text:
Combs GF Jr., Principles of Nutritional Assessment: Selenium

3rd Edition
October 2020

Abstract

In only a few decades, the trace element selenium (Se) was added to the Nutrition agenda as an essential nutrient with potential to reduce cancer risk. Found in the 1950's to prevent vitamin E deficiency disorders in animals, initial investigations in animal nutrition spawned studies of metabolic mechanisms starting in the 1960's. It is now known that Se functions as an essential constituent of some 25 proteins that contain a previously unrecognized Se-containing amino acid, selenocysteine. These selenoproteins are thought to discharge the nutritional functions of Se. The relationship of one, glutathione peroxidase, to the level of Se intake was used in 2000 to establish an RDA for Se. Se is typically obtained from protein-rich foods, particularly those produced on Se-rich soils. Low Se status occurs in areas of low soil Se, and among individuals consuming low-protein diets. Many consequences of Se deprivation are sub-clinical in nature, requiring other precipitating factors (vitamin E deficiency, low iodine intake, viruses, carcinogens) to reveal the effects of sub-optimal expression of selenoenzymes and/or insufficient amounts of active Se-metabolites. Studies that started in the 1960's showed that Se can prevent carcinogenesis in animal and cell models, and that anti-tumorigenic activities required Se doses greater than those required to support selenoenzyme expression. Only a few clinical intervention trials have been conducted to test the hypothesis that Se supplementation can reduce cancer risk in humans; most, but not all have shown positive results. Hence, whether Se may be a risk modifier for cancer remains unclear.

CITE AS: Combs GF Jr, Principles of Nutritional Assessment: Selenium https://nutritionalassessment.org/Selenium/
Email: gfc2@cornell.edu

25b.1 Overview

Selenium (Se) is an essential nutrient with several multiple biological activities. It was first recognized for its toxic potential in the 1930's when it Se was identified as an active principal in a plant-induced neuropathy of grazing horses and cattle in the northern Great Plains of the United States In the 1950s its nutritional role was discovered with experiments with laboratory and livestock species that found the element to prevent pathologies in vitamin E-deficient animals Then, in the 1980s its role in human health was indicated with the finding that very low blood Se levels were associated with an endemic heart disease in women and children in parts of China and Se-supplementation was found to be preventive by the Keshan Disease Research Group (1979). In parallel studies starting in the 1960s, Se was shown to have anti-tumorigenic capabilities in a variety of animal models Clinical trials later showed cancer risk reduction for subjects of low-to-moderate Se status ,although one showed no effect

That the various roles of Se have different dose-response relationships has been demonstrated in experimental animals. Biochemical and physiological lesions of Se deficiency are prevented by relatively low dietary levels, e.g., 0.1mg/kg Reductions in experimental tumorigenesis occur when Se is fed at 10–20 times the nutritional level, i.e., ≥ 1.5mg/kg Ip, 1998). Adverse effects are not seen unless still greater dietary levels are used, i.e., > 5mg/kg Because Se intakes of free-living people can seldom be ascertained accurately, Se status in humans must be inferred from measures related to the intake and disposition of Se.

25b.2 Selenium Chemistry

The chemistry of Se has similarities to that of sulfur Hence, Se can be incorporated in plants and animal tissues in lieu of sulfur. However, Se-compounds have higher redox potentials. Thus, while sulfides are metabolized to sulfates, selenate is metabolized to selenide. The biochemistry of Se involves mainly its three anionic forms: Se2- (selenide and hydrogen selenide [H2Se]), SeO2+
3
(selenite and selenous acid (H2SeO3), and SeO2+
4
(selenite and selenic acid [H2SeO4]). Selenide is pivotal in Se metabolism, as HSe is the obligate precursor for the biosynthesis of selenocysteine (SeCys) , the functional form of the element. Selenite is easily reduced. At low pH it is readily reduced by such agents such as ascorbic acid and SO2. It can also readily react with nonprotein thiols (e.g., reduced glutathione [GSH]) or with protein-sulfhydryl groups subsequently to be reduced to selenide via sequential formation of selenotrisulfides (e.g., oxidized glutathione [GSSeSG]) and selenodisulfides (e.g., glutathione selenol [GSSeH]). Selenate is much more resistant to reduction; it is activated to adenosine-5-phosphoselenate as a first step in its physiological reduction.

The major forms of Se in cells are the selenoamino acids selenocysteine and selenomethionine (SeMet). In each, Se is covalently bound to carbon. selenocysteine is co-translationally synthesized in animal tissues; whereas, selenomethionine is produced in plants and microorganisms using elemental Se in lieu sulfur. Animal tissues can incorporate selenomethionine into proteins nonspecifically in place of methionine (Met).

25b.3 Health Effects

25b.3.1 Animals

Selenium was recognized as an essential nutrient when it was found to be the active component of yeast that prevented necrotic liver degeneration in vitamin E-deficient rats and exudative diathesis in vitamin E-deficient chicks Se deficiency is now known to play roles, with vitamin E, in preventing several nutritional diseases of livestock skeletal myopathy of lambs, calves, horses, chickens and ducks; gizzard myopathy in turkey poults; cardiomyopathy in pigs; placental retention in dairy cows; infertility in boars. Accordingly, Se, typically in the form of sodium selenite (Na2SeO3), is commonly included as a nutritional supplement in formulated animal feeds.

25b.3.2 Humans

Severe endemic Se deficiency has been linked with two diseases of humans: a juvenile cardiomyopathy (Keshan disease) and an osteoarthropathy (Kashin-Beck disease) These disorders were described in rural, mountainous areas of central and northeastern China and Russia (eastern Siberia) where food systems were exceedingly low in Se (soils < 125µgSe/kg; grains < 40µgSe/kg) and humans had blood Se levels < 25ng/mL (compared to 85–200ng/mL in the United States).

Keshan disease is a multifocal myocarditis primarily affecting children 2–10y and, to a lesser extent, women of child-bearing age. Diagnosis is based on signs of acute or chronic cardiac insufficiency, cardiac enlargement, arrhythmia, and electrocardiographic abnormalities Affected individuals may show cardiogenic shock or congestive heart failure. In the 1970s, Chinese scientists found Se effective in preventing the disease This led to the widespread use of Se supplements (oral doses of sodium selenite at 0.5–1mg Se/wk, or table salt fortified with selenite at 10–15mg Se per kilogram body weight) Such interventions have virtually eliminated Keshan disease from previously affected areas. It appears likely that Keshan disease may be caused by cardiophilic RNA viruses the virulence of which can be potentiated by severe Se deficiency through increased viral mutation This suggests that Se deficiency may also increase risks for other diseases caused by RNA viruses (e.g., measles, influenza, hepatitis, and HIV/AIDS).

Kashin-Beck Disease is an osteoarthropathy affecting the epiphyseal and articular cartilage, and epiphyseal growth plates of growing bones. However, the etiology is unclear. It presents as enlarged joints (especially of fingers, toes and knees); shortened fingers, toes and extremities; and, in severe cases, dwarfism. A meta-analysis of 15 clinical trials suggested that Se supplementation had some value in preventing the disease. However, additional factors, including iodine deficiency and exposure to fungal toxins, have been suggested as etiological factors.

Microbiome. Dietary Se may also affect the hindgut microbiome, which is involved in immunologic signaling, energy abstraction from non-digested carbohydrates, and carcinogenic risk. Se reaches the hindgut in the form of non-digested Se from the diet and endogenous Se from enterohepatic circulation and sloughed mucosal cells. Selenium has been shown to promote taxonomic diversity of the microbiome of the rat which is capable of producing methylated Se-metabolites independent of the host Because methanogenic Archaea and gram+ bacteria express selenoproteins it is possible that these species may be growth-limited by Se supply.

25b.3.3 Anti-carcinogenesis

That Se may be anti-carcinogenic was first suggested in the late 1960s based on inverse relationships of cancer mortality rates and forage crop Se contents in the US

Animal models. The results of virtually all animal and cell models used, show that both inorganic and organic Se compounds can prevent or reduce carcinogenesis (Ip, 1998). Some of these effects may involve actions of selenoenzymes preventing DNA damage by reducing hydroperoxides. Other anticarcinogenic effects, particularly those associated with supranutritional Se intakes, may involve Se metabolites increasing programmed cell death by way of redox cycling, attacking protein thiols and/or labilizing proteins critical for tumor cell growth and their spread The results of studies with animal tumor models are clear: Se can inhibit both primary and secondary carcinogenesis.

