This book is called Erwin Schrödinger's philosophical testament. It outlines the worldview of a natural scientist who has had a significant impact on the development of modern physics. Everything is possible exactly until a choice is made. Imagine that you have a box with a radioactive core and a container of poisonous gas. The probability that the nucleus will disintegrate and trigger the mechanism that opens the container is 50%. If you put a cat in this box and close it, the Schrödinger paradox will arise. According to quantum mechanics, if no observation is made over the nucleus, then its state is described by the mixing of two states - a disintegrated and non-disintegrated nucleus, therefore, a cat sitting in a box is both alive and dead at the same time. For those who want to know more, for those who dare to find out what exactly is the paradox of Schrödinger's theory, for those who want to know what life is from the point of view of physics, the great scientist wrote his last and best work.
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The given introductory fragment of the book Quantum Cat of the Universe (Erwin Schrödinger, 1944,1961) provided by our book partner - Liters company.
What is life?
Introduction
A free man thinks about nothing so little as about death, and his wisdom consists in thinking not about death, but about life.
Spinoza, Ethics, Part IV, Theor. 67
It is generally accepted to think that a scientist should know a certain area of \u200b\u200bscience perfectly first-hand, and therefore it is believed that he should not write on such issues in which he is not an expert. This is viewed as a noblesse oblige question. However, in order to achieve my goal, I want to abandon noblesse and ask, in this regard, to release me from the obligations arising from this. My apologies are as follows.
We have inherited from our ancestors a keen desire for unified, all-encompassing knowledge. The very name given to the highest institutes of knowledge - universities - reminds us that since antiquity and for many centuries, the universal character of knowledge was the only one in which there could be complete confidence. But the expansion and deepening of diverse branches of knowledge over the past hundred wonderful years has presented us with a strange dilemma. We clearly feel that we are only now beginning to acquire reliable material in order to combine everything that we know into one whole; but on the other hand, it becomes almost impossible for one mind to fully master more than any one small special part of science.
I do not see a way out of this situation (so that our main goal is not lost forever), if some of us do not dare to take up the synthesis of facts and theories, even if our knowledge in some of these areas was incomplete and obtained from second hand and at least we were in danger of appearing to be ignorant.
Let this be my excuse.
Difficulties with language are also of great importance. Everyone's native language is like a well-fitted clothing, and one cannot feel completely free when your language cannot be relaxed and when it needs to be replaced by another, new one. I am very grateful to Dr. Inkster (Trinity College, Dublin), Dr. Padraig Brown (St. Patrick's College, Maynooth), and finally (but no less than others), Mr. S.K. Roberts. It gave them a lot of worries to fit a new outfit on me, and this was aggravated by the fact that sometimes I did not want to give up my somewhat "original" own style. If any of it has survived, despite the desire of my friends to soften it, then it should be attributed to me, and not to their account.
It was originally intended that the subheadings of numerous sections would have the character of summary margins, and the text of each chapter would have to be read in continue.
I am greatly indebted to Dr. Darlington and the publisher of Endeavor for the illustration clichés. They retain all the original details, although not all of these details are relevant to the content of the book.
Dublin, September 1944. E. Sh.
The approach of the classical physicist to the subject
Cogito, ergo sum.
DescartesGeneral nature and objectives of the study
This small book arose out of a course of public lectures given by a theoretical physicist to an audience of about 400 people. The audience almost did not diminish, although from the very beginning they were warned that the subject of presentation was difficult and that lectures could not be considered popular, despite the fact that the most terrible tool of physics - mathematical deduction - can hardly be applied here. And not because the subject is so simple that it can be explained without mathematics, but rather the opposite - because it is too confusing and not quite accessible to mathematics. Another feature that creates at least appearance popularity, it was the intention of the lecturer to make the basic idea associated with biology and physics clear to both physicists and biologists.
Indeed, despite the variety of topics included in the book, as a whole it should convey only one thought, only one small explanation to a large and important question. In order not to deviate from our path, it will be useful to outline our plan in advance.
A big, important and very often discussed question is the following: how can physics and chemistry explain those phenomena in space and time that take place inside a living organism?
The preliminary answer that this small book will try to give and develop can be summarized as follows: the apparent inability of modern physics and chemistry to explain such phenomena does not at all give any reason to doubt that they can be explained by these sciences.
Statistical physics.
