The Quantum Theory of Reproduction – How Unique is an Individual?

Abstract

Our understanding of nature’s way is founded on quantum mechanics. In its existence of over 80 years, quantum theory has been describing the physical world. The attraction of studying quantum mechanics is the perception of the conceptual structure of nature. This is aided by the mathematical structure that exposes the internal logic of the subject by inventing a notation that embeds the philosophy of the question. To describe how unique each individual is. A calculation method was applied. The uniqueness of an individual is one in two nonillion, octillion, septillion, sextillion, quintillion, quadrillion, trillion, billion, million and thousand. Individuals are indefinitely unique.

1. Introduction

The development of a human being begins with fertilization, a process by which two highly specialized cells, the spermatozoon from the male and the oocyte from the female, unite to give rise to a new organism, the zygote.

1.1 Oogenesis

In humans, the ovaries begin to form during embryonic formation in the first few weeks of the first trimester of pregnancy. It starts at the yolk sac, where the primordial germ cells originate, followed by migration along the hindgut to the gonadal ridge around the fifth and sixth week of the embryonic development [1, 2].

At around the sixth-week post-conception, the ovary contains around 26,000 oogonia. The number of oogonia increases by invasion and local proliferation, whereby the ninth week the number of oogonia would be around 250,000 in each ovary [3].

At around this stage of development, the first oogonia of the ovary enter meiosis, although most oogonia continue the mitotic cycle up to the time of the initiation of meiosis [4]. At the start of meiosis, the oogonia lose their ability to divide mitotically and will be described as oocytes [5]. The mitotic division of the oogonia finishes around the 20th week of gestation, where the formation of new oocytes ends [6].

The early development of the ovary and the relation between oogonia and somatic cells is a delicate process. Interfering with ovarian formation during this critical period may have consequences on the number of oocytes a girl is born with and thus on her fertility later on in life [7, 8, 9].

1.2 Spermatogenesis

From puberty to old age, male germ cells originate at the seminiferous tubules from a self-renewing stem cell pool. This spermatogenic process is a cascade of developmental stages that provide the mechanism of successful spermatogenesis [10].

There are intratesticular and extratesticular hormonal regulatory mechanisms for successful spermatogenesis in the testicular Leydig cells and the intertubular space, where thin septula divide the parenchyma into about 370 conical lobules. These lobules contain the seminiferous tubules, Leydig cells, and other cellular elements [10, 11].

The seminiferous tubules are coiled loops with two ends that open in the rete testis [11], where their secreted fluid is delivered to the epididymis. The seminiferous tubules consist of germinal epithelium and the peritubular tissue that include different developmental stages of germ cells, namely spermatogonia, primary and secondary spermatocytes, and spermatids that are located in the Sertoli cells [12].

The Sertoli cells have a specialized germinal epithelium in a basal and an adluminal zones, called “tight junctions” that form the blood-testis barrier of the testis. The germ cells pass through this barrier to the adluminal compartment, thus avoiding the possibly diffused nextraneous substances. With the advancement in age, Sertoli cells exhibit increasing amounts of lipid droplets as an indicator of the testicular “biological clock” [13].

Other functions that are attributed to Sertoli cells include nutrition of the germ cell, delivery of spermatids to the tubular lumen; a process that is described as spermiation; production of endocrine and paracrine factors that play a role in spermatogenesis, and secretion of androgen-binding protein to help maintain the duct system [14].

The process of germ cell development during spermatogenesis passes through various stages that include spermatogoniogenesis, meiosis, maturation of spermatocytes, spermiogenesis, and spermiation [15, 16, 17, 18, 19].

Spermatocytes go through meiosis with its associated change in chromatin configuration after spermatogonial division. These cells go through two divisions during meiosis and are called primary spermatocytes before the first division and secondary spermatocytes before the second division [20].

Spermiogenesis begins after spermatocytes complete two quick successive meiotic reductive divisions to produce haploid round spermatids. During cytodifferentiation of spermatids, there is condensation of the nuclear chromatin, formation of the acrosome cap, and the development of flagellum, to enable them to leave the germinal epithelium as the process of spermiation takes place [19, 20].

Leydig cells surround the testicular capillaries and secrete androgens, including testosterone. Testosterone activates the hypophyseal-testicular axis, masculinizes the brain, initiates and maintains spermatogenesis, and commands the differentiation of the male genital organs and secondary sexual characteristics [21].

Furthermore, Leydig cells have neuroendocrine activities added to their endocrine role as they express serotonin, catecholamine-synthesizing enzymes, neurohormones, cell adhesion molecules, components of the renin-angiotensin system, growth factors, and their receptors [19, 22].