Studies by Ip and colleagues indicated methylselenol (CH3SeH, produced by the methylation of H2Se; Fig 1) as active in Se-antitumorigenesis. CH3SeH can modulate the expression of key genes in the p53 pathway and lymphocyte cell surface ligands that trigger immune activation and reduces plasma proteases and angiogenic factors required for tumor spreading 2014). The involvement of CH3SeH and perhaps other methylated Se-metabolites in Se-antitumorigenesis suggests underlying mechanisms that may become significant at supranutritional Se intakes redox cycling of H2Se and/or CH3SeH to generate reactive oxygen species (ROS); modifications of protein-thiols by H2Se and/or CH3SeH to affect protein function/turnover; Met mimicry by selenomethionine in proteins to sensitize critical regulatory proteins to ROS.

Humans. Whether Se supplementation can be useful in reducing cancer risk in human populations is less clear. Only a few clinical trials have been conducted to test the hypothesis that Se-supplementation can reduce cancer risk While one trial with males of relatively high Se status found no effects on prostate cancer risk most found cancer risk reductions for subjects of low-to-moderate baseline Se status. One well designed trial found supplemental Se to reduce prostate cancer risks in subjects with baseline plasma Se < 106ng/mL, but not in those of greater baseline Se status Meta-analyses of prospective studies and Se-intervention trials concluded that Se supplementation had a preventive effect on cancer incidence in populations with baseline serum Se levels < 126ng/mL and in high-risk populations for cancer. Subsequent systematic reviews indicated that people of higher Se status or with greater Se intakes had lower risks of several types of cancer; but no protective effects of Se supplementation were detected Overall, it appears that high Se status can reduce the risk of certain cancers in many people, especially those with low or nutritionally adequate, but not high, Se status

25b.3.4 Selenosis

That Se can be toxic was recognized before its nutritional function. Almost nine decades ago it was found to be the an active principal in a neuropathy of grazing horses and cattle, grazing on Se-accumulator plants growing on seleniferous soils of the northern Great Plains of the United States Subsequent investigations have characterized selenosis in both its acute and chronic forms

Acute Selenosis has occurred in humans due to accidental ingestion of gram quantities of Se in high-Se solutions including gun bluing, sheep drench and anti-dandruff shampoo Each case involved rapid development of severe gastrointestinal and neurological symptoms followed by acute respiratory failure, myocardial infarction and renal failure. Some cases showed garlic odor of the breath, an early sign in Se-intoxicated animals due to the excretion of dimethylselenide ([CH3]2Se) across the lung In rodents, injected selenite causes a dose-dependent increase in excreted (CH3)2Se even at sub-toxic doses when it can represent nearly 30% of the dose

Chronic Selenosis. Endemic selenosis occurred in the early 1960s in Enshi County, Hubei Province, China where residents consumed foods containing very high levels of Se (several hundred mg/kg) due to the use of the ash from local high-Se coal ash to amend agricultural soils 1989c). During the years of peak prevalence (1961-1964), the five most heavily affected villages experienced morbidity rates approaching 50% and some individuals having blood Se levels as high as 3,200ng/mL. The most common signs were hair and nail loss; lesions of the skin, nervous system and teeth were also reported. Dietary Se intakes, estimated a few years later, averaged about 5mg/day, with individuals with Se intakes less 1500µg/day not showing adverse effects.

Diabetes Risk. Two clinical trials found plasma Se concentrations exceeding about140ng/mL to be associated with increased risk of type 2 diabetes (T2D) Those findings were based on self-reports of T2D and/or medication use consistent with T2D, unconfirmed with measures of circulating glucose, insulin or glycated hemoglobin (HbA1c). They have not been confirmed in other randomized Se-intervention trials, including one in which subjects showed plasma Se concentrations exceeding 200ng/mL Nevertheless, a study of gestating rats found the high-level Se exposure (3mg Se/kg diet) of dams to induce insulin resistance and glucose intolerance late in gestation and in offspring after several weeks postpartum A similar experiment with pigs found fed a diet containing 3mg Se/kg to support greater circulating insulin levels, with normal glucose levels, compared to those fed the nutritional level

25b.4 Selenium Requirements

The Institute of Medicine of the National Academy of Sciences Recommended Dietary Allowance (RDA) was based on maximal expression of Glutathione Peroxidase 3 observed in two studies The first study involved Chinese adults with a basal intake of 11µg Se/day supplemented with graded levels of selenite It indicated that Glutathione Peroxidase 3 activity increased until it plateaued at a total Se intake of 41µg/day. Adjusting for differences in the body weights of the subjects and most Americans, this yielded an estimated requirement of 52µg Se/day. The second study involved adult New Zealanders with baseline intake of 28µg Se/day and supplemented with graded levels of Se as selenomethionine Significant increases in Glutathione Peroxidase 3 activity were seen with 10µg supplemental Se/day, suggesting a requirement of 38µg Se/day. The IOM used the average of the two estimates, 45µg/day, as the Estimated Average Requirement (EAR). Assuming a 10% coefficient of variation, the RDA for was set at 55µg/day for both men and women. RDAs for children were extrapolated from this value based on body weight. Those for infants, however, were based on projected Se intakes from breast milk (birth–6mos: 15µg/day), and from breast milk plus complementary foods (6mos–1y: 20µg/day). Additional Se was recommended during pregnancy and lactation, bringing those RDAs to 60µg/day and 70µg/day, respectively. The World Health Organization (1996) based its recommendations on amounts of Se needed to support two-thirds of maximal Glutathione Peroxidase 3 activity. Based on the data of a single study that intake was imputed to be 26µg Se/day. Adjusting for body weight and assumed interindividual variation, the WHO recommended Se intakes for men and women were set at 40 and 30µg Se/day, respectively. Neither of these groups considered the clear differences in the bioeffacies of selenite and the major form of Se in foods, selenomethionine. Xia et al. (2005) showed that selenomethionine was more effective than selenite in supporting Glutathione Peroxidase 3 expression in low-Se Chinese subjects with graded levels of Se over a 4-month period

The US Food and Drug Administration set a “no observed adverse effect level” (NOAEL) for Se at a whole blood Se concentration of 1000ng/mL, which they calculated to correspond to a dietary intake of 853g/day in an adult male The Institute of Medicine set a tolerable upper Se intake level (UL) for adults at 400ug/d, i.e., about half the NOAEL; other national bodies adopted similar recommendations, i.e., 350–450µg/d for adults

25b.5 Food Sources

Plant Foods. The Se contents of foods vary widely due to the differences in the soluble Se contents of soils, in the capacities for various plant species to access soil Se, and, for livestock products, in the amounts of biologically available Se in feeds. The Se contents of plant foods tend to be influenced by the local soil Se environment. For example, cruciferous vegetables, which are naturally rich in sulfur, can accumulate nutritionally significant amounts of Se (1–10mg/kg) if grown on high-Se soils or if fertilized with selenite or selenate salts. Studies in many countries have shown the effects of geographic variation in the Se contents of foods Wheat grain may contain > 2–5mg Se/kg if produced in parts of the northern plains of North America; but as little as 0.1mg Se/kg if produced in Kansas or New Zealand; and only 0.005mg Se/kg if produced in Shaanxi Province, China. On a global basis, foods with the lowest Se contents are found in the provinces of Heilongjiang, northern Shaanxi, and Sichuan in China.

Animal Foods. Because of the intimate relationship between plants and animals in the food chain, the Se contents of foods of animal origins tend to be influenced by the local soil Se environment. Se is widely used as a supplement to livestock feeds, usually as sodium selenite/selenate. This practice has reduced geographic variation in the Se contents of animal food products. It does not, however, markedly increase tissue Se contents, as the incorporation of inorganic Se is limited to the synthesis of selenocysteine in the selenoproteins. Because both selenocysteine and selenomethionine are found mainly as constituents of proteins, the Se contents of foods of animal origin tend to be correlated with their protein content. Therefore, muscle meats from most species tend to contain 0.3–0.5mg Se/kg higher (4–15 times) amounts.

Human Diets. In most human diets, the dominant food sources of Se are cereals, meats and fish. In American diets fewer than two dozen foods provide most of the total dietary Se, with five foods contributing half: beef, bread, pork, chicken and eggs Dairy products contribute small amounts of Se to the total intakes in most countries, except in cases where their consumption is relatively high or where the rest of the diet provides little Se, or both (e.g., New Zealand). Vegetables and fruits are uniformly low in Se and provide only small amounts in most diets.

