Hemoglobin

Leghemoglobin: In leguminous plants, such as alfalfa or soybeans, the nitrogen fixing bacteria in the roots are protected from oxygen by this iron heme containing, oxygen binding protein. Georg Cantor makes an appearance as a character, and the hero finds a physical correlate for Cantor's Continuum Problem. Brown manganese-based porphyrin protein. Rudy Rucker's novel White Light describes a mathematician who leaves his body and travels to a kind of afterworld that includes a mountain whose Absolute Infinite height matches that of the class of all ordinals. Pinnaglobin: Only seen in the mollusk Pinna squamosa. Looking up into the night sky is looking into infinity -- distance is incomprehensible and therefore meaningless.". Giant free-floating blood protein, contains many dozens even hundreds of Iron heme containing protein subunits bound together into a single protein complex with a molecular masses greater than 3.5 million daltons. Another quote from The Hitchhiker's Guide to the Galaxy states: "Infinity itself looks flat and uninteresting.

Erythrocruorin: found in many annelids, including earthworms. The Hitchhiker's Guide to the Galaxy contains the following definition of infinity:. Vanabins: also known as Vanadium Chromagen are found in the blood of Sea squirt and are hypothesised to use the rare metal Vanadium as its oxygen binding prosthetic group, but this hypothesis is unconfirmed. Brouwer, David Hilbert, Bertrand Russell, Kurt Gödel and Georg Cantor. Appears pink/violet when oxygenated, clear when not. The footnote on p.335 of his book suggests the consideration of the following names: Abraham Robinson, Plato, Thomas Aquinas, L.E.J. Hemerythrin: Some marine invertebrates and a few species of annelid use this iron containing non-heme protein to carry oxygen in their blood. Rudy Rucker, in his book Infinity and the Mind -- the science and philosophy of the mind (1982), has worked out a model list of representatives of each of the eight possible standpoints.

Uses copper prosthetic group instead of iron heme groups and is blue in color when oxygenated. And in between there are the various possibilities. Found in the blood of many arthropods and molluscs. There are scientists who hold that all three really exist and there are scientists who hold that none of the three exist. Hemocyanin: Second most common oxygen transporting protein found in nature. Besides the mathematical infinity and the physical infinity, there could also be a philosophical infinity. Is very similar to hemoglobin in structure and sequence, but is not arranged in tetramers, it is a monomer and lacks cooperative binding and is used to store oxygen rather than transport it. If the universe is indeed ever expanding as science suggests then you could never get back to your starting point even on an infinite time scale.

Myoglobin: Found in the muscle tissue of many vertebrates including humans (gives muscle tissue a distinct red or dark gray color). The universe, at least in principle, might have a similar topology; if you fly your space ship straight ahead long enough, perhaps you would eventually revisit your starting point. Other organisms including bacteria, protozoans and fungi all have hemoglobin-like proteins whose known and predicted roles include the reversible binding of gaseous ligands. By walking/sailing/driving straight long enough, you'll return to the exact spot you started from. Hemoglobin is by no means unique; there are a variety of oxygen transport and binding proteins throughout the animal (and plant) kingdom. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. It measures the degree of glycation (glucose binding) to albumin, the most common blood protein, and reflects average blood glucose levels over the previous 18-21 days, which is the half-life of albumin molecules in the circulation. Note that the question of being infinite is logically separate from the question of having boundaries.

In these individuals an alternative test called "fructosamine level" can be used. An intriguing question is whether actual infinity exists in our physical universe: Are there infinitely many stars? Does the universe have infinite volume? Does space "go on forever"? This is an important open question of cosmology. In individuals with abnormal RBCs, whether due to abnormal hemoglobin molecules (such as Hemoglobin S in Sickle Cell Anemia) or RBC membrane defects - or other problems, the RBC half-life is frequently shortened. In quantum field theory infinities arise which need to be interpreted in such a way as to lead to a physically meaningful result, a process called renormalization.
This Hb A_1c level is only useful in individuals who have red blood cells (RBCs) with normal survivals (i.e., normal half-life). Physicists however require that the end result be physically meaningful. This test is especially useful for diabetics. For convenience sake, calculations, equations, theories and approximations often use infinite series, unbounded functions, etc., and may involve infinite quantities.

