# Draft:Phosphate budgets

Triplite is a rare fluoro-hydroxide phosphate mineral that forms in phosphate rich granitic pegmatites and high temperature hydrothermal veins. Credit: Gemshare.

"The amount of phosphate needed or available for a purpose, including estimates of phosphate in and phosphate out, and the phosphate form, determine the phosphate budget for a cell or an entire organism."[1] Bold added. For a "standard man" of 70 kg the available phosphate is ~1.52 x 1025 molecules of phosphate in some form. The available phosphate of an adult human female may differ from the "standard man".

"A well-fed adult in the industrialized world consumes and excretes about 1-3 g of phosphorus per day in the form of phosphate (2-6 x 1022 molecules). Per the elemental composition of the "standard man" of 70 kg, phosphorus is 780 g or 1.1% (as 1.52 x 1025 molecules of phosphate).[2] Of this 1.4 g/kg (98 g, 1.9 x 1024 molecules of phosphate) are present in soft tissue with the remainder (1.33 x 1025 molecules of phosphate) in mineralized tissue such as bone and teeth.[3] Only about 0.1% of body phosphate (about 2 x 1022 molecules) circulates in the blood, but this amount reflects the amount of phosphate available to soft tissue cells. Blood plasma contains orthophosphate (as HPO42-) and H2PO4- in the ratio of about 4:1.[3]"[1]

"The total quantity of ATP in the human body is about 0.1 mole (about 6 x 1022 molecules). This ATP is constantly being broken down into ADP, and then converted back into ATP. At any given time, the total amount of ATP + ADP remains fairly constant. The energy used by human cells requires the hydrolysis of 100 to 150 moles (6 to 9 x 1025 molecules) of ATP daily which is around 50 to 75 kg. Typically, a human will use up their body weight of ATP over the course of the day.[4] This means that each ATP molecule is recycled 1000 to 1500 times daily, or about once every minute."[1]

## Orthophosphoric acids

Def. "[a] colourless liquid, H3PO4"[5] is called phosphoric acid.

Def. "[o]rdinary phosphoric acid, H3PO4", after orthophosphoric acid, is called orthophosphoric acid.

Orthophosphoric acid is a non-toxic, inorganic, rather weak triprotic acid, that is a very polar molecule soluble in water. Triprotic means that an orthophosphoric acid molecule can dissociate up to three times, giving up an H+ each time, which typically combines with a water molecule, H2O, as shown in these reactions:

H3PO4(s)   + H2O(l) <=> H3O+(aq) + H2PO4(aq)       Ka1= 7.25×10−3
H2PO4(aq)+ H2O(l) <=> H3O+(aq) + HPO42−(aq)       Ka2= 6.31×10−8
HPO42−(aq)+ H2O(l) <=> H3O+(aq) +  PO43−(aq)        Ka3= 3.98×10−13

"The anion after the first dissociation, H2PO4, is the dihydrogen phosphate anion. The anion after the second dissociation, HPO42−, is the hydrogen phosphate anion. The anion after the third dissociation, PO43−, is the phosphate or orthophosphate anion. For each of the dissociation reactions shown above, there is a separate acid dissociation constant, called Ka1, Ka2, and Ka3 given at 25 °C. Associated with these three dissociation constants are corresponding pKa1=2.12 , pKa2=7.21 , and pKa3=12.67 values at 25 °C."[6]

"For a given total acid concentration [A] = [H3PO4] + [H2PO4] + [HPO42−] + [PO43−] ([A] is the total number of moles of pure H3PO4 which have been used to prepare 1 liter of solution), the composition of an aqueous solution of phosphoric acid can be calculated using the equilibrium equations associated with the three reactions described above together with the [H+][OH] = 10−14 relation and the electrical neutrality equation. Possible concentrations of polyphosphoric molecules and ions is neglected. The system may be reduced to a fifth degree equation for [H+] which can be solved numerically, yielding:"[6]