Because Se in foods is almost exclusively associated with protein, individuals with chronically low protein intakes are at risk for Se deficiency. Accordingly, Se-responsive muscular pain and weakness was been described in patients receiving long-term total parenteral nutrition without Se-supplementation and protein-malnourished children with kwashiorkor or marasmus were found to have low plasma Se levels

Selenium Intakes. Data from 68 countries indicated that suboptimal Se status (plasma/serum Se < 70–80ng/mL) is prevalent in almost half of those countries Estimates of the average Se intakes in 18 countries varied from as low as 3µg/d in a Keshan disease-endemic part of China to as high as 224µg/d in Canada and Venezuela. The estimated intakes of several countries (Greece, Libya, New Guinea, Sweden, Turkey and the United Kingdom) fall below the U.S./Canadian RDA These differences are reflected in the average plasma/serum Se levels of residents of various countries, which span an order of magnitude

25b.6 Enteric Absorption

In general, food Se is well utilized. For the Se-amino acids, this involves digestion of their respective proteins, and absorption of the digestive products by active transport. For inorganic forms of Se, which do not require digestion, this involves absorption by simple (selenite) or carrier-mediated (selenate) diffusion Wastney et al (2011) found that the enteric absorption of single doses (200µg) by humans was 98% for selenomethionine-Se and 84% for selenite-Se. Similar results were obtained by Thomson and Robinson (1986).

25b.7 Metabolism

Figure 25b.1. illustrates the metabolism of the major dietary forms of Se (selenomethionine, selenocysteine and, if supplemented, selenite). Selenium from each of these forms can be incorporated into functional selenoproteins as selenocysteine or non-specifically into general proteins as selenomethionine, and ultimately excreted as several methylated metabolites. selenocysteine and selenite can each be incorporated only into the selenoproteins by processes first involving reduction to selenide followed by the de novo incorporation into selenocysteine during its biosynthesis via the co-translational conversion of tRNA-bound serine to selenocysteine. selenomethionine is incorporated differently; because it can charge the tRNAMet, selenomethionine can be incorporated directly but nonspecifically into proteins in lieu of Met. For this reason, albumin is a primary component of plasma Se in Se-fed individuals. SeO2+
3
(selenite and selenous acid (H2SeO3), and SeO2+
4
(selenite and selenic acid [H2SeO4]).

Se is excreted by conversion to methylated metabolites (Combs, 2018). The primary route of Se excretion in individuals with low-to-moderate Se intakes is across the kidney. The dominant urinary metabolite is a selenosugar, 1β-methylseleno-N-acetyl-galactosamine Individuals with relatively high Se intakes can also excrete trimethylselenonium or other selenosugars in the urine, as well as methylselenol in the breath. The latter is responsible for the “garlic breath” associated with selenosis in livestock. Metabolic tracer studies have shown that, over a 12-day period, Se-adequate adults excrete a total of 17% of Se from an oral selenite dose, but only 11% of Se from an oral selenomethionine dose, the longer turnover being due to the nonspecific incorporation of selenomethionine into body proteins Under normal circumstances, there appears to be only a small enterohepatic circulation of absorbed Se; therefore, fecal Se constitutes mostly unabsorbed dietary Se.

25b.8 Biochemical Functions

The nutritional activities of Se are discharged by a group of selenoproteins, i.e., proteins containing selenocysteine. Selenoproteins are relatively rare in nature, occuring in bacteria, archaea, and eukaryota in varying numbers. None have been identified in fungi and plants. In eukaryotes, the greatest number of selenoproteins occurs in aquatic organisms (many fishes and algae have > 30 selenoproteins); 25 selenoproteins have been identified in humans Most, if not all, are involved in the regulation of redox signalling.

The best understood and most abundant members of the human selenoproteome include:

• Glutathione Peroxidases (GPXs), which reduce hydroperoxides using reducing equivalents from reduced glutathione
• Selenoprotein P (SEPP), produced and excreted by the liver, functioning as the primary transporter of Se to peripheral tissues, and comprising 40–60% of total plasma Se
• Iodothyronine Deiodinases (DIOs), which remove iodine from the thyroid hormones (T4, T3) in the metabolism of the active hormone, T3 (Köhrle, 2013).
• Thioredoxin Reductases (TRRs), NADPH-dependent flavoenzymes that function in intracellular redox regulation by reducing thioredoxin

Genomic searching has revealed additional selenoproteins:

• SepH: a nuclear protein of unknown function.
• SepI: a protein homologous to human choline/ethanolamine phosphotransferase with seven putative transmembrane domains.
• SepK, SePS : proteins of unknown function localized to endoplasmic reticulum (ER) and plasma membranes of mammalian cells.
• SepM, SepN, SepO, SepT: proteins of unknown function localized in the endoplasmic reticulum .
• SepV: a paralog of SepW apparently expressed only in the seminiferous tubules of the testes.

25b.9 Assessing Selenium Status

Se status refers to the amount of metabolically active or potentially metabolically active Se in the body. It includes the Se pool that is metabolically functional and, thus, the most nutritionally relevant, as well as other Se pools that can be mobilized to functional forms. It is a product of an individual's intake, retention and metabolism of Se-containing compounds. Accordingly, Se status has four components: Se intake, tissue Se, Se excretion and Se function (Figure 25b.2). (Combs, 2015).

25b.9.1 Biomarkers of Selenium Intake

Se intakes of individuals or populations can be assessed as the sum of the products of the Se contents of particular foods and the amounts of those foods consumed. In practice, this is done using standard food composition tables and food frequency questionnaires, which may not yield accurate estimates of actual Se intake because of the geographic variation in food Se contents not captured in those tables. Therefore, determination of food Se by actual analysis of representative samples is necessary to produce valid Se intake estimates. Speciation of Se has been accomplished only for a few foods, e.g., lentil However, such information would not add value in understanding Se status; estimates of total Se intake are sufficient to determine whether individuals and populations meet the recommended Se intakes.

Imputing Se intake from measured Se biomarkers is most straightforward in subjects of deficient-to-low Se status whose plasma Se concentrations respond to supplemental Se in proportion to the magnitude of supplementation For non-deficient subjects, however, the relationship of Se intake and plasma Se level depends on the form of Se consumed. Inorganic Se typically produces only minimal increases (< 20%) in subjects with plasma Se concentrations greater than about 70ng/mL while selenomethionine or selenomethionine-containing foods produce increases in plasma Se over a wide range, including subjects of relatively high Se status The former effect reflects the fact that the central organ of Se metabolism, the liver, can convert inorganic Se to forms incorporated only into selenoproteins (Fig. 1), including two in the plasma, the extracellular Glutathione Peroxidase 3 and the Se-transporter Selenoprotein P that show plateaued expression at Se intakes recommended as being nutritionally adequate. The latter, continuing effect is due to the unregulated, non-specific incorporation of selenomethionine into albumin and other proteins over a virtually unlimited range of intakes 1986; For Se-nondeficient individuals consuming Se mostly as selenomethionine, Se intake can be predicted from the Se concentration of plasma.

25b.9.2 Biomarkers of Selenium Retention

Most absorbed Se is taken up by liver to re-enter the circulation as a component of Selenoprotein P A significant amount (15–20%) is released in the urine over several days. Under normal conditions, there appears to be only a small enterohepatic circulation of absorbed Se; therefore, fecal Se is comprised mostly of the unabsorbed portion of ingested Se. In animals fed nutritionally adequate levels of selenite, fecal Se comprises about a fifth of Se excretion fecal Se increases at higher Se intakes.

Inferring Retention. Retention of Se in the body can be determined by the difference between the amount of Se ingested and the sum of urinary and fecal Se losses. For humans, this requires total collections of urine and stools, ideally over a few days. Alternatively, convenient samples of urine can be used if indexed to creatinine concentration to reduce errors associated with variation in urine output; a non-absorbable dietary marker that can be measured in the stool samples, can be used to calculate the amount of diet corresponding to the fecal sample analyzed for Se.

Assessment of Se retention is useful in livestock nutrition where it can be used as a measure of the bioavailability of feed forms of Se, or as a proxy for the amount of Se in edible tissues Tissues retain Se largely in protein-bound forms, selenocysteine being specifically incorporated into selenoproteins and selenomethionine being nonspecifically incorporated into all proteins (Fig 1). Accordingly, animals fed dietary sources of selenomethionine will accumulate relatively large amounts of Se in both the specific and non-specific pools; whereas, those fed inorganic Se-compounds, e.g., selenite, will accumulate lesser amounts due to that form only entering the specific (selenocysteine) pool.