Hb A_1c values which are more than 7.0% are elevated. This point of view does not mean that infinity cannot be used in physics. People whose Hb A_1c runs 6.0% or less show good longer-term glucose control. Likewise, perpetual motion machines theoretically generate infinite energy by attaining 100% efficiency or greater, and emulate every conceivable open system; the impossible problem follows of knowing that the output is actually infinite when the source or mechanism exceeds any known and understood system. For this reason a blood sample may be analyzed for Hb A_1c level, which is more representative of glucose control averaged over a longer time period (determined by the half-life of the individual's red blood cells, which is typically 50-55 days). There exists the concept of infinite entities (such as an infinite plane wave) but there are no means to generate such things.
Glucose levels in blood can vary widely each hour, so one or only a few samples from a patient analyzed for glucose may not be representative of glucose control in the long run. It is for example presumed impossible for any body to have infinite mass or infinite energy.

For conversion, 1 g/dl is 0.62 mmol/L. It is therefore assumed by physicists that no measurable quantity could have an infinite value, for instance by taking an infinite value in an extended real number system (see also: hyperreal number), or by requiring the counting of an infinite number of events. Results are reported in g/L, g/dl or mmol/L. counting). Hemoglobin levels are amongst the most commonly performed blood tests, usually as part of a full blood count or complete blood count. In physics, approximations of real numbers are used for continuous measurements and natural numbers are used for discrete measurements (i.e. Because of the slow rate of Hb A combination with glucose, the Hb A_1c percentage is representative of glucose level in the blood averaged over a longer time (the half-life of red blood cells, which is typically 50-55 days). The number Infinity plus 1 is also used sometimes in common speech.

In diabetics whose glucose usually runs high, the percent Hb A_1c also runs high. These terms describe things that are only potential infinities; it is impossible to play a video game for an infinite period of time or keep a computer running for an infinite period of time. As the concentration of glucose in the blood increases, the percentage of Hb A that turns into Hb A_1c increases. See halting problem. The resulting molecule is often referred to as Hb A_1c. In practice however, some programming loops considered as infinite will halt by exceeding the (finite) number range of one of its variables. To a small extent, hemoglobin A slowly combines with glucose at a certain location in the molecule. In theory, as long as there is no external interaction, the loop will continue to run for all time.

King George III of the United Kingdom was probably the most famous porphyria sufferer. An infinite loop in computer programming is a conditional loop construction whose condition always evaluates to true. There is a group of genetic disorders, known as the porphyrias that are characterized by errors in metabolic pathways of heme synthesis. In video games, infinite lives and infinite ammo refer to a never-ending supply of lives and ammunition. Mutations in the globin chain are associated with the haemoglobinopathies, such as sickle-cell disease and thalassemia. For example, "The movie was infinitely boring, but we had to wait forever to get tickets.". In hemolysis (accelerated breakdown of red blood cells), associated jaundice is caused by the hemoglobin metabolite bilirubin, and the circulating hemoglobin can cause renal failure. In common parlance, infinity is often used in a hyperbolic sense.

Other anemias are rarer. Leopold Kronecker rejected the notion of infinity and began a school of thought, in the philosophy of mathematics called finitism, which led to the philosophical and mathematical school of mathematical constructivism. As absence of iron decreases heme synthesis, red blood cells in iron deficiency anemia are hypochromic (lacking the red hemoglobin pigment) and microcytic (smaller than normal). One example of this is Hilbert's paradox of the Grand Hotel. Anemia has many different causes, although iron deficiency and its resultant iron deficiency anemia are the most common causes in the Western world. Our intuition gained from finite sets breaks down when dealing with infinite sets. Decreased levels of hemoglobin, with or without an absolute decrease of red blood cells, leads to symptoms of anemia. Certain extended number systems, such as the hyperreal numbers, incorporate the ordinary (finite) numbers and infinite numbers of different sizes.

Improperly degraded haemoglobin protein or haemoglobin that has been released from the blood cells can clog small blood vessels especially the delicate blood filtering vessels of the kidneys, causing kidney damage. Cantor's views prevailed and modern mathematics accepts actual infinity. Increased levels of this chemical are detected in the blood if red cells are being destroyed more rapidly than usual. If a set is too large to be put in one to one correspondence with the positive integers, it is called uncountable. The major final product of haem degradation is bilirubin. The smallest ordinal infinity is that of the positive integers, and any set which has the cardinality of the integers is countably infinite. When the porphyrin ring is broken up, the fragments are normally secreted in the bile by the liver. Cardinal numbers define the size of sets, meaning how many members they contain, and can be standardized by choosing the first ordinal number of a certain size to represent the cardinal number of that size.