 [A] (mol/L) pH [H3PO4]/[A] (%) [H2PO4−]/[A] (%) [HPO42−]/[A] (%) [PO43−]/[A] (%) 1 1.08 91.7 8.29 6.20×10−6 1.60×10−17 10−1 1.62 76.1 23.9 6.20×10−5 5.55×10−16 10−2 2.25 43.1 56.9 6.20×10−4 2.33×10−14 10−3 3.05 10.6 89.3 6.20×10−3 1.48×10−12 10−4 4.01 1.30 98.6 6.19×10−2 1.34×10−10 10−5 5.00 0.133 99.3 0.612 1.30×10−8 10−6 5.97 1.34×10−2 94.5 5.50 1.11×10−6 10−7 6.74 1.80×10−3 74.5 25.5 3.02×10−5 10−10 7.00 8.24×10−4 61.7 38.3 8.18×10−5

## Pyrophosphoric acids

Def. the "[syrupy liquid] acid formed by the dehydration of [i.e., removing a molecule of water from] two molecules of phosphoric acid [to form one molecule of] H4P2O7"[7] is called pyrophosphoric acid.

## Oligophosphoric acids

Def. a series of phosphoric acids condensed into one molecule when the number of phosphoric acids is small, per the general formula Hn+2PnO3n+1, where n is usually greater than 5, is called an oligophosphoric acid.[8]

## Phosphates

Notation: let the symbols ATP, CTP, GTP, NTP, and UTP stand for adenosine triphosphate, cytidine triphosphate, guanosine triphosphate, nucleotide triphosphate, and uridine triphosphate, respectively.

Notation: let the symbols ADP, CDP, GDP, NDP, and UDP stand for adenosine diphosphate, cytidine diphosphate, guanosine diphosphate, nucleotide diphosphate, and uridine diphosphate, respectively.

Notation: let the symbols AMP, CMP, GMP, NMP, and UMP stand for adenosine monophosphate, cytidine monophosphate, guanosine monophosphate, nucleotide monophosphate, and uridine monophosphate, respectively.

Def. "[a]ny salt or ester of phosphoric acid"[9] is called phosphate.

Def. any "salt or ester of pyrophosphoric acid"[10] is called a pyrophosphate.

Def. "any of a class of inorganic polymers containing linked phosphate groups"[11] is called a polyphosphate.

## Nucleotides

This is a diagram of the major nucleotides. Credit: Sjef.

When nucleotide hydrolysis is coupled to the polymerization process, the two ends of the polymer behave differently, and the critical concentration required for assembly at one end is different from that required for the opposite end. However, NTP hydrolysis is usually associated but not directly coupled with polymerization. When there are NTP-bound subunits at the ends, the polymer is stable and continues to grow slowly. When at the polymer ends there are subunits containing NDP, the polymer is in a shrinking phase, depolymerizes rapidly and completely, and much faster at lower mer concentrations.

## Catalytic phosphates

The catalytic phosphate in a nucleotide is usually the phosphate farthest from the nucleoside.

"The γ phosphate of ATP is the catalytic phosphate."[1]

"A phosphate which affects the catalytic activity of an enzyme is a catalytic phosphate.[12] Occasionally, an enzyme contains a structural phosphate and a catalytic phosphate.[12]"[1]

"Catalytic phosphates are acid-labile and base-stable. Structural phosphates are acid-stable, base-labile.[13]"[1]

## Structural phosphates

Structural phosphate may be inside a cell, "structural to a nucleic acid such as DNA and RNA or a phospholipid. Outside the cell, phosphate may be dissolved in extracellular fluid (ECF) or form structures such as bone and teeth. Bringing phosphate in any form into the cell from a phosphate containing structure or for such a structure and when needed transporting phosphate out of the cell perhaps to a structure is a necessary activity of phosphate homeostasis for that cell."[1]

Structural phosphate is a part of each polymer whether it is a microfilament, microtubule, phospholipid, or nucleic acid. Inorganic phosphates such as Pi and PPi can be precipitated with divalent cations like Ca2+, Mg2+, or others, e.g. Mn2+, to form a variety of tissue and mineral composites: cartilage, teeth, andbone. These in turn eventually become localized to the natural environment and form phosphorites.

## Bones

The bones, or fossilized remains of bones, here a dinosaur, may be reassembled to suggest the animal's original shape and movements. Credit: Chase Elliott Clark.