Estimating retained Se is useful in human studies as indicators of the degree to which an individual has met his/her Se requirement and may have Se reserves. This can be inferred from analyses of the two specific selenoproteins (Selenoprotein P, Glutathione Peroxidase 3) as well as the non-specific component of plasma Se. Those selenoproteins show maximal expression at plasma Se concentrations of 50–70ng/mL

Urinary Selenium. Excess absorbed Se can be eliminated in the urine by way of metabolism to methylated products including trimethylselenonium ion ([CH3]3Se+) and a selenosugar 1β-methylseleno-N-acetyl-D-galactosamine. The dominant chemical form of urinary Se varies among species. In rodents, TMSe+ can comprise 90% of urinary Se; in humans, the predominant form is the selenosugar In both rodents and humans, urinary Se excretion increases with increasing Se intake Urinary Se excretion is related to both Se status, the form(s) of Se consumed and the availability of the methyl donor S-adenosylmethionine Urinary Se excretion is negatively associated with plasma homocysteine concentrations, but positively associated with plasma concentrations of folate and vitamin B12 Urinary Se excretion of men and women differ, probably relating to sexually dimorphic selenoprotein biosynthesis as has been described in rodents In a cohort of healthy, non-deficient Americans, the dose-dependent urinary Se excretion of women was 74% greater than that of men, despite the fact that both showed similar plasma Se responses to comparable intakes of Se This indicates that women do not retain selenomethionine-Se as well as men.

Urinary Se excretion also has a genetic determinant. The increase in urinary Se of non-deficient humans with increasing Se intake was 59% greater for individuals with the GPX1 679 T/T genotype compared to those with the GPX1 679 C/C genotype while at baseline, the former individuals had slightly lower plasma Se levels. Because GPX1 accounts for some 60% of tissue Se differences in its turnover are likely to affect Se retention and be manifest as differences in urinary Se excretion.

25b.9.3 Biomarkers of Tissue Selenium

Selenium can be retained in many organs. Greatest concentrations are found in the kidney, liver and pancreas, followed by cardiac and skeletal muscle; this pattern is remarkably similar across species, particularly under non-deficient conditions Because of its non-specific incorporations into proteins, food sources of selenomethionine support greater tissue Se accumulation than comparable intakes of Se in inorganic forms. For this reason, animal studies using tissue Se accumulation as the measure of bioavailability typically show Se in foods/feedstuffs to be more highly available than selenite or selenate

Whole Blood. Earlier studies employed whole blood for the assessment of Se status. Those showed good correlations with functional biomarkers in cohorts of relatively low Se status, as well as responsiveness to supplementation with food sources of Se (largely selenomethionine). Blood samples can be dried and later analyzed by X-ray fluorescence analysis Nevertheless, whole blood Se measures can be difficult to interpret in as much as they comprise both cellular and non-cellular constituents both of which have specific and non-specific components.

Plasma/Serum. The most useful tissue for assessing Se status, particularly in humans, is plasma (or serum, which is virtually equivalent with respect to Se-containing components and, therefore, total Se contents). Se is stable in plasma as long as microbial growth is prevented; it can be determined with good sensitivity and precision by automated atomic absorption spectrophotometry reducing interferences by using either graphite-furnace-AAS, or tandem inductively coupled plasma/mass spectrometry (ICP/MS). Plasma Se consists mostly of Se that has been incorporated both specifically as selenocysteine and non-specifically as selenomethionine into various proteins. Selenocysteine occurs in only two plasma selenoproteins, Selenoprotein P and Glutathione Peroxidase 3, which contain 10 and 4 selenocysteine residues, respectively. The synthesis of each, occurring in the liver and kidney, respectively, depends on an ample metabolic supply of selenide for the co-translational biosynthesis of selenocysteine

Plasma also contains a non-specific Se pool comprised of selenomethionine incorporated into proteins in lieu of Met with which it competes for tRNAMet binding. The potential for the unregulated, non-specific incorporation into proteins is a function of their various Met contents. In plasma, the most quantitatively important of these is albumin, which contains 6 Met residues per mole. Assuming that selenomethionine can compete for incorporation at each of those positions, selenomethionine protein would provide a plasma Met space equivalent to nearly 4mM. The non-specific pool can be estimated from the difference between the specific and total Se pools. By this approach, more than half of plasma Se of a non-deficient cohort was present in specific components (Glutathione Peroxidase 3 and Selenoprotein P comprising roughly equal amounts), with almost as much Se present in non-specific components Further, the increase in plasma Se produced by selenomethionine-supplementation consisted entirely of expansion of the non-specific component, which reached 73% of plasma Se in subjects consuming some 300µg Se/day. Still, that amount comprised less than 0.05% of the potential selenomethionine space, indicating that the latter is unsaturable under practical conditions.

In contrast to selenocysteine and selenite, which enter the specific selenoprotein pool by a highly regulated process, the incorporation of selenomethionine into the nonspecific Se pool is unregulated, its size reflecting the intake of selenomethionine over a wide range. Accordingly, sources of selenomethionine are also more effective than inorganic Se in increasing tissue Se levels

While Se intake is its primary determinant, plasma Se level can be also affected by other factors affecting any of the Se-containing proteins, e.g., gender, age, smoking status protein malnutrition pregnancy and lactation and inflammation Plasma Selenoprotein P levels have been found to be lower in obese individuals (BMI >30) and in African Americans compared to white Americans

The informative value of plasma Se as a biomarker, therefore, depends on Se status (Figure 25b.3).

Measurements of Glutathione Peroxidase 3 activity and Selenoprotein P can identify the risk of nutritional deficiency. Measurements of total Se and, perhaps, the non-specific pool can identify luxus Se status. Thus, it is apparent that the largest contributor to the global variation in plasma Se, particularly among subjects with plasma Se concentrations greater than about 70ng/mL, is the non-specific pool.

For Se-nondeficient individuals consuming Se mostly as selenomethionine, Se intake can be predicted from the Se concentration of plasma. Such a prediction was made for a cohort of Americans with relatively high baseline plasma Se levels (142ng/mL) using the amounts of Se administered as daily supplements of selenomethionine plus Se coming from the subjects' diets as estimated from a self-administered food frequency questionnaire and the USDA National Nutrient Database for Standard Reference, Release 27 Results showed estimated Se intake expressed as µg/kg0.75/d to be significantly correlated with measured Se-plasma, expressed as ng/mL. From that regression it is possible to predict Se intake:

$\small \mbox{Se intake}_{µg/kg^{0.75}}/d = 0.44 + 0.03 × \mbox{Se plasma}_{ ng/mL}$

Because virtually all circulating Se is bound to proteins, protein-deficient subjects will have low plasma/serum levels. This has been observed in children with kwashiorkor or marasmus who may also have increased needs for Se and other antioxidant nutrients, due to the pro-oxidative effects of malnutrition and inflammation. Neonates typically have lower blood Se levels than their mothers and low plasma Se levels have been associated with increased risk of respiratory morbidity among low-birth-weight newborns. Low blood Se levels have been observed in infants with phenylketonuria, but these effects have been due to the use of parenteral feeding solutions that had not been supplemented with Se.

Cells. Three cell types are accessible for use in assessing tissue Se status in humans: erythrocytes, lymphocytes and buccal cells. The Se contents of each respond to selenomethionine supplementation. Erythrocyte Se requires digestion after which it can be determined by GF-AAS. Because erythrocytes are collected with blood, they seldom offer advantages over plasma as a specimen for assessing Se status based on Se content. Buccal cells offer the possibility of a minimally invasive biomarker of somatic cell Se status. These cells can easily be collected in amounts sufficient for analyzing Se and can be acid-solubilized rather than digested prior to GF-AAS analysis. Nevertheless, few groups to have used buccal cells for this purpose . In a non-deficient cohort, buccal Se concentration was positively associated with age and nutritional supplement use, and to respond to selenomethionine supplementation.

Hair and Nail Selenium. Because hair and nails contain sulfur-rich proteins, each can accumulate Se. In addition, hair and nail specimens are stable and can be collected non-invasively, and can be stored at very low cost. For these reasons, these specimens have been used to assess Se status in epidemiological studies. Such studies have shown the amounts of Se in hair to be greater in individuals with high Se intakes and increase with Se-supplementation Very high hair and nail Se levels were observed among residents of seleniferous locales in cases of Se-poisoning and in users of Se-containing antidandruff shampoos

The analysis of Se in hair and nails calls for careful cleaning, with special concern for hair as to whether subjects may have used Se-containing, anti-dandruff shampoos. Selenium can be determined in these matrices by neutron activation analysis, and electrothermal (graphite furnace) atomic absorption spectrophotometry (GF-AAS) after acid-digestion. With standardized procedures, e.g., Bank et al., (1981) for collecting these samples, both hair and nail Se levels correlate well with blood/plasma Se concentration

It bears pointing out that the use of these specimens to assess Se status relies on the implicit but never validated assumption that their Se contents reflect some metabolically relevant component of body Se. In fact, hair/nail Se is not in dynamic equilibrium with any component of circulating Se; it is actually an excretory form of the element. As such, samples of each contain Se secreted at some time past, presumably reflecting Se status at that time and making them most useful in studies of populations with stable dietary practices. These contributions are very small in comparison to urinary Se output and can be ignored in estimating Se retention.

