Equivalency Law in the metal requirement of the living organisms
Acta Alimentaria 27 (4):
( Acta Alimentaria )
Institute of Materials and Environmental Chemistry, Research
Centre for Natural Sciences
Hungarian Academy of Sciences
H-1117 Budapest, Magyar Tudosok Korutja 2. Hungary
From information referring to metal requirements of the human organism as well as metal contents of human and cow`s milk and cereal grains it was concluded that an Equivalency Law exists in the metal balance of the living organisms. According to this law the alkali metal requirement (mainly potassium and sodium) is chemically equivalent with that of polyvalent metals (namely calcium, magnesium, zinc, iron etc.). Theoretical considerations are given for proving the existence of the Equivalency Law.
Keywords: equivalency law, living organisms, metal requirements, milk, RDA
With the development of science, more and more knowledge has been accumulated on nutrient requirements ensuring optimal function of human, animal (and plant) organisms. In addition to information on protein, carbohydrate, vitamin, etc., requirements current knowledge extends to mineral substances, macro-, meso- and microelements, as well. The values recommended on the basis of most recent information concerning nutrient requirements of the human organism, are collected in Recommended Dietary Allowances (RDA, 1989) by the Food and Nutrition Board of the National Research Council, National Academy of Sciences in the US, republished from time to time.  Surveying RDA data the following regularity can be observed: the daily alkali metal requirement (S M+, mainly potassium and sodium) of the human organism is chemically equivalent to the sum of the polyvalent metal requirement (S Mz+, namely calcium, magnesium, zinc, iron etc.). Taking into account metal contents of samples of biological origin (milk and cereal grains) as well as simple theoretical considerations, it can be concluded that this regularity exists in the metal balance of all the living organisms on the Earth.
The regularity mentioned may be termed as Equivalency Law, which can be described by the following formula: S M+ = S Mz+. Respective RDA data referring to adult men aged 19-24 years may represent the relevancy of the Equivalency Law (see Table 1).
Table 1. Metal requirement of adult men aged 19-24 years
|Alkali metals; S M+||92.085|
|Polyvalent metals; S Mz+||89.853|
* The equivalents are calculated for iron with 2.5+ charge, and for manganese with 3+ charge.
The data in Table 1 show there is hardly any difference between alkali metal requirement, amounting to 92.085 milliequivalent/day (meq/day), and polyvalent metal requirement, which is 89.853 meq/day. According to RDA data, the difference is greater, for example, in the case of children aged 7-9 years (Ca: 800 mg, Mg: 170 mg, Fe: 10 mg, Zn: 10 mg, Mn: 2-3 mg, Cu:1-2 mg, Na: 400 mg, K: 1600 mg); on the basis of which, alkali metal requirement is 58.322 meq/day, and the sum of polyvalent metal requirement is 54.849 meq/day. This difference, however, can not question the existence of the Equivalency Law, since RDA tables gives data estimated as optimal values.
It is advisable to express the deviation from the Equivalency Law by calculating relative deviations, in percent, for example, by considering half the equivalents of the total amount of metals as standard. Thus, the relative deviation is 3.07% (A+) for children. ("A+" denotes alkali metal excess.) [E.g. (58.322 + 54.849) / 2 = 56.586, the deviation from this is 58.322 - 56.586 = 1.736, which amounts to 1.736 Ă— 100 / 56.586 = 3.07%]. Relative deviation is 1.23% (A+) for adult men. The Equivalency Law can also be expressed by the formula: S M+ / S Mz+ = 1. In this way the deviation from the law (Quotient of Equivalency) can be calculated by: EQ = S M+ / S Mz+. The value of EQ is greater than one for alkali metal surplus and is lower for the opposite case.
There are data referring to the Equivalency Law in the vegetable kingdom, as well. Results of my measurements concerning metal content of natural cereal flakes and cereal flake flours produced in 1994 in Hungary are given in Table 2. (After digestion with nitric acid and hydrogen peroxide, the metal contents have been measured by a plasma emission spectrometer, Thermo Jarrell Ash Corp., AtomScan 25 type ICP.)
