Thursday, September 30, 1999

High Fat Diets and Grass Disease - For Sancho - Jackie Laurents

Introduction

In my last article (Cheval Endurance [Horse Endurance] No. 8) I emphasized the fact that a diet rich in fats was beneficial for an endurance horse, and constituted, at the same time, an antidote for grass disease (Valery Kanavy, the world champion from the USA, feeds her horses in this way).

I continued my research in the hope that it will be seen as definitive progress in the understanding and the treatment of this disease, although initially I did not wish to publicize it out of my resentment against the community of endurance races. I write this for Sancho.

Summary

In 1989, a series of droughts in the area of Médoc (in southwest France) caused chronic azotemy in my horses, which manifested itself during endurance training. In the spring of 1992, a year after I had decided to replace grain with whole meal and fluffy foods, hoping that grass from pastures would serve as a ballast, grass disease broke out. I lost just one filly due to an affected nervous system, and transported the rest of the herd to Dordogne to new pastures.

The horses recovered, but their athletic shape remained rather unstable, with relapses. They could not stand grain, granule, complete vitamins, or excessively grazed pastures. Since my research had led me to discover the protective function of fats in this pathology, in 1998 I was able to obtain significant results using fats. However, because of financial constraints, I had to cease this treatment in the fall of 1998. I did not have to wait too long for results; at the end of winter, my horses were in disastrous shape, and one of them died of neoplasmatic lung cancer. An extremely skinny 23-year-old mare suffered from high anemia and serious liver problems so much so that it was diagnosed by my veterinarian as piroplasmosis; the liver problems were further accompanied by a skin disease and a very low level of phosphorus in the blood. All these symptoms could be noticed in the other horses, mares, colts and stallions.

Thus, I went back to the project that I had abandoned in the spring of 1998 by putting my horses on a diet which consisted purely of organic hay, and embarking on a treatment with B vitamins in injectable solution (vitamins B1, B2, B5, B6, and PP—water-soluble vitamins with trace elements of Fredop). To my greatest delight, I witnessed an amazing athletic recovery of my horses. The 23-year-old mare regained her magnificent shape in two months. Three stallions, untried for 10 years (they could cover at most 1 mile) started their sporting career.

Consequently, I contacted Dr. Zientaras at the Central Research Laboratory in Maison-Alfort (a French veterinary school), the author of an article published in Science et Vie, N°909, June 1993. I acquainted him with my observations, namely that the disease in question was caused by nitrates affecting the respiratory system through the impairment of the oxidation-reduction mechanism (B6 and PP vitamin deficiency). Dr. Zientaras confirmed that the disease was not viral, but rather nutritional and that my hypothesis was plausible.

I continued my investigation by contacting Dr. Daniel Maume, the discoverer of dihydroxindole 2.5, at the veterinary school in Nantes. He confirmed the plausibility of my theory and sent me his research project on "hepatic encephalosis." Drs. T. Rouillon and F. Sickel, both Drs. of Science, as well as veterinary practitioner D. Langronne also participated in this project. Their research from 1992 did not get much publicity at the time.

History and Clinical Approach to Grass Disease

For the first time, grass disease appeared in Great Britain in 1920, on the west coast of Scotland. From the beginning, it was known as a fatal condition in horses, with unknown causes and no remedy. The symptoms of this epidemic of grass sickness which became endemic begin with the usual series of colics accompanied by stomach ache, sweating in certain body areas, muscle trembling, accelerated pulse and increased respiratory rate. In the final stage, one may notice a complete intestinal stasis. The horse's stomach gets more and more pulled up, and this situation deteriorates, resulting in the animal's death. Baron Guy de Rothschild writes on this subject in "Courses et Elevage" in 1990. His father Edward had to scatter 90 brood mares in distant areas in 1930, in order to save his Normandy farm from "horse sickness" which, in his opinion, is caused by overgrazing and overstoring. If I hadn't moved my horses in 1992, I would have lost them.

Dr. Maume’s clinical description of the symptoms of hepatic encephalosis is as follows: jaundice, high cardiac frequency//elevated pulse, incomplete digestive paralysis, photosensitivity on light body parts (horse's white stockings), atoxy, pushing against the wall, abnormal behavior (walking across the hedges), amaurosis, muscular fasciculation, and convulsions in the final phase.