Bones are rigid organs that constitute part of the endoskeleton of vertebrates. They support and protect the various organs of the body, produce red and white blood cells and store minerals. Bones act as reserves of minerals important for the body, most notably calcium and phosphorus. Bone controls phosphate metabolism by releasing fibroblast growth factor – 23 (FGF-23), which acts on kidneys to reduce phosphate reabsorption]]. "The primary tissue of bone, osseous tissue, is mostly made up of a composite material incorporating the mineral calcium phosphate in the chemical arrangement termed calcium hydroxylapatite (this is the osseous tissue that gives bones their rigidity) and collagen, an elastic protein which improves fracture resistance."[14]

"Osteoblasts are mononucleate bone-forming cells that descend from osteoprogenitor cells. They are located on the surface of osteoid seams and make a protein mixture known as osteoid, which mineralizes to become bone. ... Osteoblasts also manufacture hormones, such as prostaglandins, to act on the bone itself. They robustly produce alkaline phosphatase, an enzyme that has a role in the mineralisation of bone, as well as many matrix proteins."[14]

"Mineralisation involves osteoblasts secreting vesicles containing alkaline phosphatase. This cleaves the phosphate groups and acts as the foci for calcium and phosphate deposition."[14]

## Teeth

The image shows a tool-using, intelligrant life form, a chimpanzee, displaying some of its teeth. Credit: Richard.

"A tooth (plural teeth) is a small, calcified, whitish structure found in the jaws (or mouths) of many vertebrates and used to break down food. Some animals, particularly carnivores, also use teeth for hunting or for defensive purposes. The roots of teeth are covered by gums. Teeth are not made of bone, but rather of multiple tissues of varying density and hardness. The cellular tissues that ultimately become teeth originate from the embryonic germ layer, the ectoderm".[15]

"The general structure of teeth is similar across the vertebrates, although there is considerable variation in their form and position. The teeth of mammals have deep roots, and this pattern is also found in some fish, and in crocodilians. In most teleost fish, however, the teeth are attached to the outer surface of the bone, while in lizards they are attached to the inner surface of the jaw by one side. In cartilaginous fish, such as sharks, the teeth are attached by tough ligaments to the hoops of cartilage that form the jaw.[16]"[15]

"Mammals are diphyodont, meaning that they develop two sets of teeth. In humans, the first set (the "baby," "milk," "primary" or "deciduous" set) normally starts to appear at about six months of age, although some babies are born with one or more visible teeth, known as neonatal teeth. Normal tooth eruption at about six months is known as teething and can be painful."[15]

## Cartilage

Here, a spotted gar larva 22 days old is stained for cartilage (Alcian blue) and bone (Alizarin red). Credit: Dr. Yi-lin Yan and Dr. Brian Eames.

Def. a "type of dense, non-vascular connective tissue, usually found at the end of joints, the rib cage, the ear, the nose, in the throat and between intervertebral disks"[17] is called cartilage.

"Ossification (or osteogenesis) is the process of laying down new bone material by cells called osteoblasts. It is synonymous with bone tissue formation. There are two processes resulting in the formation of normal, healthy bone tissue:[18] Intramembranous ossification is the direct laying down of bone into the primitive connective tissue (mesenchyme), while endochondral ossification involves cartilage as a precursor. ... Calcification is synonymous with the formation of calcium-based salts and crystals within cells and tissue. It is a process that occurs during ossification, but not vice versa."[19]

"[M]atrix vesicles (MV) are primary initiators of extracellular mineral deposition in endochondral calcification. ... direct cellular metabolism of Ca2+ and inorganic phosphate (Pi), and cellular interaction with the matrix, are involved in the formation of calcifiable MV. ... chondrocytes in growth plate (GP) cartilage ... induce the formation of calcificable MV. ... GP chondrocytes are depleted of ATP and have elevated cytosolic Pi, a condition prerequisite to formation of Ca2+-acidic phospholipid (APL)-Pi complex-primed MV. [The] interaction between the extracellular matrix and chondrocytes [may] facilitate Ca2+ loading of chondrocytes, formation of Ca2+ and Pi-primed MV and rapid induction of mineralization in GP cartilage."[20]

The spotted gar larva at right is a "living fossil" that shows cartilage beginning to be transformed into bone by endochondral calcification followed by extracellular mineralization of bone composed of calcium phosphate.