25b.9.4 Biomarkers of Selenium Function

In principle, measurement of any of the selenoproteins would yield information immediately relevant to the physiological function of Se as an essential nutrient. The most widely used as biomarkers in animal studies are the GPXs. These, the thioredoxin reductasess, and the iodothyronine deiodinasess show maximal expression in most species with dietary Se concentrations of 0.1–0.2mg/kg Only one selenoprotein, SepW, is known not to be maximally expressed under such conditions, but to be upregulated by doses of Se in the anti-tumorigenic range

Selenoenzymes. The list of practical biomarkers of Se function is much shorter, being limited to those occuring in accessible tissues: The extracellular isoform of GPX (Glutathione Peroxidase 3), which comprises 10–25% of plasma Se (lower levels being associated with greater plasma Se concentrations); Selenoprotein P, which comprises 20–70% of plasma Se (lower percentages being associated with greater plasma Se concentrations); and the intracellular isoform (GPX1), which can be assayed in erythrocytes, lymphocytes, buccal cells and tissue biopsy specimens.

Activities of the GPXs can be measured spectrophotometrically using a glutathione reductase-coupled assay Because heme iron can cause interfering glutathione oxidation in that assay, it is necessary to treat erythrocyte samples with Drabkin's reagent when assessing GPX1. The GPXs are homotetramers; each 23kD subunit contains a selenocysteine residue at its active center. Unlike GPX1, Glutathione Peroxidase 3 is a glycoprotein produced mostly by the kidney. Selenoprotein P is present in plasma as multiple variants with an average molecular weight of 60kD Although its genetic coding would suggest as many as 10 selenocysteine residues per mole studies in the rat have shown only 7–8 residues per mole Selenoprotein P can be measured by immunoassay

The dependency of the expression of these selenoproteins on Se intake has been demonstrated in humans for Glutathione Peroxidase 3 and Selenoprotein P in studies conducted in parts of China with endemic Se deficiency. In both cases, pooled analyses of subjects from different communities with differing plasma Se concentrations showed Glutathione Peroxidase 3 activity and plasma Selenoprotein P1 concentration each to be directly related to plasma Se concentration over ranges of about 8–80ng Se/mL. This work has provided the basis for setting dietary Se requirements, which have been based on either two-thirds or maximal Glutathione Peroxidase 3 expression, yielding dietary recommendations for adults from 26–70µg Se/d

Maximal Glutathione Peroxidase 3 expression may occur at a lower level of Se status than maximal Selenoprotein P expression. Xia et al (2020) found that Se-deficient subjects supplemented with selenomethionine for 20wks reached maximal Glutathione Peroxidase 3 activities with plasma Se levels about 66ng/mL, but that their plasma Selenoprotein P concentrations were not maximized until their plasma Se levels were at least a third higher. However, Selenoprotein P may have taken longer to reach new steady-state levels, as after 40wks of intervention the threshold of maximal expression of Selenoprotein P approached that of Glutathione Peroxidase 3 both being in the range of 35–45µg Se/d corresponding to plasma Se concentrations of 50–70ng/mL (Nève, 1995). These thresholds are typically exceeded in western populations; Nève (1995). noted that subjects with plasma Se concentations > 70ng/mL do not show Glutathione Peroxidase 3 responses to Se-supplementation. Accordingly, negative Glutathione Peroxidase 3 and Selenoprotein P responses to Se supplementation are typical in trials conducted in cohorts with greater Se intakes such as in the US and UK

Obesity can affect Selenoprotein P expression. In a cohort of non-deficient subjects, plasma Selenoprotein P levels were slightly depressed among subjects with body mass index (BMI) greater than 30. Méplan et al (2007) also found relatively low-Se (mean plasma Se 90ng/mL) subjects with BMI> 30 to have lower baseline plasma Se concentrations than non-obese subjects; obese females also showed lower Glutathione Peroxidase 3 activities. These findings may reflect influences of pro-inflammatory cytokines, which have been found to inhibit Selenoprotein P1 expression or dysregulation of gluconeogenesis, as Selenoprotein P appears to be regulated as a gluconeogenic enzyme 2009).

Genetic Variability and gender contribute to variance in biomarkers of Se function. Individuals with GPX1 679T/T genotype (which has been associated with increased cancer risks) had lower plasma Se levels than those with GPX1 679C/C alleles; those with the Selenoprotein P1 24731 A/A genotype had 27% greater plasma Selenoprotein P levels than those with the Selenoprotein P1 24731 G/A or G/G genotypes; and those with the SEP15 811 T/C genotype had greater buccal cell Se levels than those with the SEP15 811 C/C genotype Hurst et al (2010). found two variants of Selenoprotein P to affect circulating concentrations of selenoproteins. One variant at position 234 of the protein may affect Selenoprotein P turnover; the other variant at r25191 in the 3'-untranslated region may affect Se incorporation into Selenoprotein P. They found women with the Selenoprotein P1 234GA genotype showed lower Selenoprotein P levels than men of the same genotype; while women with the Selenoprotein P1 234GG genotype showed lower Selenoprotein; P levels than men of that genotype. Subjects with the Selenoprotein P1 234AA genotype showed lower plasma TR1 concentrations compared to those of the other genotypes. Variants in r25191 did not affect Selenoprotein P1 levels; however, individuals with the r25191GG genotype showed greater plasma TR1 concentrations than women of that genotype, while males of the r25191GA genotype were the only subjects to show TR1 responses to Se supplementation.

Non-specific parameters. Several non-specific parameters have been used to assess metabolic impacts of Se deficiency. The plasma triiodothyronine / thyroxine (T3:T4) ratio ratio, normally about 20:1, is elevated by Se-deficiency 1993) reflecting limited expression of the iodothyronine deiodinasess. While useful as an indicator of thyroid hormone status, the T3:T4 ratio lacks specificity for Se status, as not only can the conversion of thyroxine to triiodothyronine be impaired by Se deprivation, but also the synthesis of thyroxine can be impaired by deprivation of Se and/or iodine. That the pattern of low molecular weight Se-metabolites in the hindgut lumen corresponds with that of feces, would appear to suggest that a fecal sample may ve useful as an indicator of the Se in the colon.

25b.9.5 Biomarkers Relevant to Anti-tumorigenesis.

Studies with animal models have demonstrated anti-tumorigenic effects of Se involving several aspects of cell proliferation, migration and apoptosis These effects are manifest with dietary Se levels of at least 1.5mg/kg, while most selenoproteins are maximally expressed at far lower dietary levels (0.1–0.2mg/kg). For that reason, the anti-tumorigenic effects of supranutritional doses of Se would appear to involve functions of Se-metabolites and not of selenoproteins Still, that certain selenoproteins may play roles in Se-antitumorigenesis is suggested by the finding of Hawkes et al. (2009) that the mRNA for SEPW1 is up-regulated by supranutritional Se treatment, and that silencing SEPW1 is associated with reduced stability of the tumor suppressor protein p53, suggesting that SEPW1 may serve in its stabilization

Evidence from human trials is consistent with the view of anti-tumorigenic Se-metabolites, such as methylselenol (CH3SeH), showing reduction in cancer risk among subjects of nutritionally adequate (i.e., maximal Glutathione Peroxidase 3 expression), but not high Se status. For example, the Nutritional Prevention of Cancer Trial found supplemental Se to reduce cancer risk in non-deficient Americans only if their baseline plasma Se levels were less than about 120ng/mL. This is consistent with the results of the larger Selenium and Vitamin E Cancer Prevention Trial (SELECT) which found no risk reduction in a cohort with baseline plasma Se concentrations exceeding that level. Although CH3SeH and, perhaps, other methylated Se-metabolites would be candidate biomarkers relevant to Se-antitumorigenesis, none have been reported in biological specimens. At the moment, therefore, the most useful biomarker relevant to Se-antitumorigenesis is plasma Se, the target level being about 120ng/mL above which current evidence indicates no further risk reduction.