Biochemically, one finds a considerably increased level of GAMMA GT, alkaline phosphates and a high level of SGOT, as well as hyperammoniemia, doubled bilirubin, and hemoglobinuria.

Moreover, in the latent phase I observed anemia, an extremely low level of phosphorus in the blood, slow growth, and pellagrous injuries on the back. Sometimes, there are also mouth injuries and edemas.

In order to complete this clinical description, I should add that the term "encephalosis" was invented by Charton to describe a syndrome similar to that of encephalitis or encephalo-myelitis, caused by nutritional imbalance with the intervention of clostridium-Welchii.

Robin and Belloc bring our attention to a grass disease in Brittany which appears in a great number of animals, either at the initiation of grazing in spring, or in stables, due to nutrition based on clover and roots.

Biochemical Analysis

Using gas chromatography as well as mass spectrometry at high resolution, Dr. Maume proved the presence of an unusual molecule in the urine of sick mares; a dehydroxindole 2.5 with a formula C17H31NO2SI3, and mass 365. The only thing to be determined now is the position of OH groups. According to Dr. Maume, the presence of this molecule might cause problems with tryptophan metabolism that can be solely of nutritional origin. Consequently, the profound alteration of this metabolism could cause all the aforementioned symptoms. Now one has to identify the factors which indirectly disrupt tryptophan metabolism, or a substance which directly affects it. Dr. Maume examined pyrrolizinidic alcaloids in over one hundred white clover samples collected during the epidemic, but in vain. In his opinion, frequently occurring copper deficiency in the Norman livestock could make the situation worse. As in the study by M.R. Paradis, "Tryptophan and indole toxicity in ponies" (USA, 1989), Dr. Maume came to the conclusion that tryptophan is toxic only when ingested. Therefore, indole is the only toxic agent, produced when tryptophan is altered by intestinal flora. In this way, the passage of cynurenin is blocked, which causes nicotinamide shortages, pellagra symptoms, hypoexcretion of indolacetic acid and indole in urine, as well as liver biotransformation.

At this point, a presentation of general characteristics of tryptophan would be desirable. It is one of the twenty amino acids that make up proteins. It consists of lateral, aromatic and non-polar chains. It is indispensable because the animal organism does not seem to be able to synthesize the indole nucleus. It participates in the formation of niacin.

Tryptophan is largely responsible for the absorption of ultraviolet light in proteins (around 280 N-M). An average proportion of tryptophan in every protein is 1 to 100 amino acids. Some proteins, such as insulin, acetylcholine, or ribonucleas A do not have tryptophan.

Tryptophan is completely destroyed in the course of acid hydrolysis, when there is a strong concentration of reactive and increase in molecule movement, or an extreme pH and high temperature.

Biosynthesis of Tryptophan

The transformation of tryptophan into cynurenic and xanthurenic acids represents the fundamental stage of its catabolism.

The first step in this process is triggered by FE heminic tryptonasis pyrrolasis oxydasis. Cynurenic and xanthurenic acids are eliminated with urine in a variable proportion; its increase is one of the first signs of vitamin B6 deficiency. In the process of oxidation in the chromaffin cells of the intestinal mucous membrane, about 2% of tryptophan is transformed into oxytryptophan. Other extremely rapid chemical transformations take place in most of the tissues. Through decarboxidation in intestinal flora, tryptophan produces tryptamin and oxytryptamin or serotonin. Tryptamin and oxytryptamin are quickly destroyed by monoaminooxydasis (MAO) which transforms them respectively into indoleacetic acids (Auxin or plant growth hormone) and into oxy-5 indoleacetic acid, which inhibits decarboxylasis and which could act as a regulator in the synthesis of serotonin through retro-inhibition. The other substance that affects decarboxylase is phosphate pyridoxal (vitamin B6). The level of serotonin decreases along with a deficiency of vitamin B6. Serotonin has important vasocontractive properties. It reinforces intestinal peristaltis and plays a certain role in the brain. Like dopamine and noradrenaline, serotonin is a neurotransmitter; it reduces tension and acts as an alarming and controlling device in an adaptative situation. It controls aggression as well as the functioning of kidneys and blood coagulation.