When red cells reach the end of their life due to aging or defects, they are broken down, and the haemoglobin molecule broken up and the iron recycled. Generalizing finite and the ordinary infinite sequences which are maps from the positive integers leads to mappings from ordinal numbers, and transfinite sequences. As a result, fetal blood in the placenta is able to take oxygen from maternal blood. Ordinal numbers may be identified with well-ordered sets, or counting carried on to any stopping point, including points after an infinite number have already been counted. This means that the oxygen binding curve for fetal hemoglobin is left-shifted (i.e., a higher percentage of hemoglobin has oxygen bound to it at lower oxygen tension), in comparison to that of adult hemoglobin. Cantor defined two kinds of infinite numbers, the ordinal numbers and the cardinal numbers. A variant hemoglobin, called fetal hemoglobin (Hb F, α₂γ₂), is found in the developing fetus, and binds oxygen with greater affinity than adult hemoglobin. An infinite set can simply be defined as one having the same size as at least one of its "proper" parts; this notion of infinity is called Dedekind infinite.

This phenomenon, where molecule Y affects the binding of molecule X to a transport molecule Z, is called a heterotropic allosteric effect. Dedekind's approach was essentially to adopt the idea of one-to-one correspondence as a standard for comparing the size of sets, and to reject the view of Galileo (which derived from Euclid) that the whole cannot be the same size as the part. In people acclimated to high altitudes, the concentration of 2,3-diphosphoglycerate (2,3-DPG) in the blood is increased, which allows these individuals to deliver a larger amount of oxygen to tissues under conditions of lower oxygen tension. This modern mathematical conception of the quantitative infinite developed in the late nineteenth century from work by Cantor, Gottlob Frege, Richard Dedekind and others, using the idea of collections, or sets. Nitrogen dioxide and nitrous oxide are capable of converting hemoglobin to methemoglobin. Georg Cantor developed a system of transfinite numbers, in which the first transfinite cardinal is aleph-null (), the cardinality of the set of natural numbers. Oxidation to Fe⁺³ state converts hemoglobin into hemiglobin or methemoglobin which cannot bind oxygen. A different type of "infinity" are the ordinal and cardinal infinities of set theory.

The iron atom in the heme group must be in the Fe⁺² oxidation state to support oxygen transport. This is because zero times infinity is undefined. Hemoglobin also has competitive binding affinity for sulfur monoxide (SO), nitrogen dioxide (NO₂) and hydrogen sulfide (H₂S). Notice that . In heavy smokers, up to 20% of the oxygen-active sites can be blocked by CO. Infinity is not a real number but may be considered part of the extended real number line, in which arithmetic operations involving infinity may be performed. When inspired air contains CO levels as low as 0.02% headache and nausea occur; if the CO concentration is increased to 0.1%, unconsciousness will follow.
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When hemoglobin combines with CO, it forms a very bright-red compound called carboxyhemoglobin. One important example of such functions is the group of Möbius transformations. Hemoglobin binding affinity for CO is 200 times greater than its affinity for oxygen, meaning that small amounts of CO dramatically reduces hemoglobin’s ability to transport oxygen. The domain of a complex-valued function may be extended to include the point at infinity as well. CO competes with oxygen at the heme binding site. In this context is often useful to consider meromorphic functions as maps into the Riemann sphere taking the value of at the poles. The binding of oxygen is affected by molecules such as carbon monoxide (CO) (for example from tobacco smoking, cars and furnaces). When this is done, the resulting space is still a one-dimensional complex manifold and called the extended complex plane or the Riemann sphere.

This control of hemoglobin's affinity for oxygen by the binding and release of carbon dioxide is known as the Bohr effect. A point labeled can be added to the complex plane as a topological space giving the one-point compactification of the complex plane. Conversely, when the carbon dioxide levels in the blood decrease (i.e., around the lungs), carbon dioxide is released, increasing the oxygen affinity of the protein. means that the magnitude | x | of x grows beyond any assigned value. Protons bind at various places along the protein and carbon dioxide binds at the alpha-amino group forming carbamate. As in real analysis, in complex analysis the symbol , called "infinity", denotes an unbounded limit. Hemoglobin can bind protons and carbon dioxide which causes a conformational change in the protein and facilitates the release of oxygen. Infinity is often used not only to define a limit but as if it were a value in the extended real numbers in real analysis; if f(t) ≥ 0 then.

So blood with high carbon dioxide levels is also lower in pH (more acidic). Projective geometry also introduces a line at infinity in plane geometry, and so forth for higher dimensions. Carbon dioxide reacts with water to give bicarbonate, carbonic acid freed protons via the reaction, which is catalyzed by carbonic anhydrase:. We can also treat and as the same, leading to the one-point compactification of the real numbers, which is the real projective line. Carbon dioxide occupies a different binding site on the hemoglobin. Adding algebraic properties to this gives us the extended real numbers. Hemoglobin's affinity for oxygen is decreased in the presence of carbon monoxide because both gases compete for the same binding sites on hemoglobin, carbon monoxide binding preferentially to oxygen. Points labeled and can be added to the real numbers as a topological space, producing the two-point compactification of the real numbers.

