K levels decreased the brain sulfatide concentrations in rats at the (p < 0.01) significance level. Another study involving rats has indicated that different species, strains and genders of rats required different amounts of vitamin K intake, depending on how much was stored in their livers.[124] This may indicate that different humans should have different needs for their vitamin K intake. A third study looked at the way rats and chicks are able to recycle parts of vitamin K. The study found that chicks are about 10% less efficient in recycling the vitamin K than their rat counterparts.[125] This evidences also helps to confirm that vitamin K levels are unique to each species, and the previous study shows that required vitamin K intake also varies within species.

History of discovery

In 1929, Danish scientist Henrik Dam investigated the role of cholesterol by feeding chickens a cholesterol-depleted diet.[3] After several weeks, the animals developed hemorrhages and started bleeding. These defects could not be restored by adding purified cholesterol to the diet. It appeared that—together with the cholesterol—a second compound had been extracted from the food, and this compound was called the coagulation vitamin. The new vitamin received the letter K because the initial discoveries were reported in a German journal, in which it was designated as Koagulationsvitamin. Edward Adelbert Doisy of Saint Louis University did much of the research that led to the discovery of the structure and chemical nature of vitamin K.[126] Dam and Doisy shared the 1943 Nobel Prize for medicine for their work on vitamin K (K1 and K2) published in 1939. Several laboratories synthesized the compound(s) in 1939.[127]

For several decades, the vitamin K-deficient chick model was the only method of quantifying vitamin K in various foods: the chicks were made vitamin K-deficient and subsequently fed with known amounts of vitamin K-containing food. The extent to which blood coagulation was restored by the diet was taken as a measure for its vitamin K content. Three groups of physicians independently found this: Biochemical Institute, University of Copenhagen (Dam and Johannes Glavind), University of Iowa Department of Pathology (Emory Warner, Kenneth Brinkhous, and Harry Pratt Smith), and the Mayo Clinic (Hugh Butt, Albert Snell, and Arnold Osterberg).[128]

The first published report of successful treatment with vitamin K of life-threatening hemorrhage in a jaundiced patient with prothrombin deficiency was made in 1938 by Smith, Warner, and Brinkhous.[129]

The precise function of vitamin K was not discovered until 1974, when three laboratories (Stenflo et al.,[130] Nelsestuen et al.,[131] and Magnusson et al.[132]) isolated the vitamin K-dependent coagulation factor prothrombin (Factor II) from cows that received a high dose of a vitamin K antagonist, warfarin. It was shown that, while warfarin-treated cows had a form of prothrombin that contained 10 glutamate amino acid residues near the amino terminus of this protein, the normal (untreated) cows contained 10 unusual residues that were chemically identified as gamma-carboxyglutamate, or Gla. The extra carboxyl group in Gla made clear that vitamin K plays a role in a carboxylation reaction during which Glu is converted into Gla.

The biochemistry of how vitamin K is used to convert Glu to Gla has been elucidated over the past thirty years in academic laboratories throughout the world.

Geoengineering and Climate Change

Original link:  http://davidbrin.blogspot.com/2015/03/geoengineering-and-climate-change.html

A  National Academy of Sciences panel said that, with proper governance and other safeguards,  we should commence more research on geoengineering — technologies that might let himanity deliberately intervene in nature to counter climate change.  With the planet facing potentially severe impacts from global warming in coming decades, drastically reducing emissions of carbon dioxide and other greenhouse gases was by far the best way to mitigate the effects of a warming planet. But society would be foolish not to at least carefully commence small scale experiments looking into other means of reducing the net harm.
Geoengineering options generally fall into two categories: capturing and storing some of the carbon dioxide that has already been emitted, so that the atmosphere traps less heat, or reflecting more sunlight away from the earth so there is less heat to start with.

Opponents of geoengineering have long argued that even conducting research on the subject presents a moral hazard that could distract society from the necessary task of reducing the emissions that are causing warming in the first place.

I have long held that this reflex reveals  a monomaniacal insanity, almost 1% as bad as the insanity of the climate denialist cult.  (Yes, that insane.)   Such zero-sum, "don't-negotiate" thinking will doom us all, whether it comes (mostly) from the right or else (in this case) from the left.  We need to remember that a war has many fronts.  This one -- against wastrel stupidity and short-sightedness -- has many fronts.

(PS... the one geoengineering method with the best promise of simply emulating what nature does, herself, to remove CO2 in all-natural ways, is ocean fertilization.  Preliminary results have been all-good and with zero substantial ore verifiably measurable bad outcomes. It is inherently stoppable -- unlike some of the scary proposals to inject aerosals into the upper atmosphere.  Moreover, ocean fertilization offers a possible side benefit of richer fisheries. Experiments in this method are self-limiting and hence should continue, or be encouraged -- under very close supervision.)