As an aside, I would like to comment here on my 23-year-old mare, born from a thoroughbred father of the most prestigious provenance. He was totally uncontrollable and so were his few foals. Certain aspects of the mare's morphology, such as the unusual length of her kidneys, could qualify as pathological. Convinced of this fact, I was rather surprised to notice that at the European endurance championships in Florac in 1984, according to analyses carried out during and after the race, this mare’s level of serotonin was 8 times higher than that of all the other horses, i.e., about 1000 micrograms per liter. At that time, I was sure that serotonin causes nervousness. During a race of 4500 m in mountainous territory, this mare did not stop galloping. At the 90th kilometer, reached at the speed of 16 mph, a blood test showed a complete absence of lipomobilization. Having in mind the French mathematician René Thom’s catastrophe theory, I was sure that this mare possessed all the characteristics of an organism on an evolutionary edge which, once destabilized in specific circumstances (such as endurance breed), could evolve towards a new equilibrium.

But this is a completely different story...

Anyway, only this mare and her descendants, i.e., 2 daughters, 5 grand-daughters and 3 grandsons, survived grass sickness, as if the increased metabolism interacting with serotonin constituted some kind of protection.

The other possible transformation of serotonin is its conversion into melanic pigments. Melanins are as widely present in animal organisms as they are in the kingdom of plants. Our skin abounds in melanin (a macromolecule). The production of melanins requires enzymatic and non-enzymatic stages. In the latter, red pigments are formed by a lateral chain which becomes cyclic and forms a nucleus. Then, in brief, polymenization and formation of melanin take place. Pathologically, pigment produced in large quantities by melanomas is excreted with urine. Through the comparison of ultraviolet absorption spectra and the observation of melanogenesis, the formation of dehydroxindole, an ephemeral compound with physiological pH, was also proved. The synthesis of serotonin is influenced by light; thus we have an accumulation of serotonin during the day and of melatonin during the night.

Under the impact of intestinal flora, tryptophan is eliminated with urine in the form of indole. The latter abounds in urine of the Equidae species, whose gut flora are particularly active.

Tryptophan in mammals participates in numerous stages of biosynthesis of coenzymes to nicotinamid NAD and NAD+ (tryptophan oxygenasis). Quinolinic acid constitutes the final stage of these transformations. Nicotinic acid or vitamin PP intervenes in the process of oxydoreduction.

Acute hemolytic anemia after oral administration of tryptophan and indole in ponies

In this study, Mary-Rose Paradis shows that after oral administration of tryptophan (0.35 g/kg) in ponies, one can detect restlessness, increased respiratory rate, hemolysis, hemoglobinuria and bronchiolar degeneration. Two peaks in mean plasma tryptophan values were observed 6 and 12 hours after the administration. Analyses proved that from 5.84% to 16.75% of tryptophan was converted into indole. The compound 3-methylindole was not found. In ruminants, 3-methylindole is a toxic factor in the development of acute pulmonary edema and emphysema.

In the horse, 3-methylindole administered orally and intravenously causes severe obstructive pulmonary disease. Not all the species are susceptible to the pneumotoxic effects of 3-methylindole. However, decarboxylation of indoleacetic acid by anaerobic «Lactobacillus» species takes place in a large number of organisms. Among the factors involved in the production of 3-methylindole from dietary tryptophan are: the availability of tryptophan substrate, the percentage conversion of tryptophan to indoleacetic acid, and of indoleacetic acid to 3-methylindole, as well as the presence of a suitable microbial environment. Pneumotoxicity of 3-methylindole and indole further depends on monoxygenase toxification and detoxification processes in the lungs and other tissues.

Overall, the increase in bilirubin (4-5 fold), and in iron blood serum (2 fold) corresponds to hemolysis. A similar increase in phosphatase alkaline serum could suggest "cholestasis". The observed degeneration of tissues could have been caused by ischemia and anoxia rather than by a direct effect of hemoglobin (reduction of oxygen transmitted to cells). Indole inhibits cellular respiration in kidney and liver tissues, thus causing renal and hepatic anoxia.

The toxic metabolites indole and 3-methylindole have similar biochemical properties, as they are both non-polar, lipophilic and soluble in ether. The lipophilic qualities of these compounds could cause their adherence to cellular membranes. Indole and 3-methylindole attach themselves to red blood cells and break ciliated protozoa. Indole provokes hemoglobinuric nephrosis, but contrary to 3-methylindole, does not cause lung disease. Cattle are less prone to hemolitic effects of indole. The lipophilic properties of indole and 3-methylindole allow them to interact with one another and with cellular membranes, especially with the membranes of red cells, and to create Heinz bodies. Scientists described an identical syndrome in horses with methemoglobinuria, after the ingestion of red maple leaves. This case, linked with the ingestion of tryptophan, could be the result of several toxic agents, since the intestinal flora have the ability to convert tryptophan into indole and the latter is found in high concentration in green pastures.