The main difference in structure
The previous remark would be very trivial if it was only intended to stimulate hope to achieve in the future what has not been achieved in the past. It, however, has a much more positive meaning, namely, that the failure of physics and chemistry to date to give an answer is fully explainable.
Thanks to the skillful work of biologists, mainly geneticists, over the past 30 or 40 years, enough has now become known about the actual material structure of organisms and about their functions, to understand why modern physics and chemistry could not explain the phenomena in space and time that occur inside living things. organism.
The arrangement and interaction of atoms in the most important parts of the body are fundamentally different from all those arrangements of atoms with which physicists and chemists have dealt with in their experimental and theoretical research so far. However, this distinction, which I have just called fundamental, is of a kind that can easily seem insignificant to anyone except a physicist, saturated with the idea that the laws of physics and chemistry are statistical through and through. It is from a statistical point of view that the structure of the most important parts of a living organism is completely different from any piece of matter that we, physicists and chemists, have dealt with until now, practically - in our laboratories and theoretically - at our desks. Of course, it is difficult to imagine that the laws and rules, which we have discovered, were directly applicable to the behavior of systems that do not have the structures on which these laws and rules are based.
It cannot be expected that a non-physicist could encompass (let alone evaluate) all the difference in "statistical structure" formulated in terms as abstract as I have just done. To give life and color to my assertion, let me first draw attention to what will be explained in detail later, namely, that the most essential part of a living cell - the chromosomal filament - can reasonably be called an aperiodic crystal. In physics, we have dealt only with periodic crystals so far. For the mind of a simple physicist, they are very interesting and complex objects; they constitute one of the most fascinating and complex structures with which inanimate nature confuses the intelligence of a physicist; however, in comparison with aperiodic crystals, they seem somewhat elementary and boring. The difference in structure here is the same as between ordinary wallpaper, which repeats the same pattern at the correct frequency over and over again, and an embroidery masterpiece, say, Raphael tapestry, which does not give boring repetition, but complex, consistent and full of meaning. drawing drawn by the great master.
By calling a periodic crystal one of the most difficult objects of research, I had in mind the physicist proper. In the study of more and more complex molecules, organic chemistry has indeed come much closer to that “aperiodic crystal” which, in my opinion, is the material carrier of life. Therefore, it is not very surprising that the organic chemist has already made a large and important contribution to the solution of the problem of life, while the physicist has contributed almost nothing.
A naive physicist's approach to the subject
After I have thus briefly indicated the general idea, or rather the main purpose of our investigation, let me describe the very line of attack.
I intend first to develop what you might call the "naive physicist's notions of an organism." These are the ideas that can arise in his mind if, having studied his physics and, in particular, its statistical foundations, a physicist begins to think about organisms, about their behavior and life and honestly asks himself - can he, based on his knowledge , from the standpoint of their relatively simple, clear and modest science, to make some useful contribution to this problem.
It turns out that he can do it. The next step should be to compare the theoretical expectations of the physicist with biological facts. Here it will be found that, although on the whole his ideas seem quite reasonable, they nevertheless need to be significantly improved. In this way, we will gradually move closer to the correct point of view, or, more modestly, to the point of view that I consider correct.
Even if I was right about this, I do not know if my path is really the best and simplest. But, in short, this was my path. The "naive physicist" was myself. And I cannot find any better and clearer path towards the goal than my own, albeit perhaps a winding path.
Why are atoms so small?
A good way to develop the "naive physicist's beliefs" is to first ask a strange, almost ridiculous question: Why are atoms so small? And they are really very small. Every little piece of substance we touch in everyday life, contains a huge number of them. Many examples have been offered to make this clear to the general public, but there hasn't been a single more telling example than the one given by Lord Kelvin: suppose you can label all the molecules in a glass of water; after that, you pour the contents of the glass into the ocean and mix the ocean thoroughly so as to distribute the marked molecules evenly in all the seas of the world; if you further take a glass of water anywhere, anywhere in the ocean, you will find in this glass about a hundred of your marked molecules.
The actual sizes of the atoms are between approximately 1/5000 and 1/2000 of the wavelength of yellow light. This comparison is of particular importance because the wavelength roughly indicates the size of the smallest particle that can still be seen under a microscope. Thus, we see that such a particle contains thousands of millions more atoms.
So why are atoms so small?
It is clear that this question is a workaround, since in reality it is not aimed at the size of atoms.