Table 2. Metal content of cereal flakes and flake flours [mg/kg]
|metal||flake||f. flour||flake||f. flour||flake||f. flour||flake||f. flour|
On the basis of data in Table 2, Table 3 shows alkali metal contents (S M+), polyvalent metal contents (S Mz+), half of the total metal contents ((S +S )/2) and relative deviations from the Equivalency Law (D [%] and EQ respectively). Iron and manganese contents are calculated as above, "(A-)" denotes the lack of alkali metal.
Table 3. Cereal flakes and flake flours and the Equivalency Law
|S M+ [meq/kg]||S Mz+ [meq/kg]||(S +S )/2 [meq/kg]||D [%]||EQ|
|barley flakes||76.216||86.349||81.283||6.23 (A-)||0.8827|
|barley flake flour||86.451||86.848||86.650||0.229 (A-)||0.9954|
|wheat flakes||88.278||108.50||98.389||10.28 (A-)||0.8136|
|wheat flakes flour||91.045||105.95||98.499||7.57 (A-)||0.8593|
|rye flakes||101.42||103.39||102.41||0.96 (A-)||0.9810|
|rye flakes flour||143.85||146.29||145.07||0.84 (A-)||0.9833|
|oat flakes||93.763||149.80||121.78||23.01 (A-)||0.6259|
|oat flake flour||65.249||102.27||83.760||22.10 (A-)||0.6380|
The data for barley, wheat and rye seem to "conform" to the Equivalency Law surprisingly well, and the highest deviation (for oat) is only 23%. At the same time, e.g. the ratios of sodium-potassium and calcium-magnesium in each sample considerably deviate from those considered to be optimal, according to RDA. Quantitative ratios of the various metals do not necessarily correspond to human requirements however, since the nutrients are stored in the seeds of cereals in order to satisfy the needs of their "descendants", the seedlings in their first phase of life.
The composition of milk also points to a genetically programmed supply of food requirements for descendants i.e. new-born children. BUTTE  and co-workers (1987) gave data on the composition of human milk (and intake of human milk on 45 healthy mother-infant pairs) and to its changes during the first four months of lactation. Table 4 shows these data recalculated in accordance with the above.
Table 4. Metal content of human milk during the first 4 months of lactation [meq/kg]
|(S +S )/2||17.4632||16.8501||16.5433||16.0281||16.7033|
|D [%]||1.877 (A+)||4.180 (A-)||4.304 (A-)||6.479 (A-)||3.00 (A-)|
PORTER  (1978) published data of the composition of human and cow`s milk. Table 5 gives values obtained by recalculating these data.
Table 5. Metal content of human and cow`s milk [meq/liter]
|metal||human milk||cow`s milk|
|(S +S )/2||20.9292||64.9554|
|D [%]||4.498 (A+)||7.454 (A-)|
The data mentioned before unanimously verify the existence of the Equivalency Law, but are not sufficient to answer all questions. It is not evident from the data of BUTTE et al (1987), whether there is any significant change in the metal composition of human milk from the range of alkali excess to the steadily increasing deficiency. This question could be answered either by re-elaboration of the original, individual data, taking into account the Equivalency Law or by new measurements. An answer to this question may be of particular significance for producing baby food of optimal composition. In 1989 a dairy product for babies (namely Drikkeklar Allomin, Beauvais Industri A/S, Tastrup, Sweden) contains the following metals [mg/liter]: Na: 160, K: 585, Ca: 470, Mg: 50, Fe: 7, Zn: 4, Cu: 0.4. Relative deviation from the Equivalency Law is calculated 12.2% (A-). Investigations related to the Equivalency Law may lead to significant practical results e.g. in food science, stock-raising, plant cultivation, and in biotechnology as well. It would be feasible to carry out research related to the Equivalency Law, for determining concentration of further metals (e.g. Li, Co, Cr etc., and Al, Cd, Pb etc.), micro or toxic metals, present in low concentration. The metals mentioned could influence, however, the sum of equivalents only at a small extent. The equivalents of metals with varying valences, e.g. Fe, Mn etc., should be calculated by taking into consideration a uniform degree of oxidation; e.g. the average of the most common degrees of oxidation in biological systems. Thus, iron and cobalt could be calculated with 2.5+ and manganese with 3+ charge.