This positive cooperative binding is achieved through steric conformational changes of the hemoglobin protein complex: When one subunit protein in hemoglobin becomes oxygenated, it induces a confirmation or structural arrangement change in the whole complex causing the other 3 subunits to gain an increased affinity for oxygen. means that x grows beyond any assigned value, and means x is eventually less than any assigned value. As a consequence, the oxygen binding curve of hemoglobin is sigmoidal, or 'S'-shape, as opposed to the normal hyperbolic (noncooperative) curve. In real analysis, the symbol , called "infinity", denotes an unbounded limit. The binding affinity of hemoglobin for oxygen is increased by the oxygen saturation of the molecule. The infinity symbol is represented in Unicode by the character ∞ (∞). In the tetrameric form of normal adult hemoglobin, the binding of oxygen is a cooperative process. Another conjecture is that he derived it from the Greek letter ω (omega), the last letter in the Greek alphabet.

In adults:. One conjecture about why he chose this symbol is that he derived it from a Roman numeral for 1000 that was in turn derived from the Etruscan numeral for 1000, which looked somewhat like CIƆ and was sometimes used to mean "many". In the fetus:. John Wallis is usually credited with introducing ∞ as a symbol for infinity in 1655 in his De sectionibus conicus. In the embryo:. However, this explanation is improbable, since the symbol had been in use to represent infinity for over two hundred years before August Ferdinand Möbius and Johann Benedict Listing discovered the Möbius strip in 1858. There are two kinds of contacts between the α and β chains: α₁β₁ and α₁β₂. Again, one can imagine walking along its surface forever.

The four polypeptide chains are bound to each other by salt bridges, hydrogen bonds and hydrophobic interaction. A popular explanation is that the infinity symbol is derived from the shape of a Möbius strip. Haemoglobin A is the most intensively studied of the haemoglobin molecules. One can imagine walking forever along a simple loop formed from a ribbon. Each subunit has a molecular weight of about 16,000 daltons, for a total molecular weight of the tetramer of about 64,000 daltons. One possibility is suggested by the name it is sometimes called — the lemniscate, from the Latin lemniscus, meaning "ribbon". The subunits are structurally similar and about the same size. The precise origins of the infinity symbol ∞ are unclear.

This is denoted as α₂β₂. Unlike the traditional empiricists, he thought that the infinite was in some way given to sense experience. In adult humans, the most common haemoglobin type is a tetramer (which contains 4 subunit proteins) called haemoglobin A, consisting of two α and two β subunits non-covalently bound. An exception was Wittgenstein, who made an impassioned attack upon axiomatic set theory, and upon the idea of the actual infinite, during his "middle period".². The iron atom can either be in the Fe²⁺ or Fe³⁺ state, but ferrihaemoglobin (Methaemoglobin) (Fe³⁺) cannot bind oxygen. Modern discussion of the infinite is now regarded as part of set theory and mathematics, and generally avoided by philosophers. Two additional bonds perpendicular to the plane on each side can be formed with the iron to form the fifth and sixth positions, one connected strongly to the protein, the other available for binding of oxygen. A potential infinity is allowed by letting an infinitely-large quantity be cancelled out by an infinitely-small quantity.

The iron atom is bonded equally to all four nitrogens in the center of the ring, which lie in one plane. Potentiality lies in the definitions of this operation, as well-defined and interconsistent mathematical axioms. This iron atom is the site of oxygen binding. Such seeming paradoxes are resolved by taking any finite figure and stretching its content infinitely in one direction; the magnitude of its content is unchanged as its divisions drop off geometrically but the magnitude of its bounds increases to infinity by necessity. A heme group consists of an iron atom held in a heterocyclic ring, known as a porphyrin. Not reported, this motivation of Hobbes came too late as curves having infinite length yet bounding finite areas were known much before. This folding pattern contains a pocket which is suitable to strongly bind the heme group. Famously, the ultra-empiricist Hobbes tried to defend the idea of a potential infinity in the light of the discovery by Evangelista Torricelli, of a figure (Gabriel's horn) whose surface area is infinite, but whose volume is finite.