== Burden of Proof ==

American scientists and general public have widely differing views about certain scientific issues, as per a recent survey. Climate change and genetically altered food are the two subjects in which prominent differences can be observed.
Cause and effect tend to be murky in elastic, multivariable and non-linear systems.  The Denialist Cult uses this relentlessly to show that the observed correlations between theory and observation are still rough and hence "there's doubt"... leading thereupon to the howler... that we should do nothing till the correlations become perfect.
I have learned not to go sumo with them over correlations graphs. It is far more effective to show that they are being profoundly and stunningly illogical, demanding "more research" while their side has sabotaged climate investigators at every turn, canceling satellites, slashing atmospherics budgets and ordering NASA and NOAA not to look Earthward. At intervals, the Bush Administration, various GOP-controlled Congressional committees, and most recently the State of Florida have banned discussion of these topics and even forbidden mention of "climate" or "rising seas"... a special irony in Florida, which is already suffering from rising seas.

Those actions -- and countless more -- show they want the obscurity and doubt. It is not a flaw, but a feature. Hence the War on Science.

But here is where you can and must corner them.It is in the matter of Burden of Proof that you'll find the weak point in the incantations that they rely on, concocted at Heritage and AEI and Fox, at the behest of coal barons and petro-sheiks. Dig this well, and learn how to hammer it home:
When a scientific field has competitively settled on a Standard Model, that SM is not always right!  But it is usually right -- to the limits of last year's instrumentation. 

While the Standard Model in any field normally improves incrementally, under relentless competitive pressure by young upstart scientists, outsiders are free to try to topple the whole SM... but thos outsiders and upstarts bear the burden of proof. The professionals are obliged to take note of such proof... but they are not obliged to prove the SM over and over and over again to politically propelled critics. They get plenty of challenges already, from their own grad students.

Yes, some of you will twist what I just said into sounding like elitism and appealing to authority.  Bull. If that is your reflex then you simply do not understand what I just said.  You do not understand science -- the most vibrantly competitive and productive and honest field of endeavor our species ever invented. Ingrates shrug off all the ways they have benefited from these traits of science, and that's fine. It's a free country and -- unlike all the priesthoods of the past -- scientists don't demand worship. But if you cannot grasp your burden of proof, when decrying some field's Standard Model -- well-tested and credited by women and men who are verifiably vastly smarter than you are, then all you are being is a yammer-puss.

Put it in stark terms. A society that ignores a major scientific model, backed by 97% of the smart men and women who turned the old, joke of a 4 hour weather forecast into a 10 DAY miracle is clearly a very stupid society.

Human beings’ ancestors have routinely stolen genes from other species



OPPONENTS of genetically modified crops often complain that moving genes between species is unnatural.
Leaving aside the fact that the whole of agriculture is unnatural, this is still an odd worry. It has been known for a while that some genes move from one species to another given the chance, in a process called horizontal gene transfer. Genes for antibiotic resistance, for example, swap freely between species of bacteria. Only recently, though, has it become clear just how widespread such natural transgenics is. What was once regarded as a peculiarity of lesser organisms has now been found to be true in human beings, too. 

Alastair Crisp and Chiara Boschetti of Cambridge University, and their colleagues, have been investigating the matter. Their results, just published in Genome Biology, suggest human beings have at least 145 genes picked up from other species by their forebears. Admittedly, that is less than 1% of the 20,000 or so humans have in total. But it might surprise many people that they are even to a small degree part bacterium, part fungus and part alga.
Dr Crisp and Dr Boschetti came to this conclusion by looking at the ever-growing public databases of genetic information now available. They did not study humans alone. They looked at nine other primate species, and also 12 types of fruit fly and four nematode worms. Flies and worms are among geneticists’ favourite animals, so lots of data have been collected on them. The results from all three groups suggest natural transgenics is ubiquitous.
To avoid getting bogged down in the billions of base pairs of an animal genome the researchers looked at what is known as the transcriptome. This is the set of messenger molecules, made of a DNA-like chemical called RNA, that pick up instructions on how to make proteins from genes in the nucleus and deliver them to the subcellular factories which turn those proteins out. Broadly speaking, each type of messenger RNA corresponds to a single gene. By looking at the messengers Dr Crisp and Dr Boschetti could be certain they were recording active genes and not stretches of nuclear DNA that had once been genes but now no longer work.