## Microtubules

"During polymerization, both the α- and β-subunits of the tubulin dimer are bound to a molecule of GTP. The GTP bound to α-tubulin is stable, but the GTP bound to β-tubulin may be hydrolized to GDP shortly after assembly. The kinetics of GDP-tubulin are different from those of GTP-tubulin; GDP-tubulin is prone to depolymerization. A GDP-bound tubulin subunit at the tip of a microtubule will fall off, though a GDP-bound tubulin in the middle of a microtubule cannot spontaneously pop out. Since tubulin adds onto the end of the microtubule only in the GTP-bound state, there is generally a cap of GTP-bound tubulin at the tip of the microtubule, protecting it from disassembly. When hydrolysis catches up to the tip of the microtubule, it begins a rapid depolymerization and shrinkage. This switch from growth to shrinking is called a catastrophe. GTP-bound tubulin can begin adding to the tip of the microtubule again, providing a new cap and protecting the microtubule from shrinking. This is referred to as rescue."[21]

## Microfilaments

"In vitro actin polymerization, nucleation, starts with the self-association of three G-actin monomers to form a trimer. ATP-actin then binds the plus (+) end, and the ATP is subsequently hydrolyzed with a half time of about 2 seconds[22] and the inorganic phosphate released with a half-time of about 6 minutes,[22] which reduces the binding strength between neighboring units and generally destabilizes the filament. In vivo actin polymerization is catalyzed by a new class of filament end-tracking molecular motors known as actoclampins (see next section). Recent evidence suggests that ATP hydrolysis can be prompt in such cases (i.e., the rate of monomer incorporation is matched by the rate of ATP hydrolysis)."[23]

"ADP-actin dissociates slowly from the minus end, but this process is greatly accelerated by ADP-cofilin, which severs ADP-rich regions nearest the (–)-ends. Upon release, ADP-actin undergoes exchange of its bound ADP for solution-phase ATP, thereby forming the ATP-actin monomeric units needed for further (+)-end filament elongation. This rapid turnover is important for the cell's movement. End-capping proteins such as CapZ prevent the addition or loss of monomers at the filament end where actin turnover is unfavourable like in the muscle apparatus."[23]

## Phospholipids

The diagram shows a location of a phospholipid. Credit: Ties van Brussel.

"Phospholipids are a class of lipids that are a major component of all cell membranes as they can form lipid bilayers. Most phospholipids contain a diglyceride, a phosphate group, and a simple organic molecule such as choline; one exception to this rule is sphingomyelin, which is derived from sphingosine instead of glycerol. ... The structure of the phospholipid molecule generally consists of hydrophobic tails and a hydrophilic head. Biological membranes in eukaryotes also contain another class of lipid, sterol, interspersed among the phospholipids and together they provide membrane fluidity and mechanical strength. Purified phospholipids are produced commercially and have found applications in nanotechnology and materials science.[24]"[25]

## Nucleic acids

Def. "[a]ny acidic, chainlike biological macromolecule consisting of multiply repeat units of phosphoric acid, sugar and purine and pyrimidine bases"[26] occurring in cell nuclei is called a nucleic acid.

Def. a nucleic acid "in which the sugar component is threose"[27] is called threose nucleic acid, or threonucleic acid.

## Cellular allocations

Likely Cellular Phosphate Allocation for a Human Adult
Component Type Number of molecules Accumulating total
cell membrane structural ~1.6 x 108 ~1.6 x 108
endoplasmic reticulum structural ~1.7 x 108 ~3.3 x 108
mitochondrial DNA structural ~3.3 x 108 ~6.6 x 108
ATP 2 structural, 1 catalytic ~2.7 x 109 ~3.4 x 109
CTP 2 structural, 1 catalytic ~2.7 x 109 ~6.1 x 109
GTP 2 structural, 1 catalytic ~2.7 x 109 ~8.8 x 109
UTP 2 structural, 1 catalytic ~2.7 x 109 ~12 x 109
chromatin DNA structural ~6.8 x 109 ~19 x 109
others all ~0.4 x 109 ~19 x 109
all all ~19 x 109 ~19 x 109

## Phosphate reactions

A phosphate reaction is a chemical reaction that leads to the transformation of one set of phosphates into another.