In addition, Leydig cells are involved in autocrine and paracrine regulation mechanisms of the testes and are considered a part of the general neuroendocrine cell system, and their main regulator is the luteinizing hormone of the pituitary gland [22, 23].

The kinetics of spermatogenesis that exists throughout the reproductive life of man is due to the large reservoir of stem cell in the seminiferous tubules. The continuous process of spermatogenesis features cell differentiation and migration from the basal to the adlumin of the germinal epithelium [24, 25, 26].

In all parts of the germinal epithelium, there is a 16-day cycle of standard differentiation processes. This “space of time” is called “cycle of the seminiferous epithelium.” The production of an A type spermatogonium to become a mature spermatid requires 74 days. Mature spermatids leave the germinal epithelium as spermatozoa and pass through the epididymis. This additional transport takes another 12 days. Thus, the complete spermatogenetic cycle from spermatogonium to mature spermatozoa takes around 86 days [27, 28].

Spermatozoa, the products of spermatogenesis are unique in their shape and function making them capable of progression through the female genital tract to meet the oocyte at the lateral end of the Fallopian tubes. At this point, the acrosome reaction takes place. This enables the spermatozoon to pass through the zona pellucida of the female gamete and to get into the cytoplasm and merge with the pronucleus of the zygote [28].

The efficiency of spermatogenesis is questionable. Germ cell loss (oligozoospermia), percentage of malformed spermatozoa (teratozoospermia), and motility problems (asthenozoospermia) in the ejaculate can be extremely high. A high percentage of the developed germ cells are lost by apoptosis and degeneration. Only a fraction of the male germ cells reaches the ejaculation including a high percentage of malformed gametes. Thus, only around 10% of the spermatogenetic potential might serve the reproductive process [28].

The fecundability of the human race is compared poorly with laboratory animals. The mean elongate spermatid-Sertoli cell ratio is 3–4 for the human germinal epithelium versus 12 in rats [28]. The daily rate of spermatozoa production in humans is around 3–4 million per gram of testicular tissue. Accordingly, a higher number of ejaculate spermatozoa are expected in relation to the 20 million spermatozoa per ml as considered a normal value by the WHO [29].

Recent observations report a recent decline of sperm counts in the ejaculates of healthy individuals. This might be due to detrimental prenatal factors including hormones and their metabolites in the drinking water that may adversely affect the different internal and external processes of spermatogenesis in the seminiferous tubules [30].

The intrinsic factors include testosterone, neuroendocrine substances, and growth factors (IGF1, TGFβ, NGF) that represent an independent intratesticular regulation of spermatogenesis. The extrinsic influence is provided by the pulsatile secretion of gonadotropin-releasing hormone by the hypothalamus and the gonadotrophins of the pituitary gland. Other factors include nutrive substances, drugs, different toxic substances, and radiation that may adversely affect testicular function [30, 31, 32, 33, 34].

2. How unique is an individual?

Each human individual is unique to an extreme. Each zygote is the result of a certain probability. At around the fifth month of development, the ovaries of the fetus contain around 12 million oogonia [6]. A single man’s ejaculation contains around 422 million spermatozoa [35], only one of which may fertilize an ovum.

The probability of a certain spermatozoon fertilizing a certain oocyte follows the rule of statistically independent events. For example, if a coin and a dice are tossed at the same time, the probability of getting a head with the coin and a six with the dice are quite independent of each other. The probability of a head and a six at the same time = p (H) x p [6], that is:

P (H) x P (6) = 1/2 x 1/6 = 1/12.

Listing an array of possible results can check this:

H1, H2, H3, H4, H5, H6.

T1, T2, T3, T4, T5, T6.

P (H + 6) = 1/12.

This is known as the multiplication law of probability.

To extend this to the probability of a given spermatozoon fertilizing a given oocyte and resulting in the birth of a baby to a certain couple is as follows:

P (embryo) = P (oocyte) x P (spermatozoon).

= $\frac{1}{12x{10}^6}$ x $\frac{1}{422x{10}^{6}x1.93x52x62}$

= $\frac{1}{3.17x{10}^{20}}$

= $3.17x{10}^{-20}$

where 12 x 106: average number of oogonia [6], 422 x 106: average number of spermatozoa per ejaculate [35], 1.93: average frequency of sexual intercourse per week [36], 52: number of weeks per year, 62: mean male reproductive life span = average life span [37]—the average age of adolescence [38].

On one hand, the figure of (3.17 x 10^–20) is only each individual’s chance of being the descendant of a given couple in our present time. On the other hand, each individual could have been born in a different period that may date back to a time that might be easily defined. The true figure for this notation should cover all possible combinations since human life started and between all men and women that have ever existed.