For every transcribed messenger, they searched the world’s databases, looking for matches. They excluded the immediate relatives of each of their three groups of animals (that is, no arthropods were compared with the flies, no vertebrates with the primates and no other nematodes with the worms). They then asked whether similar-looking genes to those in a transcriptome were found more often in other animals, or in non-animals. If the former, the most likely explanation would be that they were there by common descent from animal ancestors. If the latter, then, a horizontal gene transfer from species to species seemed the most probable explanation. On average, worms had 173 horizontally transferred genes, flies had 40 and primates had 109. Humans thus had more than the primate mean.
Many of the matches are to genes of unknown purpose—for it is still the case, more than a decade after the end of the human genome project, that the jobs of many genes remain obscure. But some human transgenes are surprisingly familiar. The ABO antigen system, which defines basic blood groups for transfusion purposes, looks bacterial. The fat-mass and obesity-associated gene, the effect of which is encapsulated in its rather long-winded name, seems to come from marine algae. And a group of genes involved in the synthesis of hyaluronic acid originates from fungi. Hyaluronic acid is a chemical that is an important part of the glue which holds cells together. (It is also a frequent ingredient of skin creams.)

Altogether, the researchers found two imported genes for amino-acid metabolism, 13 for fat metabolism and 15 which are involved in the post-manufacture modification of large molecules. They also identified five immigrants that generate antioxidants and seven that are part of the immune system.

This is quite a catalogue. If anything similar were inserted by genetic engineers into corn or cattle, there would no doubt be an outcry. In humans, however, they are doing a good job. It is fair to point out that many of them seem to have been cohabiting with the line that led to humanity for millions of years, and both sides have thus had ample time to adjust. Nevertheless there was once a moment for all of them when they were just as alien as a bacterial insecticide is in a maize plant or a herbicide-resistance gene is in a soyabean.

Scientists develop cool process to make better graphene

Original link:  http://phys.org/news/2015-03-scientists-cool-graphene.html

Caltech scientists develop cool process to make better graphene
 
 
 
 
 
 
 
 
 
 
 
 
 
Schematic of the Caltech growth process for graphene. Credit: D. Boyd and N. Yeh labs/Caltech
A new technique invented at Caltech to produce graphene—a material made up of an atom-thick layer of carbon—at room temperature could help pave the way for commercially feasible graphene-based solar cells and light-emitting diodes, large-panel displays, and flexible electronics.
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"With this , we can grow large sheets of electronic-grade graphene in much less time and at much lower temperatures," says Caltech staff scientist David Boyd, who developed the method.

Boyd is the first author of a new study, published in the March 18 issue of the journal Nature Communications, detailing the new manufacturing process and the novel properties of the graphene it produces.

Graphene could revolutionize a variety of engineering and scientific fields due to its unique properties, which include a tensile strength 200 times stronger than steel and an electrical mobility that is two to three orders of magnitude better than silicon. The electrical mobility of a material is a measure of how easily electrons can travel across its surface.

However, achieving these properties on an industrially relevant scale has proven to be complicated. Existing techniques require temperatures that are much too hot—1,800 degrees Fahrenheit, or 1,000 degrees Celsius—for incorporating graphene fabrication with current electronic manufacturing. Additionally, high-temperature growth of graphene tends to induce large, uncontrollably distributed strain—deformation—in the material, which severely compromises its intrinsic properties.

"Previously, people were only able to grow a few square millimeters of high-mobility graphene at a time, and it required very high temperatures, long periods of time, and many steps," says Caltech physics professor Nai-Chang Yeh, the Fletcher Jones Foundation Co-Director of the Kavli Nanoscience Institute and the corresponding author of the new study. "Our new method can consistently produce high-mobility and nearly strain-free graphene in a single step in just a few minutes without high temperature. We have created sample sizes of a few square centimeters, and since we think that our method is scalable, we believe that we can grow sheets that are up to several square inches or larger, paving the way to realistic large-scale applications."

The new manufacturing process might not have been discovered at all if not for a fortunate turn of events. In 2012, Boyd, then working in the lab of the late David Goodwin, at that time a Caltech professor of mechanical engineering and applied physics, was trying to reproduce a graphene-manufacturing process he had read about in a scientific journal. In this process, heated copper is used to catalyze graphene growth. "I was playing around with it on my lunch hour," says Boyd, who now works with Yeh's research group. "But the recipe wasn't working. It seemed like a very simple process. I even had better equipment than what was used in the original experiment, so it should have been easier for me."

Representation of a Lie group

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Representation_of_a_Lie_group...