Each phosphate reaction that occurs in living cells is a part of phosphate metabolism. These reactions are the basis of life, allowing cells to grow and reproduce, maintain their structures, and respond to their environments. Metabolism is usually divided into two categories: catabolism which yields energy such as the breakdown of food in cellular respiration, and anabolism which uses this energy to construct components of cells such as proteins and nucleic acids.

The KEGG[28] database contains biochemical phosphate reactions, some of which may include a nucleotide such as nucleoside monophosphate (NMP). Various possible phosphate reactions number up to 2371 as of October 20, 2009. Not all of these occur in humans. A list of biochemical phosphate reactions may contain these phosphate reactions. Those that have human genes or have products occurring in humans contribute to human life.

## Catabolism

Def. "destructive metabolism, usually including the release of energy and breakdown of materials"[29] is called catabolism.

An decrease in the number of phosphates per molecule is phosphate catabolism.

For example, in phosphate catabolism, ATP is reduced to ADP with the release of an orthophosphate (Pi) and energy.

Def. any "enzyme that hydrolyzes an organic phosphate group"[30] is called a phosphohydrolase.

Def. any "of several enzymes that hydrolyze phosphate esters"[31] is called a phosphatase.

## Anabolism

Def. the "constructive metabolism of the body"[32] is called anabolism.

An increase in the number of phosphates per molecule is phosphate anabolism.

For example, in phosphate anabolism, GDP is oxidized to GTP with the use of energy and the bonding of an orthophosphate (Pi) to GDP.

Def. any "enzyme that catalyzes the production of"[33] a phosphate by the addition of an inorganic phosphate to a molecule is called a phosphorylase.

## Phosphate utilization rates

Phosphate in the nucleosol is utilized at a rate λ which represents the uptake of nutrients. The timescale 1/λ gives a measure of the residence time for phosphate in the surface layers. The maximum uptake rate is modulated by a periodic cycle, such as the daily feedings, and decreases exponentially with interiority.

## Remineralization

"In biogeochemistry, remineralisation (UK spelling; US remineralization) refers to the transformation of organic molecules to inorganic forms, typically mediated by biological activity.[34]"[35]

"Usually remineralisation relates to organic and inorganic molecules involving biologically important elements such as carbon, nitrogen and phosphorus. For example, the following simplified equation shows the complete remineralisation of organic material with a standard Redfield ratio to oxidised inorganic minerals such as carbon dioxide, nitrate (nitric acid) and phosphate (phosphoric acid).[34]"[35]

(C106H124O36) (NH3)16 (H3PO4) + 150 O2 ${\displaystyle \rightarrow }$ 106 CO2 + 16 HNO3 + H3PO4 + 78 H2O + energy

"In reality, such complete remineralisation is likely to involve several stages each involving different organisms and metabolic pathways. For example, in the case of nitrogen, its transformation from ammonia (NH3) in the equation above, to nitrate involves the process of nitrification, usually mediated by a series of bacteria.[36]"[35]

"The remineralization of teeth is a process in which minerals are returned to the molecular structure of the tooth itself, and can reverse bacterial infestation of the enamel of a tooth. This process cannot replace lost tooth material (that is, it won't fill a cavity that has developed into a hole). The human body naturally remineralizes teeth through the use of carbonic acid[37]."[38]

## Remineralization rates

The remineralization rate (r) is given by r = w/z, where w is the sinking rate and z is the optimum depth reached before conversion from organic phosphate to inorganic phosphate.