It concerns the size of organisms and in particular the size of our own body. Indeed, an atom is small when it is compared to our civilian measure of length, say, a yard or a meter. In atomic physics, the so-called angstroms (abbreviated Å) are accepted, which are equal to 10–10 m, or in the decimal image -0.0000000001 m. Atomic diameters lie between 1 and 2 Å. Civil units (in comparison with which atoms are so small) are directly related to the size of our body. There is a story that attributes the origin of the yard to the humor of an English king. When the members of his council asked him what unit of length should be set, he stretched out his hand to the side and said: "Take the distance from the middle of my chest to the tips of my fingers, it will be just." True or not, this story has a lot to do with our question. Naturally, the king wanted to indicate a length comparable to the length of his body, since he knew that otherwise the measure would be very inconvenient. For all his fondness for angstroms, the physicist would still prefer to be told that his new suit would require 6 1/2 yards of tweed rather than 65,000 million angstroms of tweed.
Thus, it is clear that in reality our question concerns not one size, but the ratio of two sizes - our body and the atom - taking into account, of course, the undoubted primary and independent existence of the atom. The question really is: why do our bodies have to be so large compared to atoms?
I think that many who passionately study physics or chemistry have more than once regretted that all our senses, which constitute a more or less essential part of our body, and therefore (taking into account the considerable size of the given ratio) themselves composed of innumerable atoms, turn out to be too coarse to perceive the impact of a single atom. We can neither see, nor hear, nor feel individual atoms. Our hypotheses about atoms are far removed from direct perception of our enormous senses, and these hypotheses cannot be verified by direct observation.
Does it have to be like this? Are there substantial grounds for this? Is it possible to explain this position by some basic principle in order to be convinced and understand that nothing else is compatible with the laws of nature?
This is already a problem that a physicist is able to figure out completely. The answer to all questions will be yes.
The work of the body requires precise physical laws
If this were not the case, if the human body were so sensitive that a few atoms or even a single atom could make a noticeable impression on our senses - oh, heaven, what life would be like! One point must be emphasized: an organism of this kind would surely be incapable of developing that ordered thought which, after going through a long series of earlier stages, finally produced, among many other ideas, the very idea of \u200b\u200bthe atom.
Although we choose only this example as an illustration, all the following considerations are also quite applicable to the function of other organs (and not just the brain and sense organs). However, there is only one and only thing of particular interest to us in ourselves, and that is what we can feel, think and understand. With regard to those physiological processes that are responsible for our thoughts and feelings, all other processes in the body play an auxiliary role, at least from the human point of view, if not from the point of view of objective biology. Moreover, our task will be greatly facilitated if we choose for research such a process that is accompanied by subjective events, although we do not know the true nature of this parallelism. Indeed, in my opinion, the nature of this parallelism lies outside the realm of natural sciences and, quite possibly, beyond any human understanding.
Thus, we are faced with the following question: why should our brain and the system of sensory organs associated with it necessarily consist of such an immensely large number of atoms so that physiologically variable states of the brain could be in close and intimate correspondence with a highly developed thought? For what reasons, this correspondence is incompatible with such a delicate and sensitive structure of the entire mechanism (or at least its peripheral parts), which would allow, when interacting with the environment register and respond to the push of a single atom from the outside?
This is based on the fact that the phenomenon that we call thought is itself something ordered and is applicable only to such material, that is, to perceptions or experiences, which also have a certain degree of ordering. This has two consequences: 1) the physical organization, in order to be in close correspondence with the thought (as, for example, my brain with my thought), must be a very well-ordered organization, which means that the events occurring in the brain must obey strict physical laws, at least with a very high degree of accuracy; 2) the physical impressions made on this physical, well-organized system by bodies from the outside obviously correspond to the cognition and experience of the corresponding thoughts, forming, as I mentioned, their material. Consequently, physical interactions between our system and others should, as a rule, themselves possess a certain degree of physical order, or, in other words, they must also obey strict physical laws with a certain degree of accuracy.
Physical laws are based on atomic statistics and therefore only approximate
Why can't all this be done if the organism consists only of a moderate number of atoms and is already sensitive to the effects of one or a few atoms?
Because we know that all atoms all the time go through completely disordered thermal movements, which, so to speak, oppose their ordered behavior and do not allow the events that occur between small numbers of atoms to be attributed to any recognizable law. Only in the combination of a huge number of atoms do statistical laws begin to operate and control the behavior of these associations with an accuracy that increases with an increase in the number of atoms involved in the process. It is in this way that events acquire truly regular features. All physical and chemical laws that are known to play an important role in the life of organisms belong to this statistical category. Every other kind of regularity and order that one can imagine is continuously violated and made invalid due to the non-stop thermal motion of atoms.