2. Theoretical conclusions
A long list of literature data could be enumerated here to verify the existence of the Equivalency Law, but it can be proved theoretically as well. As is well known, in the aqueous electrolytes of living organisms metals change ligands as positive ions. As strict chemical stoichiometrical rule of these cation exchange processes is that they proceed with the exchange of an equivalent amount of positively charged counter-ions. The various polyvalent metals hardly can act as counter-ions of each other since they are present as free ions in the electrolytes of organisms only in low concentration and form far more stable compounds (complexes) with various proteins and simple acids. Apart from a few exceptions, the different polyvalent metals cannot act as counter-ions of each other because they cannot substitute each other at the specific bonding sites of the individual protein molecules (enzymes, transport proteins etc.). Ammonium ions cannot act as counter-ions of polyvalent metals either, since they are present in the electrolytes of living organisms only in rather low concentration. Hydrogen ions (or more precisely, H3O+ ions) can also be counter-ions of polyvalent metals only in a very low ratio, as the pH value in living organisms is nearly neutral, thus, the concentration of hydrogen ions is very low; it is in the range of 10-7 mol/l. Contrarily, the total concentration of alkali metals (mainly potassium and sodium ions) is of 0.1 mol/l order of magnitude. Thus, in ligand exchange processes of polyvalent metal ions, primarily alkali metal ions can act as counter-ions. Life on Earth is uniformly based on proteins. Chemical and physical properties of proteins and other macromolecules allow vital processes in the electrolytes of organisms only at a very low concentration range. Economical utilization of energy and food is a common characteristic of living creatures. It does not allow any surplus of metal ions. Finally, it is commonplace that every living organisms are related genetically. Consequently, it may be supposed that the Equivalency Law referring to the alkali and polyvalent metals must exist in the metal metabolism processes of various living creatures on Earth.
It should be mentioned, that the metal content of oceanic and sea-water is significantly shifted from the Equivalency Law, towards alkali metal excess (D Â» 57%). During the evolution, after the appearance of living creatures with calcareous skeleton, limestone layers constituting today the enormous calcareous mountain ranges of continents have accumulated in the depths of oceans and seas. Thus, it may be assumed that many million years ago the water of primordial oceans and seas contained more calcium and more magnesium, iron, zinc etc. than recently. This greatly depended on the carbon dioxide content of the primordial atmosphere. In the course of time, the amount of calcium, magnesium etc. decreased in water. At the same time, due to the higher solubility of alkali metal compounds, the amount of these did not change substantially. Consequently, millions of years ago the metal content of the water of primordial oceans and seas must have been closer to the EQ = 1 value, as compared to present-day metal content, which may have played an important role in the course of biological evolution.
 Recommended Dietary Allowances 10th ed., National
Academy Press, NW, Washington DC 1989.
(Nutrition Reviews 48 (1): 28-30. 1990.)
Nat'l Academies Press, Recommended Dietary Allowances: (1989), Table of Contents
 Butte, N. F., Garza, C., O`Brian Smith, E., Wills, C.
& Nichols, B. L.: Macro- and trace-mineral intakes of
exclusively breast-fed infants. Am. J. Clin. Nutr., 45,
42-48. 1987. Butte
AJCN-Abstracts: Butte et al. 45(1):42-48(1987) Entrez PubMed-AJCN-Abstr:Butte et al. 45(1):42-48(1987)
 Porter, J. W. G.: Milk as a source of lactose, vitamins
and minerals. Proc. Nutr. Soc., 37, 225-230.
Additional references -
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