A simplified phosphate-cycling model is used to examine how changes in circulation might influence phosphate export production via the supply of phosphate to the phosphate utilization zone and the preservation of organic phosphate which is controlled by the oxygen content.[39] The model uses coupled equations: phosphate utilization, phosphate remineralization, and the oxygen concentration. The initial conditions for all the integrations of the model consist of uniform values for the concentration of each component: [PO4] = 2 x 10-4 mol m-3, [D] = 0, and [O2] = 0.1 mol m-3, where D refers to the organic phosphate.

## Dynamic models

“The relations between the external nutrient loading of lakes, recycling through sediments and the resulting productivity are complicated by feed-back mechanisms, seasonal variations and trends.”[40] In a dynamic phosphate budget model the variables “include inorganic and organic particulate phosphate and dissolved o-phosphate, in both sediments and overlying water. Sediments may be aerobic or anaerobic, depending on topography, temperature and composition. The major processes described are primary production, mineralization, sedimentation, adsorption and diffusion. ... The sediment dilution rate, the extent of anaerobic conditions and the number and character of adsorption sites are important controlling factors.”[40] Units of loading are g P m-2 yr-1.[40]

"A dynamic phosphate budget can be modeled by determining the relations between the external phosphate loading, recycling through the formation of structural phosphates, and the resulting productivity, which are complicated by feed-back mechanisms, periodic variations and trends.[40] In a dynamic phosphate budget model the variables include inorganic and organic particulate phosphate and dissolved phosphate, in both structural phosphate and nucleosol. Structural phosphate may be aerobic or anaerobic, depending on localization, temperature (or pH) and composition. The major describeable processes are primary production, mineralization, precipitation, adsorption and diffusion. The precipitate dilution rate, the extent of anaerobic conditions and the number and character of adsorption sites are important controlling factors.[40]"[1]

## Minerals

Apatite-(CaF) (fluorapatite) is the doubly-terminated crystal in calcite. Credit: Didier Descouens.
This fluorapatite specimen is primarily violet. Credit: Vassil.
The color of the purple apatites (which are to almost 1 cm in size) leaps out at you. Credit: Rob Lavinsky.
Torbernitte is a hydrated green copper uranyl phosphate mineral. Credit: Didier Descouens.

"Apatite is a group of phosphate minerals, usually referring to hydroxylapatite, fluorapatite and chlorapatite, named for high concentrations of OH, F and Cl ions, respectively, in the crystal. The formula of the admixture of the four most common endmembers is written as Ca10(PO4)6(OH,F,Cl)2, and the crystal unit cell formulae of the individual minerals are written as Ca10(PO4)6(OH)2, Ca10(PO4)6(F)2 and Ca10(PO4)6(Cl)2."[41]

"Apatite is one of a few minerals produced and used by biological micro-environmental systems."[41]

"Hydroxyapatite, also known as hydroxylapatite, is the major component of tooth enamel and bone mineral. A relatively rare form of apatite in which most of the OH groups are absent and containing many carbonate and acid phosphate substitutions is a large component of bone material."[41]

"Fluorapatite [a sample of which is shown at right] ... is a mineral with the formula Ca5(PO4)3F (calcium fluorophosphate). ... Fluorapatite as a mineral is the most common phosphate mineral. It occurs widely as an accessory mineral in igneous rocks and in calcium rich metamorphic rocks. It commonly occurs as a detrital or diagenic mineral in sedimentary rocks and is an essential component of phosphorite ore deposits. It occurs as a residual mineral in lateritic soils.[42]"

At lower left is another fluorapatite example that is violet in color on quartz crystals.

"Torbernite ... is a radioactive, hydrated green copper uranyl phosphate mineral, found in granites and other uranium-bearing deposits as a secondary mineral. Torbernite is isostructural with the related uranium mineral, autunite. The chemical formula of torbenite is similar to that of autunite in which a Cu2+ cation replaces a Ca2+. The number of water hydration molecules can vary between 12 and 8, giving rise to the variety of metatorbernite when torbernite spontaneously dehydrates."[43]

## Phosphorites

"Phosphorite is a phosphate-rich sedimentary rock, that contains between 18% and 40% P2O5. The apatite in phosphorite is present as cryptocrystalline masses referred to as collophane."[41]

## Hypotheses

1. The phosphate budget required to run a default human genome daily is the same as running any daily human genome.

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