Thus, one should investigate the substances supporting tryptophan as well as the other possible toxic agents and their behavior.

Question of Vitamins

Vitamin B6, in particular pyridoxale phosphate, act as enzymes, as transaminases in bacterium and in certain animals. The action of cotrasaminases consists of a reversible fixation of NH3 groups. · Pyridoxale phosphate is a coenzyme in decarboxyphases of certain amino acids and vice versa. · It participates in the process of degradation and synthesis of tryptophan in some microbes. Its intervention in the synthesis of amino acids explains its intervention in the synthesis of hemoglobin. · Vitamin B6 intervenes in the oxidation of fats. The relationship between B6 and fatty non-saturated acids explains the protective function of fatty acids against B6 vitamin deficiency.

Acid lactoses, obtained in the oxidation of pyridoxine, reinforce anti anemic protection and stimulate the production of folic acid. ·

It is important to keep in mind that vitamin B6 deficiency causes acrodynie, inhibits growth and produces convulsive attacks in rats. Avitaminosis also provokes microcytic and hypochromic anemia accompanied by convulsions and epileptic attacks, slowing of growth and vision problems in pigs. A few of these symptoms can be also observed in poultry. In humans, one applies vitamin B6 to skin, blood and neuromuscular system infections. It is very widespread in nutritional products.

Pellagra Preventive Vitamin PP: niacin, nicotinic-acid.

Vitamin PP can be found in tissues only in the form of denucleotide, nicotinic amid and adenin (NAD and NAD+).

Vitamin PP plays a fundamental role in intermediary metabolism. The two codehydrases I and II transport hydrogen and act as coenzymes in numerous dehydrases. They participate in many different reactions, thus their importance in the metabolism of carbohydrates, amino acids and lipids. Their secondary role is the metabolism of water and metals, in particular iron.

Avitaminosis provokes pellagrous digestive injuries and mental problems. Its endemic form appears after an excessive consumption of grain (corn), whereas its conditioned form appears in alcoholism. A long time ago it was noticed that vitamin PP deficiency does not afflict pigs, as their daily intake of food contains enough tryptophan. Vitamin PP is very widespread; it is used to treat skin and mucous ailments, porphynuria, or to provoke cephalic vasodilation. Principal anti-vitamins are: pyridine acid 3, sulphonic, acetyl-pyridine 3.

Although for a long time considered useless in animals and humans, B vitamins were known to be synthesized in the digestive tracts of all animals by micro-organisms and to participate in the nutrition of their host by turning the vitamin into a simple metabolite. This allowed one to detect certain vitamin deficiencies through a simple alteration of intestinal flora. There are also cases of asymptomatic hypovitaminoses, which at first sight resemble a state of perfect health. However, a poisoned organism can suffer from deficiency, the effects of which become independent from their causes, and while the latter disappear, the former develops into something completely different from classical avitaminosis. What could be a toxic factor in this case?

Let us examine two types of poisoning: plant poisoning (from beets) and chemical poisoning through nitrates.

Plant Poisoning: Case of Beet roots in Pigs

This analogy is not unwarranted, as it could serve as a model for red maple leaf syndrome. If beet soup, made of roots and leaves, is ingested when still fresh, it is harmless. However, if it is distributed 6 hours after cooking, it causes problems; it is usually most noxious after 12 hours. The animal staggers and falls, as if struck down. It can recover through vomiting, which corresponds to ancient theories on gastric troubles. In 1950, in Russia, Lukine proved that this condition is caused by alkaline nitrates after their transformation into sodium nitrates in plants. Nitrates poison both blood and the nervous system (beets abound in sodium). My ancestors in the Dorgogne region knew that a copper kettle in which they cooked sugar beets became verdigris through oxidation, if it was not properly cleaned.