25b.9.6 Biomarkers Relevant to Adverse Effects.

Biomarkers Relevant to Adverse Effects. The potential for very high Se status to produce adverse physiological effects has been established from animal studies and accidental exposures of humans. These reports have produced an array of clinical indicators but few biomarkers with predictive value. For this reason, the default choice has been to use as risk indicators the highest Se tissue levels observed with no adverse effects. Most studies show no adverse effects in human subjects with plasma Se levels < 1000ng/mL.

25b.10 Questions Remain

Understanding of Se, the most recently recognized essential nutrient, continues to grow. It has become clear that consequences of Se deprivation are typically sub-clinical in nature, requiring other precipitating factors (deficiencies of vitamin E, iodine and/or protein; exposure to viruses, or carcinogens) to reveal physiological effects of sub-optimal expression of selenoenzymes. It is also apparent that supranutritional intakes of Se, at which selenoenzymes are fully expressed, can be beneficial. These facts raise three pressing questions:
1. Can Se prevent cancer in humans? The clinical significance of Se in cancer prevention remains a subject of debate. The nine randomized clinical trials conducted to date have yielded inconsistent results. Systematic reviews have found that Se may be effective in preventing cancer in individuals of low to adequate, but not high, Se status; and a U-shaped dose-response relationship has been proposed These conclusions are weakened by the fact that several trials have not followed robust protocols, and none has been conducted in recent years or in cohorts with individuals of both marginal and adequate Se status.
2. What is the window of safety for Se? While it is clear that very high levels of exposure are required to produce selenosis, resolving the question of whether supranutritional intakes of Se can increase T2D risk remains unclear. Clarifying that will call for well controlled trials with subjects randomized by T2D risk factors (high BMI, elevated fasting glucose) and followed with unequivocal diagnostic indicators (fasting glucose, HbA1c, oral glucose tolerance). Until then, there would appear to be no justification for any healthy adult, regardless of his/her baseline Se status, to consume more than 100µg Se/day.
3. Who Can Benefit from Se? This is the ultimate question. It is clear that supplementation of adults with basal Se intakes < 50µg/d will increase selenoenzyme expression, and that the magnitude of those increases will depend on the extent to which baseline plasma Se levels were below about 90ng/mL. That individuals with plasma Se levels less than about 120ng/mL may also benefit from increased Se intakes is suggested from results of the NPC Trial in which supplemental Se reduced cancer risk among adults with plasma Se levels in the range of 80–120ng/mL. This suggests that individuals with plasma Se levels in that range may benefit from cancer protection unrelated to selenoenzyme expression. If so, many adults may benefit from increased Se intakes: some to maximize selenoprotein expression, others to reduce cancer risks.


text:
# Electron revolutions in Bohr model

1. Apr 6, 2015

### Kavorka

1. The problem statement, all variables and given/known data
On the average, a hydrogen atom will exist in an excited state for about 10-8 s before making a transition to a lower energy state. About how many revolutions does an electron in the n = 2 state make in 10^-8 s?

2. Relevant equations

L = mvr = Iω = nħ
rn = n2a0/Z

3. The attempt at a solution

Finding the angular momentum from ħ and n=2 is just plugging in numbers. Where I'm confused is how to get the number of revolutions from the angular momentum. It would be easy to find if I had ω, but I have no idea how to calculate I in this context. On the other hand, I could find the radius of the orbit from the second equation from a0, n=2 and Z=1. If I had that and the mass of the electron, I could find the electron's velocity. From rn I could also find the circumference of the orbit and calculate the number of revolutions when t = 10-8 s from that. I don't have time to work out the math right now but I will tomorrow and I wanted to post this early. Which approach would be best?

2. Apr 6, 2015

### TSny

Your first approach might be easier. From mechanics, you should have learned the formula for the moment of inertia of a particle moving in a circle.

The second approach will also work. For both approaches you will need to know the mass of the electron, which is easy to find. Also, in both approaches you will need to use the formula for rn.

[Edit: I think both approaches require about the same amount of effort.]

3. Apr 6, 2015

### Kavorka

I looked around and found it. So I = mr2n?

4. Apr 6, 2015

Yes.

5. Apr 7, 2015

### Kavorka

I'm having an issue.

So rn = a0n2/Z = 2.12 x 10 -10 m

and L = nħ = 2.10914 x 10-34 m2kg/s

ω = L/I = L/mrn2

When I plug this in I get 5.1516 x 1015 Hz, while the back of the book says 8.22 x 1014 Hz

6. Apr 7, 2015

### TSny

Make sure you distinguish between angular frequency $\omega$ and frequency $f$. Angular frequency does not have units of Hz.

7. Apr 7, 2015

### Kavorka

Ah, thank you!

format: plain


text:
Prasanta Chandra Mahalanobis

Quick Info

Born
29 June 1893
Calcutta (now Kolkata), India
Died
28 June 1972
Calcutta (now Kolkata), India

Summary
Prasanta Mahalanobis was an Indian mathematiccian who made important contibutions to statistics and to its application in meteorology and anthropology.

Biography

Prasanta Chandra Mahalanobis's parents were Probodh Chandra and Nirodbashini. Probodh Chandra (1869-1942) worked for a while in his father's (Gurucharan (1833-1916)) chemist's shop before starting up his own business as a dealer in sports goods. He married Nirodbashini, the daughter of Nandalal Sarkar, in 1891. The family were of the Brahmo Samaj religion, relatively wealthy and influential in Bengali life. Probodh Chandra and Nirodbashini had two sons and four daughters, the eldest child being Prasanta Chandra the subject of this biography. The poet Rabindranath Tagore was a significant influence on Mahalanobis when he was a young boy. Rabindranath Tagore's father, Devendranath Tagore, had been a friend of Mahalanobis's grandfather Gurucharan and had played a major role in reviving the Brahmo Samaj religion [26]:-
[Mahalanobis's] analytical turn of mind manifested itself at a very early age and he was given to arguing things out with his friends and even with his superiors. Even at a very early age he came under the influence of Rabindranath Tagore who took a liking to young Mahalanobis, being particularly impressed by the combination in him of a love of literature with a flair for logical analysis.
Mahalanobis attended the Brahmo Boys School in Calcutta, passing the matriculation examination in 1908, his final year at the school. Entering Presidency College, Calcutta in 1908, where his uncle Subodh Chandra Mahalanobis was professor of physiology, Mahalanobis passed the Intermediate Examination in science two years later and graduated with a B.Sc. with honours in physics in 1912.

In the summer of 1913 Mahalanobis went to England where his intention was to study for a B.Sc. at the University of London. While in London, waiting for courses to start, he made a trip to Cambridge where he was stunned by the chapel of King's College. By chance he missed the train back to London and stayed the night with a friend. In the friend's house he met a student who was studying at King's College and, hearing that Mahalanobis found the chapel so attractive, suggested he apply to study there. Remarkably, he was interviewed the next day and offered a place. He matriculated at King's College in October 1913 and passed Part I of the mathematical tripos in 1914. He then transferred to the natural sciences tripos, obtained a first class pass in Part II in 1915, and was awarded a Senior Scholarship by King's College. During his time in Cambridge, he became friendly with Srinivasa Ramanujan.

In the natural sciences tripos, Mahalanobis had specialised in physics and he set up a research project at the Cavendish Laboratory. He returned to India in July 1915 to take a short holiday before beginning his research project. However, once back in India his uncle, Subodh Chandra Mahalanobis the professor of physiology at Presidency College Calcutta, introduced him to the Principal of the College who was trying to fill a temporary vacancy in the physics department. By this time World War I was in progress and a senior physicist at Presidency College was on war service. Asked if he would take on a temporary teaching role in physics at the College to help out, Mahalanobis agreed but he was still intent on returning to Cambridge to undertake his research project once the temporary position ended. However, he soon became so involved with his work in Presidency College that he gave up the idea of returning to Cambridge.