The accuracy of physical laws is based on the large number of atoms involved
Let me try to illustrate this with a few examples, chosen to some extent randomly and, perhaps, not the best, but which can be referred to the reader who first gets acquainted with this state of affairs - a position that is modern physics and chemistry is as fundamental as, say, in biology, the fact that organisms are composed of cells, or as Newtonian laws in astronomy, or even as a series natural numbers 1, 2, 3, 4, 5 ... in mathematics. A first-time acquaintance with the question should not expect that from the next few pages he will receive a complete understanding and appreciation of the subject, which is associated with the famous names of Ludwig Boltzmann and Willard Gibbs and is treated in manuals called "statistical thermodynamics".
A. First example (paramagnetism)
If you fill an elongated quartz tube with oxygen and place it in a magnetic field, you will find that the gas is magnetized. Magnetization is based on the fact that oxygen molecules are small magnets and tend to align themselves parallel to the field, as happens with a compass needle. But you shouldn't think that they all really turn in parallel. For if you double the field strength, you get a double magnetization in your oxygenated body, and this proportionality will continue until the field strength is extremely high - the magnetization increases to the same extent as the field strength you apply.
This is a particularly clear example of a purely statistical law. The orientation that this field seeks to induce is continually counteracted by thermal motion, which works in favor of random orientation. The result of this struggle is in reality only that acute angles between the axes of the dipoles and the direction of the field prevail over obtuse ones. Although individual atoms continuously change their orientation, on average they give (due to their huge number) a constant slight predominance of orientation in the direction of the field and in proportion to it. This ingenious explanation belongs to the French physicist P. Langevin. It can be verified in the following way. If the observed weak magnetization is indeed the result of two competing tendencies, namely the magnetic field, which tends to comb all the molecules in parallel, and the thermal motion, which produces a random orientation, then it is possible to increase the magnetization without strengthening the field, but by weakening the thermal motion. that is, by lowering the gas temperature. This was confirmed by experiment, which shows that magnetization is inversely proportional to absolute temperature, in quantitative agreement with theory (Curie's law). Modern experimental technology makes it possible, by lowering the temperature, to bring the thermal motion to such a small extent that the directional tendency of the magnetic field can manifest itself, if not completely, then sufficiently to produce a substantial part of the "complete magnetization".
In this case, we can no longer expect that doubling the field strength will also double the magnetization. The latter will increase less and less with increasing field, approaching what is called “saturation”. This expectation is also quantitatively confirmed by experiment.
Note that this behavior is entirely dependent on the vast number of molecules that co-operate to create the observed magnetization. Otherwise, magnetism would not be constant at all and would change completely irregularly from one second to the next, testifying to the vicissitudes of the struggle between the field and the thermal motion.
B. Second example (Brownian motion, diffusion)
If you fill the bottom of a closed glass vessel with a mist of tiny droplets, you will see that the upper limit of the fog gradually decreases at a very specific rate, depending on the viscosity of the air and the size and specific gravity of the droplets. But if you look at one of the droplets under a microscope, you will see that it does not descend at a constant speed, but performs a very irregular movement, the so-called Brownian movement, which only on average corresponds to a constant decrease.
These droplets, although they are not atoms, are already small and light enough to feel the jolts of single molecules that are continuously threshed on their surface. Droplets interpreted in this way can only on average follow the influence of gravity.
This example shows what amazing and disordered impressions we would get if our senses were susceptible to the impact of just a few molecules.
There are bacteria and other organisms so small that they are highly susceptible to this phenomenon. Their movements are determined by the thermal whims of the environment; they have no choice. If they have their own mobility, then they can still move from one place to another, but only with certain difficulties, since the heat movement hurls them like a small boat in a stormy sea.
The phenomenon of diffusion is very similar to Brownian motion. Imagine a vessel filled with a liquid, say water, with a small amount of some colored substance dissolved in it, such as potassium permanganate, but not in a uniform concentration, where the dots represent the molecules of the dissolved substance (permanganate) and where the concentration decreases from left to right. If you leave this system alone, a very slow process of "diffusion" sets in. Permanganate spreads from left to right, that is, from a place of higher concentration to a place of lower concentration, until finally it is evenly distributed throughout the water.