Chemical Poisoning by Nitrates

Nitrates, such as chlorates, can cause death in all animals. Having ingested them, the animal becomes apathetic, anorexic, and suffers dyspnoea and stomach ache with diarrhea, bloody at times. It urinates frequently, its urine being brown-red (methemoglobinuria); then its kidneys become completely blocked. The heart rate slows down, the animal falls down and goes through convulsions before dying. At the autopsy, one can notice an unusually dark color of blood. The gastrointestinal tract is congested, whereas the liver and kidneys show injuries and degeneration.

Nitrates transform the ferrous iron of hemoglobin into ferric iron. This oxidation makes hemoglobin incapable of transporting oxygen. Since 70% of hemoglobin become methemoglobin, the animal dies if nitrates or chlorates are not gradually eliminated by kidneys. One can combat the poisoning with reductants, such methylene blue or sodium thiosulfate. Nitrates are widespread in nature, and animals need them up to a certain limit which is, unfortunately, often exceeded in modern farming.

Etiology of Grass Disease

In this study, we are interested in herbivores. However, one first has to consider micro-organisms, without which, in Pasteur’s words, life would not be possible, as the work of death would remain incomplete.

Micro-organisms decompose organic matter, producing nitrogen. Ammoniacal ferments transform organic nitrogen in humus into ammoniacal gas. Nitrous ferments transform ammonia into nitric acid. The latter gets combined with lime and potassium from soil and forms soluble lime or potassium nitrates which circulate with underground water and penetrate into root hairs. Nitrification, being simply an oxidation of ammonia, takes place at the temperature of 30°C with sufficient humidity. Capillaries carry water towards the surface when the soil dries up in spring or summer.

Apart from artificial fertilizers, horses give manure which ferments very quickly (immediate action of sodium, lime and potassium nitrates). In its solid form, animal manure contains nitrogen, potassium and phosphoric acid. As liquid, animal wastes provide nitrogen, in the form of urea, uric and hippuric acid, as well as potassium. Micro-organisms transform these compounds rapidly into ammoniacal carbonate, which breaks down into ammonia and carbonic gas. The latter is given off, as is ammonia.

Bacteria that can assimilate nitrogen from air live in leguminous plants (clover, alfalfa, peas). They feed on plants’ sap, because due to the lack of chlorophyl, bacteria are incapable of breaking down carbon oxide; in return, they give the plant nitrates that they assimilate (symbiosis). Each leguminous species has a symbiotic relationship with a specific bacteria species and cannot cooperate with any other.

Plants interact with ultraviolet radiation through the intermediary of cryptochromes, which detect the intensity and the direction of light. They condition the opening of stomata, i.e., pores enabling gas exchanges in photosynthesis. Cryptochromes control the biological clock, which assures a regular 24-hour rhythm for major biological functions. It is important to keep in mind that in the morning solar radiation is polarized circularly at 1% to the right. It could destroy amino acids. Also, let us not forget that tryptophan absorbs ultraviolet radiation in proteins.

Sensitive leguminous plants can activate an anti-oxidation enzyme. They have a characteristic bulge at the base of the leafstalk, a so-called pulvinus. This organ provokes very rapid movements, at least once a second, according to the intensity of sunlight. Nitrates, liberated or absorbed in this way, can be preserved in larger quantities in organic farms rather than in the traditional ones (organic specifications forbid harvesting at the beginning of the day). The roots of leguminous plants, forced to penetrate into the ground to be away from the light source, develop horizontal shoots as soon as they detect the presence of nitrates. A special gene is responsible for this process.

Nitrates and manure have a deep impact on flora, to the advantage of the leguminous plants which increase the overall production of nitrogen in herbaceous farming. Before achieving maturity, green grass can store up to one third of its nitrogen under the form of amids (e.g., silage). The addition of urea to the ration causes an increase in protids contained in the cattle rumen from 6.8% to 10.7%. This transformation is promoted by starch (such as in beets and maples).

And finally, the greenhouse effect augments plant production, as in real greenhouses. The increase in temperature stimulates microbes' activity and the return of carbon dioxide to the soil. Also, the decomposition by micro-organisms is quicker. Overall, the modification of precipitation systems affects both the plant and animal world.