Now Mahalanobis's involvement in statistics came about, as many aspects of his life did, through a chance happening. Like the way he ended up in Cambridge by missing a train, this time it was having to wait in Cambridge for the boat journey to India. The boat was delayed due to World War I, and Mahalanobis put off time in the library of King's College. There he looked at some volumes of Biometrika and, being fascinated by what he read, bought a complete set of volumes and took them back to India with him [16]:-
He started reading the volumes on the boat during the journey, and continued to study and work out exercises on his own during spare time after arrival in Calcutta. He saw that statistics was a new science connected with measurements and their analysis, and as such capable of wide application. He tried to look for problems where he could apply the new knowledge he was acquiring. Fortunately, he found some extremely interesting problems in meteorology and anthropology, and started working on them. This was the turning point in his scientific career.
This interest in statistics did not change the career path of Mahalanobis who was appointed as Professor of Physics at Presidency College in 1922. He continued to teach physics at the College for the next thirty years but during this time he brought about profound changes which influenced the future development of statistics in India. However, before we give some details of the setting up of the Indian Statistical Institute by Mahalanobis, let us note that he married Nirmalkumari, the daughter of the Principal of City College, Calcutta, and, like Mahalanobis, an important member of the Brahmo Samaj religion. This sounds like the ideal backgrounds for a marriage but this was not quite the case since there were serious arguments within the Brahmo Samaj community. We will not go into details (see [1] or [16] or [26] for more information) but suffice it to say that Mahalanobis's views were representative of the younger members of the Brahmo Samaj and he was prominent in attacking the views of the establishment, of which Nirmalkumari's father was a part. The wedding took place on 27 February 1923 although Nirmalkumari's father showed his disapproval but refusing to take his proper role in the ceremony.

In the quote above 'extremely interesting problems in meteorology and anthropology' are mentioned and we should now look at these more closely. In 1920 he attended the Indian Science Congress in Nagpur and was approached by the Director of the Zoological Survey of India asking if he would be interested in looking at data he had collected concerning mixed race people in Calcutta. Mahalanobis was indeed interested, and his analysis of the data led to his first scientific paper Anthropological observations on the Anglo-Indians of Calcutta I Analysis of male stature (1922). This is a remarkable piece of work and for this, and many other similar investigations he carried out later, he introduced the $D^{2}$ statistic, known today as the 'Mahalanobis distance'. MathSciNet lists 144 papers in which the Mahalanobis distance plays a significant role and is mentioned in the title or review of the paper. As a result of seeing this paper, the Director General of Observatories asked Mahalanobis if he would be interested in examining some meteorology problems. The result was three papers: On the seat of activity in the upper air (1923); On errors of observation and upper air relationships (1923); and Correlation of upper air variables (1923). He also published Statistical note on the significant character of local variation in proportion of dextral and sinistral shells in samples of the snail in 1923. These were the first of over 200 papers which Mahalanobis published covering a vast range of topics from agriculture to drinking tea among middle class Indian families in Calcutta.

Perhaps the two most important contributions by Mahalanobis, other than his scientific papers, were setting up the Indian Statistical Institute and the founding of the journal Sankhya. We now look briefly at these. The Indian Statistical Institute began life in around 1920 as an unofficial group working on statistical problems in Presidency College. It soon acquired the name of the Statistical Laboratory and was located in Mahalanobis's room in the Physics Department. The official setting up of the Indian Statistical Institute was on 17 December 1931 when Mahalanobis, together with the Professor of Economics and the Professor of Applied Mathematics at Presidency College met under the chairmanship of the industrialist Sir Rajendranath Mukherjee and passed a resolution formally setting up the Indian Statistical Institute. It was formally "registered on 28 April 1932 as a non-profit distributing learned society under the Societies Registration Act XXI of 1860". Basically through the 1920s and up to 1931 almost all statistical work done in India was by Mahalanobis. However, after setting up the Indian Statistical Institute, as Director and Secretary he could build up the Institute with new appointments. For example, in December 1932 Mahalanobis offered R C Bose a part-time post at the Indian Statistical Institute. Part-time meant working on Saturdays throughout the year and full-time during the summer and Pujah vacations. Mahalanobis gave him a list of papers to read and he soon became a world-class statistician. From 1935 Bose had a full-time position at the Indian Statistical Institute as did Samarendra Nath Roy who had been appointed to a part-time post a few months after Bose. Training courses in statistics were set up, for example C R Rao began the one-year training course in statistics in 1940. Rao was soon undertaking research, went on the take a statistics degree at Calcutta University, and was appointed as a Technical Apprentice at the Indian Statistical Institute beginning in November 1943. He became one of world leaders in statistics.

In 1948 the Institute received a major grant from the Indian government allowing them to set up a Research and Training School and appoint professors, assistant professors and other academic grades. Under Mahalanobis's leadership the Institute flourished. In 1950 they purchased about 4 acres of land at 203, B T Road, Calcutta. Immediately building began on the site and the Main Building was inaugurated by R A Fisher in 1951. The Research and Training School was subsequently moved to this building. In 1959, the Indian government passed the India Statistical Institute Act (the 57th Act of 1959) - here is a short extract:-
An Act to declare the institution known as the Indian Statistical Institute having at present its registered office in Calcutta to be an institution of national importance and to provide for certain matters connected therewith. ... the Institute may hold such examinations and grant such degrees and diplomas in statistics, mathematics, quantitative economics, computer science and such other subject related to statistics as may be determined by the Institute from time to time.
The other major achievement of Mahalanobis was the founding of the statistics journal Sankhya in 1933 as a publication of the Indian Statistical Institute. We quote from Mahalanobis's editorial in the first part of the first volume:-
Those of us who are actively engaged in starting this journal are doing so because of our interest in statistics and our belief that a journal devoted to statistics will be useful in India. ... The spirit and outlook of 'Sankhya' will be universal, but its form and content must necessarily be, to some extent, regional. We shall keep the special needs of India in view without, however, restricting the scope of the journal in any way. We shall naturally devote closer attention to the collection and analysis of data relating to India, but we shall try to study all Indian questions in relation to world problems. A research journal serves that narrow borderland which separates the known from the unknown, and it is not always possible to see clearly the lines of future developments. We shall, therefore, invite papers of all kinds appraising them only on the basis of observational accuracy and logical reasoning. We shall publish carefully collected statistical materials irrespective of the subject even if they have not received any analytic treatment. We shall pay special attention to developments of the mathematical theory of statistics, and include abstracts and expositions of important papers published elsewhere. We shall try to help statistical researches on co-operative lines by bringing workers in different parts of India in contact, and by providing a medium for exchange of ideas. Bibliographies of Indian statistical publications, numerical tables tending to reduce the labour of computation, book reviews, and notes and comments on current topics are some of the ways in which we shall try to make 'Sankhya' useful to statistical workers in India. Knowing that our resources are small we shall seek guidance and help from other countries, and we shall welcome and thankfully receive papers from abroad. The study of modern statistical methods in its infancy in our country, and we do not expect to be able to achieve immediate results. We shall be satisfied if we can help by our humble efforts to lay the foundations for future work.
Mahalanobis received many honours for his remarkable contributions to the development of statistics and to life in India. For example he was awarded the Weldon Medal and prize from Oxford University (1944), the Sir Deviprasad Sarvadhikari Gold Medal (1957), the Gold Medal from the Czech Academy of Sciences (1964), and the Durgaprasad Khaitan Gold Medal from the Asiatic Society (1968). He was President of the Indian Science Congress in 1950 and President of the International Statistical Institute in 1957. He was elected a fellow of many societies and academies such as: the Royal Society of London (1945), the Econometric Society, United States (1951), the Pakistan Statistical Association (1952), the Royal Statistical Society, U.K. (1954), the USSR Academy of Sciences (1958), and the American Statistical Association (1961). He received honorary degrees from the University of Calcutta (1957), Sofia University (1961) and the University of Delhi (1964). In 1959 he was elected an Honorary Fellow of King's College, Cambridge. In 1968 the Government of India awarded him the Padma Vibhushan:-
... for his contribution to science and services to the country.
To end this biography of Mahalanobis, we quote the first paragraph of C R Rao's article [23]:-
The Professor, as Prasanta Chandra Mahalanobis was known in India, passed away on 28 June 1972, three weeks after an abdominal operation in Calcutta. The death occurred one day before his 79th birthday, when he was still active doing his research work, looking after the Indian Statistical Institute as Honorary Secretary and Director and helping the Government as Honorary Statistical Adviser. The 'Mahalanobis Era' in statistics which started in the early twenties has ended. Indeed it will be remembered for all time to come as the golden period of statistics in India, marked by intensive development of a new technology and its applications for the welfare of mankind.