What is remarkable about this rather simple and apparently not particularly interesting process is that it is in no way associated with any tendency or force that, as one might think, pulls the permanganate molecules from the area of \u200b\u200bgreater tightness to the area of \u200b\u200bless tightness, just as, for example, the population of a country settles in that part where there is more space. Nothing like this happens with our permanganate molecules. Each of them behaves completely independently of all other molecules, with which it very rarely meets.
Each of them, both in the area of \u200b\u200bgreater tightness and in the freer part, experiences the same fate. It is continuously pushed by water molecules, and thus it gradually moves in a completely unpredictable direction - sometimes towards a higher concentration, sometimes towards a lower concentration, and sometimes obliquely. The nature of the movement she performs has often been compared to the movement of a person who has been blindfolded over a large area and who wants to "walk" but does not adhere to a certain direction and thus continuously changes the line of his movement.
The fact that the random movement of permanganate molecules should nevertheless cause a regular current towards a lower concentration and eventually lead to an even distribution seems at first glance perplexing, but only at first glance. On careful examination of thin layers of almost constant concentration, one can imagine how the permanganate molecules, which are currently contained in a certain layer, by random movements will in fact move with equal probability both to the right and to the left. But precisely because of this, the surface separating two adjacent layers will be crossed by a larger number of molecules coming from the left than in the opposite direction. This will happen simply because there are more randomly moving molecules on the left than there are on the right, and as long as this is so, there will be regular movement from left to right until finally there is a uniform distribution.
If these considerations are translated into mathematical language, then we get the exact law of diffusion in the form of a partial differential equation, the explanation of which I will not bother the reader, although its meaning in ordinary language is also quite simple. The strict "mathematical accuracy" of the law is mentioned here in order to emphasize that its physical accuracy must nevertheless be checked in each specific case. Based on pure chance, the fairness of the law is only approximate. If there is, as a rule, a fairly good approximation, then this is only due to the huge number of molecules that participate in the phenomenon. The smaller their number, the more random deviations we should expect, and under favorable conditions, these deviations are actually observed.
B. Third example (measurement accuracy limits)
The last example we will give is closely similar to the second, but is of particular interest. A light body suspended on a long thin thread and in equilibrium is often used by physicists to measure weak forces deflecting it from this position, that is, to measure electrical, magnetic or gravitational forces applied so as to rotate it around a vertical axis (light body must, of course, be appropriately selected for each specific purpose). Ongoing attempts to improve the accuracy of this much used "torsion balance" device have encountered a curious limit that is extremely interesting in itself. Choosing lighter and lighter bodies and a thinner and longer thread to make the balance sensitive to weaker forces, we reached the limit when the suspended body became already sensitive to the impacts of the thermal movement of the surrounding molecules and began to perform a continuous irregular "dance" around its equilibrium positions, a dance very similar to the drop quiver in the second example. Although this behavior does not yet put an absolute limit on the accuracy of measurements obtained with such balances, it does impose a practical limit. The uncontrollable effect of thermal motion competes with the force to be measured and devalues \u200b\u200ba single observed deviation. You have to repeat your observations many times to neutralize the effect of the Brownian motion of your instrument. This example, I think, is particularly illustrative, for our senses are, after all, also a kind of instrument. We can see how useless they would be if they became too sensitive.
The √n rule
Enough examples now. I am simply adding that there is not a single law of physics or chemistry that has to do with the organism or its interaction with the environment that I could not choose as an example. A detailed explanation may be more complex, but the main point would always be the same, and thus the further description would become monotonous.
But I would like to add one important quantitative provision concerning the degree of imprecision that should be expected in any physical law. This is the so-called √n law. I will first illustrate it with a simple example, and then I will generalize it.
If I say that a certain gas at a certain pressure and temperature has a certain density, then I can express this by saying that inside a certain volume (which is suitable in size for an experiment) there are, under these conditions, just n gas molecules. If at some point in time you can check my statement, then you will find it inaccurate, and the deviation will be of the order of √n. Therefore, if n \u003d 100, you would find the variance to be about 10. So the relative error here is 10%. But if n \u003d 1 million, you would probably find the variance to be about 1000, and thus the relative error is 1/10%. Now, roughly speaking, this statistical law is very general. The laws of physics and physical chemistry are imprecise within a probable relative error of order 1 / √n, where n is the number of molecules jointly participating in the manifestation of this law - in its implementation within that region of space or time (or both) that is subject to consideration or serves for a specific experiment.