To evaluate this, it is necessary to estimate the total number of people who ever lived. The magnitude of present-day population is impressive. Yet, the inhabitants of the world today are only a certain percentage of the populations of earlier periods. It is necessary, therefore, to include the evolutionary and growth rate factors in the notation.

As to the evolutionary factor, in the past four decades, the phylogeny of the Hominidae has increasingly become the focus of investigation. On the Geologic Time Scale, early and modern humans existed in the late Pliocene Epoch of the Tertiary Period and in the Pleistocene and Recent Epoch of the Quaternary Period of Cenozoic Era (Age of Mammals).

Although the fossil record of the last 200,000 years presents an unmistakable well-defined picture of the evolution of our modern species, Homo sapiens, the final stages leading to contemporary humans present several unresolved problems. The grade of sapiens contains at least two contrastingly different anatomical types; the bulkily built and heavily muscled Neanderthals and the slim-bodied Cro-Magnons. Moreover, the traditional steps from the Homo erectus level of humans to the H. sapiens grade have yet to be disentangled [39].

The first undeniable hominid—Australopithecus—existed about 4 million years ago. The australopithecines shaded imperceptibly into Homo habilis, who integrated slowly into Homo erectus, with the latter ultimately transforming into modern H. sapiens. However, spirited debate exists over which of the australopithecines occupy a prominent place in the direct ancestry of humans.

It has been suggested that vegetarian Australopithecus robustus perished without leaving any descendants and that Australopithecus africanus was the forebear of a more advanced hominid. The discovery in 1972 of the “1470” skull and in 1975 of the fossil jaws and teeth that have been classified as the remains of Homo habilis and dating back between 1.8 and 3.8 million years, supposing that an older australopithecine gave rise to Homo habilis.

The candidate for such an ancestor appears to be the fossil hominid uncovered in 1973 that has been called “Lucy,” delineated as the new species Australopithecus aferensis. At present, it is safe to state that the A. aferensis remains, dating between 3 and 4 million years ago, constitute the earliest definitive members of the family hominidae [39].

The first undeniable hominid—Australopithecus—existed about 4 million years ago. The Australopithecus shaded imperceptibly into Homo habilis, who intern graded slowly into Homo erectus, with the latter ultimately transforming into modern H. sapiens. However, a spirited debate exists over which of the Australopithecines occupy a prominent place in the ancestry of humans.

It has been suggested that the vegetarian Australopithecus robustus perished without leaving any descendants and that Australopithecus africanus was the forbear of a more advanced hominid. The discovery in 1972 of the “1470” skull and 1975 of the fossil jaws and teeth that were between 1.8 and 3.8 million years, supposing that the older australopithecine gave rise to Homo habilis.

The candidate for such an ancestor appears to be the fossil hominid uncovered in 1973 that has been called “Lucy”, delineated as the new species Australopithecus aferensis. At present, it is safe to state that the A. aferensis, dating between 3 and 4 million years ago, constitute the earliest definitive members of the family hominidae [39].

As to the growth factor, the human population has undergone three phases of exponential growth. In the first phase of human history, from our species’ origin to about 10,000 years ago, the population grew slowly as people existed as hunter gatherers. Cultivation of plants and animal husbandry may have allowed our agricultural revolution and the second phase of exponential growth, from about 8000 _B.C. to about 1750 _A.D.

The industrial revolution, which occurred about 1850 _A.D., promoted the third phase of exponential growth that continues today [40]. Generally, the human population growth since prehistoric times displays a classic J-shaped exponential curve. This curve suggests that the total number of people alive today is approximately equal to the total number who have ever lived and died before us. As the present global population totals 6.3 people, the total number of people who ever lived is over 12.6 billion [41].

To extend this to the probability of a given spermatozoon fertilizing a given oocyte and resulting in the birth of any baby that has ever lived is as follows:

= $\frac{1}{3.17x{10}^{20}}x\frac{1}{6.3x{10}^9}$

where 6.3 x 10⁹: total number of males/females who ever lived [41].

= $\frac{1}{5.04x{10}^{30}}$

= 5.04$x{10}^{-30}$

Approximately= $5x{10}^{-30}$

Or 1 in 200,000,000,000,000,000,000,000,000,000

A two nonillion, octillion, septillion, sextillion, quintillion, quadrillion, trillion, billion, million, and thousand is an indefinitely large statistic! Mathematics used this way is irreplaceable in the pursuit of meaning in which fascination lies. But meaning does not reside in the mathematical symbols. It resides in the cloud of thought enveloping these symbols. The most important dictum in quantum mechanics is that what you can measure is what you can know [42]. To perceive the aforementioned question as inherently meaningless is what quantum mechanics teaches us.