References (show)

1. A Rudra, Prasanta Chandra Mahalanobis: A Biography (Oxford University Press, Oxford, 1996).
2. Bibliography of Prasanta Chandra Mahalanobis, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 51-62.
3. S N Bose, Prasanta Chandra Mahalanobis, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 1-2.
4. S N Bose, Prasanta Chandra Mahalanobis, Current Science 65 (1) (1993), 96-97.
5. W E Deming, P C Mahalanobis (1893-1972), The American Statistician 26 (4) (1972), 49-50.
6. In memoriam: Prasanta Chandra Mahalanobis (1893-1972), Sankhya Ser. A 34 (1972), 203-204.
7. In memoriam: Prasanta Chandra Mahalanobis (1893-1972), Sankhya Ser. B 34 (1972), 241-242.
8. T K Kumar, An Unfinished Biography: Prasanta Chandra Mahalanobis, Economic and Political Weekly 32 (23) (1997), 1321-1325; 1328-1332.
9. D B Lahiri, Prasanta Chandra Mahalanobis and large scale sample surveys, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 27-44.
10. A Linder, P C Mahalanobis (29 Juni 1893-28 Juni 1972) (German), Biometrische Z. 15 (1973), 299-300.
11. D D Majumder, Scientific contributions of Professor P C Mahalanobis, Current Science 65 (1) (1993), 97-101.
12. M Mukherjee, Professor Mahalanobis' contributions to economics: a condensed survey of research, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 45-50.
13. H K Nandi, Prof P C Mahalanobis: 1893-1972, Calcutta Statist. Assoc. Bull. 22 (1973), 1-4.
14. J Neyman, Impressions from a trip to India December 15, 1956 to February 5, 1957, a tribute to the memory of Professor P C Mahalanobis, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 63-74.
15. Prasantha Chandra Mahalanobis, 1893-1972, Gujarat Statist. Rev. 1 (1974), 1-6.
16. C R Rao, Prasantha Chandra Mahalanobis. 1893-1972, Biographical Memoirs of Fellows of the Royal Society 19 (1973), 454-492.
17. C R Rao, P C Mahalanobis, Current Science 65 (1) (1993), 90-94.
18. C R Rao, Prasanta Chandra Mahalanobis (1893-1972), Bull. Math. Assoc. India 16 (1-4) (1984), 6-19.
19. C R Rao, Prasanta Chandra Mahalanobis (1893-1972), in Some eminent Indian mathematicians of the twentieth century III (Math. Sci. Trust Soc., New Delhi, 1990), 1-13.
20. C R Rao, Prasanta Chandra Mahalanobis, 1893-1972, Internat. Statist. Rev. 41 (2) (1973), 301-302.
21. C R Rao, Homage to Professor Prasanta Chandra Mahalanobis, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 79-80.
22. C R Rao, Statistics must have a purpose: the Mahalanobis dictum, Sankhya Ser. A 55 (3) (1993), 331-349.
23. C R Rao, The Professor, Economic and Political Weekly 7 (31/33) (1972), 1461-1464.
24. C R Rao and P C Mahalanobis, Mahalanobis era in statistics, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 12-26.
25. A Roy, Two Famous Bengali Scientists: Some Personal Memories, Economic and Political Weekly 28 (17) (1993), 796-797.
26. H Sanyal, Prasantachandra Mahalanobis: a biographical sketch, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973), 3-11.

Other pages about Prasanta Chandra Mahalanobis:

Other websites about Prasanta Chandra Mahalanobis:

Honours (show)

Honours awarded to Prasanta Chandra Mahalanobis

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Written by J J O'Connor and E F Robertson
Last Update March 2011


text:
## Lecture 10/23 on Hybridization of Ethene

$sp, sp^{2}, sp^{3}, dsp^{3}, d^{2}sp^{3}$

jgreynoso 2J
Posts: 25
Joined: Fri Sep 25, 2015 3:00 am

### Lecture 10/23 on Hybridization of Ethene

Mr. Lavelle showed the lewis structure of both acethylene and ethene today. I am a little confused about the delocalized pi bonds. For acethylene with an sp hybridization, Lavelle illustrated that it contains two electrons occupying different orbitals with parallel spin in the 2p. Whereas for ethene, it has an sp2 hybridization where there is one electron occupying one orbital in the 2p. His diagrams illustrated the formation of a pi bond with both, but what does the difference between the delocalized pi bonds create? Is there multiple for the acethylene the diagram left out?

Thank you

Shaye Busse 3B
Posts: 20
Joined: Fri Sep 25, 2015 3:00 am

### Re: Lecture 10/23 on Hybridization of Ethene

For acetylene, or rather ethyne, there are two regions of electron density surrounding each carbon atom, meaning they will have 2sp hybridization for its sigma-bonding orbitals. This leaves two electrons per carbon atom, each occupying an unpaired 2p orbital. This means on each carbon atom, there is one sigma bond formed from the end-to-end overlap between the two carbon atom and one sigma bond formed from the end-to-end overlap between the carbon and hydrogen atom. This leaves two unpaired 2p orbitals around each carbon atom. Because of this, the two unpaired 2p orbitals from each carbon atom will form two weaker pi bonds with each other, accounting for the triple bond on ethyne.

In ethene, there are three regions of electron density around each carbon atom rather than one. This means the sigma-bonding orbitals for the carbon atoms will have 2sp2 hybridization. After all the sigma bonding, there is one unpaired 2p orbital per carbon atom resulting in one pi bond between the carbon atoms. This is what accounts for the double bond in ethene.


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# Variables 101, char

#### misterT

##### Well-Known Member
char

The most important variable type in 8-bit microcontroller is char. It holds 8-bits of data, which makes it very efficient for an 8-bit microcontroller to process.

A char can hold many kinds of information. An ASCII character, a decimal number, hexadecimal or bit pattern. Here are examples how you can assign these different types of data into char-variable.

C:
/* Declare four char variables */
char a, b, c, d;

a = 85;         // Decimal value
c = 0b01010101; // Bit pattern
d = 'U';        // Ascii character. Notice the use of apostrophes '
Actually, all the assigned values in above example are exactly the same. They all have exactly the same presenetation (bit pattern) inside the microcontroller. Only thing different is how you are intending to use the variable. You should always choose the most meaningful way to present data.

You can check the values by googling "0b01010101 to hex" or "0x55 to decimal". I also recommend that you google up an "ASCII table" and take a look at it.

A char variable can be unsigned or signed. C standard does not unfortunately say which one should be the default. It is better to explicitly declare variable either unsigned or signed.

C:
char a;          // Can be signed or unsigned depending what compiler you use
unsigned char b; // Unsigned. Can hold values from 0 to 255
signed char c;   // Signed. Can hold values from -128 to 127

c = 0b10000000; // c is a negative number -128. The leftmost bit is a sign-bit
/* Negative values are stored in so-called 2's complement representation,
which is another topic itself. */
It is good practice to use unsigned char when working with ASCII characters, bit patterns etc. Use signed char only when you need negative numbers.

There is a trap with signed char which can break your code. And the problem can be extremely difficult to find. When bit shifting a negative number to the right, it is filled with ones instead of zeros.

C:
unsigned char a;
signed char b;

/* Shift unsigned char three times right */
a = 0b10000000; // a is decimal number 128
a = a >> 3;     // After the shif a holds the value 0b00010000.

/* Shift signed char three times right */
b = 0b10000000; // b is a negative number -128. The leftmost bit is a sign-bit
b = b >> 3;     // After the shif b holds the value 0b11110000.
In machine code there is usually two different kinds of shift operations available: arithmetic shift and logical shift. Logical shift fills always zeros, even when right shifting a negative number. Arithmetic shift behaves like in the example above. Unfortunately there is no logical shift operator in C.

To be continued.. maybe.

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# 7 Concluding Remarks

My hope is that this book provides a nice introduction into understanding how statisticians, data scientists, and many other professionals use RStudio and R Markdown to simplify their analyses and ensure that their reports are computationally reproducible. Learning R is not nearly as intimidating as it once was, and more and more industries are shifting towards free open-source tools like R and RStudio. R Markdown provides an excellent way to document your analyses and share it with others in a variety of formats.

Of course, this book is just the tip of the iceberg in terms of showing you what R can really do. If you’d like to learn more, I encourage you to check out Modern Dive, a free, online, open-source book Albert Kim and I wrote on using modern data analysis techniques and visualization with R, RStudio, and R Markdown.

Additionally, Garrett Grolemund’s “Hands-On Programming with R” (Grolemund 2014) is an excellent resource and goes into much more depth than I do here on how to work with more complicated objects in R. It also discusses concepts in a project-based framework that is entertaining and easy-to-read.

As always, feel free to send me an email at if you’d like any further clarification or if you have suggestions on improvements. Thanks for taking the time to read through this and best wishes to you on your next steps towards reproducible, thoughtful, beautiful analyses!

- Chester

### References

Grolemund, Garrett. 2014. Hands-on Programming with R. O’Reilly.