You see from this again that an organism must have a relatively massive structure in order to enjoy the well-being of quite precise laws, both in its inner life and in its interaction with the outside world. Otherwise, the number of particles involved would be too small and the "law" is too imprecise. A particularly important requirement is the square root. Because, although a million is a fairly large number, nevertheless, an accuracy of 1 in 1000 is not overly good if the essence of the matter claims to be a "Law of Nature".
The mechanism of heredity
Das Sein ist ewig; denn Gesetze
Bewahren die lebendgen Schätze,
Aus weichen sich das All geschmückt.
GoetheThe classical physicist's expectation, while far from trivial, turns out to be wrong
So, we came to the conclusion that organisms with all biological processes taking place in them must have a very "polyatomic" structure, and it is necessary for them that random "monoatomic" phenomena do not play too large a role in them. It is essential, says the "naive physicist", that the organism can, so to speak, have sufficiently precise physical laws on which it can build the organization of its extremely regular and well-ordered work. To what extent are these conclusions reached, biologically speaking, a priori (that is, from a purely physical point of view) applicable to real biological facts?
At first glance, it might seem that these conclusions are rather trivial. A biologist, say, 30 years ago, could argue that although it is quite appropriate for a popular lecturer to emphasize the importance of statistical physics in the body, as elsewhere, this point is still, perhaps, an overly hackneyed truth. Indeed, not only the body of an adult individual of any highly developed species, but also each cell contains a "cosmic" number of individual atoms of all kinds. And every single physiological process that we observe inside the cell or in its interaction with the external environment seems - or seemed 30 years ago - to involve such a huge number of single atoms and single atomic processes that the exact fulfillment of all the laws of physics and physical chemistry related to it would be guaranteed even with the very high requirements of statistical physics in relation to "large numbers". I have just illustrated these requirements with the √n rule.
We now know that such a view would be wrong. As we shall now see, incredibly small groups of atoms, too small to exhibit precise statistical laws, play a dominant role in highly ordered and regular phenomena within a living organism. They control the visible signs of a large scale, which the organism acquires during its development, they determine important features of its functioning, and in all this very clear and strict biological laws are revealed.
I must begin by briefly summarizing the position that holds in biology and, more narrowly, in genetics; in other words, I must summarize the current state of knowledge in an area where I am not an authority. This cannot be avoided, and therefore I apologize, especially to any biologist, for the amateurish character of the presentation. On the other hand, I ask permission to present the prevailing views to you in a more or less dogmatic way. The "poor" theoretical physicist cannot be expected to do anything like a competent review of experimental data consisting of a large number of long and magnificently intertwined series of crossing experiments, conceived with unprecedented ingenuity, on the one hand, and direct observation of living cell, carried out with all the sophistication of modern microscopy, on the other.
Hereditary cipher code (chromosomes)
Let me use the word "pattern" of an organism in the sense in which a biologist calls it a "plan in four dimensions," meaning not only the structure and functioning of the organism in adulthood or at any other definite stage, but the organism in its ontogenetic development, from a fertilized egg cell to the stage of maturity, when it begins to multiply. It is now known that this whole holistic plan in four dimensions is determined by the structure of just one cell, namely, the fertilized egg. Moreover, we know that it is mainly determined by the structure of only one small part of this cell, its nucleus. Such a nucleus in the usual "resting state" of the cell is represented as a network of chromatin, distributed in a vesicle inside the cell. But in the vital processes of cell division (mitosis and meiosis, see below), it can be seen that the nucleus consists of a set of particles, usually in the form of threads or rods and called chromosomes, the number of which is 8 or 12, or, for example, in humans, 48. But in reality I would have to write these (taken as an example) numbers as 2 × 4, 2 × 6 ...., 2 × 24, and speak of two sets in order to use this expression in the usual meaning in which it is used biologist. Because while the individual chromosomes are sometimes distinctly distinguishable and individualized in shape and size, the two sets are almost completely similar to each other. As we will see shortly, one set comes from the mother (egg cell) and one from the father (fertilizing sperm). It is these chromosomes, or perhaps only the axial or skeletal thread of what we see under the microscope as a chromosome, that contain, in the form of a kind of cipher code, the entire "plan" of the future development of the individual and his functioning in a mature state. Each complete set of chromosomes contains the entire cipher, so there are usually two copies of the latter in the fertilized egg cell, which represents the earliest stage of the future individual.