Each individual protein chain arranges in a set of alpha-helix structural segments connected together in a "myoglobin fold" arrangment, so called because this arrangment is the same folding motif used in the heme/globin proteins. Our idea of infinity is merely negative or privative. Each subunit is composed of a protein chain tightly associated with a non-protein heme group. They believed all our ideas were derived from sense data or "impressions", and since all sensory impressions are inherently finite, so too are our thoughts and ideas. The Haemoglobin molecule is an assembly of four globular protein subunits. Locke, in common with most of the empiricist philosophers, also believed that we can have no proper idea of the infinite. . The idea that size can be measured by one-to-one correspondence is today known as Hume's principle, although Hume, like Galileo, believed the principle could not be applied to infinite sets.

Mutations in the gene for the haemoglobin protein result in a group of hereditary diseases termed the hemoglobinopathies, the most common members of which are sickle-cell disease and thalassemia. He thought this was one of the difficulties which arise when we try, "with our finite minds", to comprehend the infinite. The most common types of hemoglobin contains four such subunits. It appeared, by this reasoning, as though a set which is naturally smaller than the set of which it is a part (since it does not contain all the members of that set) is in some sense the same size. The name hemoglobin is the concatenation of heme and globin, reflecting the fact that each subunit of hemoglobin is a globular protein with an embedded heme (or haem) group; each heme group contains an iron atom, and this is responsible for the binding of oxygen. For example, we can match up the "set" of even numbers {2, 4, 6, 8 ...} with the natural numbers {1, 2, 3, 4 ...} as follows:. Hemoglobin transports oxygen from the lungs to the rest of the body, such as to the muscles, where it releases the oxygen load. Galileo (during his long house arrest in Siena after his condemnation by the Inquisition) was the first to notice that we can place an infinite set into one-to-one correspondence with one of its proper subsets (any part of the set, that is not the whole).

Hemoglobin or haemoglobin (frequently abbreviated as Hb) is the iron-containing oxygen-transport metalloprotein in the red cells of the blood in mammals and other animals. Aquinas also argued against the idea that infinity could be in any sense complete, or a totality. Haemoglobin F (α₂γ₂) - In adults Haemoglobin F is restricted to a limited population of red cells called F cells. However, on this view, no infinite magnitude can have a number, for whatever number we can imagine, there is always a larger one: "There are not so many (in number) that there are no more". Haemaglobin A₂ (α₂δ₂) - δ chain synthesis begins late in the third trimester and in adults, it has a normal level of 2.5%. The parts are actually there, in some sense. Haemoglobin A (α₂β₂) (PDB 1BZ0) - The most common type. The second view is found in a clearer form by medieval writers such as William of Ockham:.

Haemoglobin F (α₂γ₂) (PDB 1FDH). For example, ∀n∈Z(∃m∈Z[m>n∧P(m)]), which reads, "for any integer n, there exists an integer m > n such that P(m)". Haemoglobin Portland (ξ₂γ₂). The other is that we may quantify over infinite sets without restriction. Gower 2 (α₂ε₂) (PDB 1A9W). One is that it is always possible to find a number of things that surpasses any given number, even if there are not actually such things. Gower 1 (ξ₂ε₂). This is often called potential infinity; however there are two ideas mixed up with this.

In Europe, the traditional view derives from Aristotle:. [1] [2] The concept of different orders of infinity would remain unknown in Europe until the late 19th century. It recognises five different types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually. 400 BC) classifies all numbers into three sets: enumerable, innumerable and infinite.

The Indian Jaina mathematical text Surya Prajinapti (ca. The earliest known documented knowledge of infinity is presented in the Veda- Yajur Veda which states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity". . For a discussion about infinity and the physical universe, see Universe.

In popular culture, we have Buzz Lightyear's rallying cry, "To infinity — and beyond!", which may also be viewed as the rallying cry of set theorists considering large cardinals.¹. By some, infinity is considered to be not a number but a concept of increase beyond bounds. In mathematics, infinity is relevant to, or the subject matter of, articles such as mathematical limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals, Russell's paradox, hyperreal numbers, projective geometry, extended real numbers and the Absolute Infinite. In both theology and philosophy, infinity is explored in articles such as the Ultimate, the Absolute, God, and Zeno's paradoxes.

In philosophy, infinity can be attributed to space and time, as for instance in Kant's first antinomy. In theology, for example in the work of theologians such as Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. The word infinity comes from the Latin infinitas, "unboundedness". Popular or colloquial usage of the term often does not accord with its more technical meanings.

Infinity refers to several distinct concepts which arise in theology, philosophy, mathematics and everyday life. and . and . If then and .

If then and . and . and . means that the area under f(t) approaches 1.

means that the area under f(t) is not finite. means that f(t) does not bound a finite area from 0 to 1.