Mary-Rose Paradis' Study—Critical Assessment

Mary-Rose Paradis' study does not put enough emphasis on kinetics in enzymatic reactions. Kinetic studies measure the speed of reactions and analyze their fluctuations depending on their environment: the concentration of substratum pH, temperature, the presence of inhibitors or activators. When one talks about reaction speed, one has in mind the initial speed which affects enzyme concentration. The latter is proportional to substrate concentration. There is a certain speed limit that cannot be exceeded. In a given moment, saturation takes place according to the quantity of available enzymes (in fact, this process is much more complicated as the catalysis goes through several stages). The aforementioned study does not sufficiently explain the role of inhibitors, in particular the reversible inhibition of B6. It should also make a clearer distinction between the digestive capacities of horses and cattle (cellulose, fibers, protein level, carbohydrates, etc.).

In our hypothesis, one can speak of an irreversible inhibition, characteristic of an adulterating agent: iron and hemoglobin oxidation by nitrates. Grass sickness functions through a threshold effect.

Cell metabolism results from about 2000 enzymatic reactions. The frequency and number of these activities depend on the genetic setup. Subject to genetic regulations, enzymes change their structure. By affecting cellular respiration, as shown by Mary-Rose Paradis, indole is at the core of the mechanism which controls organelles in the mitochondrial matrix. These organelles contain a complex system of transporters and enzymes from the respiratory chain, such as cytochromes. In this way, indole alters the functioning of the respiratory chain (ATP). Mitochondria possess their own DNA. Each cell has several hundred mitochondria which have the specific characteristic of being inherited only from the mother (brother, sister and maternal cousins). All of them have the same mitochondrial DNA, but its rate changes so rapidly that it can vary from one brother to another or even within one organism.

This peculiarity was already well known at the origin of the thoroughbred Arabic breed. Modern horse breeders, such as Lord Derby, Tesio, or Boussac also know this, practicing very risky in-breeding on mares. The whole history of modern thoroughbred horses is based on the super elite mare Pocahontas.

The genetic impact of the grass syndrome results in the development of certain weaknesses; it can serve us as a warning and an example:

1. One would have to know better the structure of mitochondria and their function in adiphocytes (see thermogenesis) in ponies, which differ from horses in their ability to store fats.

2. In 1931-32, the years of grass disease, Baron Rothschild's champion Brontome, excelling in classic races (2400 m), whose flexible and easy style always delighted the crowds, ended its brilliant sporting career. This tough and incredibly fast horse had to give up a fascinating career at the age of 4, because of a cough at the end of the spring.

And finally, mitochondria take up only 4% to 5% of the total muscular volume. In the course of endurance training, this number is tripled; that way, muscles have more oxygen and more "factories" to transform the former into ATP.

Discussion (see "Hemolysis on a big scale" by Mary-Rose Paradis)

Grass disease could be considered an asymptomatic fractal pathology. It is possible that we are dealing here with Turing structures (activators), inhibitors and diffusion carried out by lipids. A different approach towards this nonlinear, fractal pathology, resulting from ultraviolet radiation on a macroscopic scale (animal and plant kingdoms), could be borrowed from mathematician Benoit Mandelbrot.

The major characteristic of fractals is that they present a certain structure, no matter the scale at which they are examined. One can zoom in on them ad infinitum. Fractals do not necessarily produce identical elements. They can show different faces, depending on the scale as described in Laurent Nottale's book "La relativité dans tous ces états" (“Relativity in all its states”). The most developed living organisms are known for the tight interlocking of different organizational stages: atoms, genetic set-up, DNA, chromosomes, nuclei, cells, tissues, organelles... All these organizational levels coexist, each one of them having its own function and being irreplaceable. Each contains new information which may not be simply reduced to those carried by a preceding level. This information circulates among various structures, from the most basic to the most complex ones, and back, maintaining coherence in the system. Multicellular organisms such as we are cannot be reduced to one enormous cell. Still, our level of organization promotes the cellular form, protects it and increases its chances of survival. Human beings as well as horses are determined by quantum movements, genetic make-up and external factors. We are entities in which the microscopic and the macroscopic interact continuously; we are in a sense quantum macroscopic objects. The hierarchy of organizational levels spreads all over the living world; animal and plant kingdoms. From a single DNA thread to the whole planet, this global coherence stems from the accumulation of structures and information which circulate between them.

Thus, if considered on the most fundamental level, where space and time are implied, fractals could be a structural manifestation of the non-differentiability of Nature.

Translated into English by Anna K. Piotrowska, Harvard University, USA and Alika Laurent.

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