By calling the structure of chromosome strands a cipher code, we mean that an all-encompassing mind, like the one that Laplace once imagined and to which every causal connection would be directly open, could, based on the structure of the chromosomes, tell whether an egg would develop under favorable conditions in black rooster or speckled chicken, fly or maize plant, rhododendron, beetle, mouse or human. To this we can add that the appearance of various egg cells is very often remarkably similar, and even when this is not so (as in the case of huge eggs of birds and reptiles), the difference is still not so much in the essential structures as in that nutrient material. , which is added in these cases for obvious reasons.
But the term "encryption code" is, of course, too narrow. Chromosomal structures serve at the same time as a tool for carrying out the development, which they also portend. They are both the code of law and the executive branch, or, to use another comparison, they are both the plan of the architect and the forces of the builder at the same time.
Body growth by cell division (mitosis)
How do chromosomes behave in ontogeny?
The growth of an organism is carried out by successive cell divisions. This cell division is called mitosis. It is not as frequent an event in the life of cells as one might expect, given the huge number of cells that make up our body. At first, growth is fast, and the egg divides into two "daughter cells", which then give a generation of four cells, then from 8, 16, 32, 64 ... etc. The division frequency will not remain the same in all parts of the growing body, and this breaks the regularity of these numbers. But from their rapid increase, it can be deduced by simple calculation that on average 50 or 60 successive divisions are enough to produce the number of cells available in an adult, or, say, ten times more, taking into account the change of cells during life. Thus, the cells in my body, on average, turn out to be only fifty or sixty descendants of the egg that I once was.
In mitosis, each chromosome doubles
How do chromosomes behave in mitosis? They are doubled, both sets are doubled, both copies of the cipher. This process is extremely interesting and has been extensively studied, but it is too complex to describe in detail here. The main thing is that each of the two daughter cells receives a "dowry" consisting of both sets of chromosomes, exactly like those of the parent cell. In this way, all bodily cells are perfectly alike with regard to their chromosomal treasure. Each, even the least important, individual cell necessarily has a full (double) copy of the encryption code. No matter how little we understand this mechanism, we cannot, however, doubt that this fact must have some important relation to the life of the organism. Some time ago we learned from the newspapers that during his African campaign, General Montgomery demanded that every single soldier in his army be informed in detail of all his intentions. If this is true (and this could be, given the high intelligence and reliability of his troops), then we have an excellent analogy to our case, in which the corresponding fact is, of course, literally true. The most surprising thing seems to be the preservation of the doubled chromosome set during all mitotic divisions. That this is a prominent feature of the genetic mechanism is most strikingly demonstrated by the one and only exception to this rule, the exception that we must now consider.
Reduction division (meiosis) and fertilization (syngamia)
Very soon after the beginning of the development of an individual, one group of cells is reserved for the formation at the later stages of the so-called gametes, that is, sperm or egg cells (depending on the sex of the individual), which are necessary for the individual to reproduce at maturity.
"Reserved" means that they do not serve other purposes at this time and experience significantly fewer mitotic divisions. The exclusive, reductive division that occurs in them is the division that completes the development of gametes in a mature individual from these reserved cells. This division, as a rule, occurs only shortly before the syngamy takes place. In meiosis, the double chromosome set of the parent cell is simply divided into two single sets, each of which goes to one of the two daughter cells - gametes. In other words, mitotic doubling of the number of chromosomes does not take place in meiosis, their number remains constant, and thus each gamete receives only half, that is, only one complete copy of the cipher code, and not two, for example, a person has only 24, not 2 * 24 \u003d 48.
Cells that have only one chromosome set are called haploid (from the Greek πλοδ единственный, unique). Thus, gametes are haploid, and ordinary cells of the body are diploid (from the Greek διπλοδς, double). Sometimes there are also individuals with three, four ... or, generally speaking, with many chromosome sets in all the cells of their body, and they are then called triploids, tetraploids ... polyploids.
In the act of syngamy, the male gamete (sperm) and the female gamete (egg) - both haploid cells - combine to form a fertilized egg cell, which is therefore diploid. One of her chromosome sets comes from her mother and one from her father.
Haploid individuals
Another point requires a reservation. Although Haploid it is not essential for our individual target, it is, however, really interesting, because it shows that each single set of chromosomes contains a completely complete cipher code of the entire "plan" of the organism.
There are examples of meiosis, followed by fertilization not immediately, and the haploid cell ("gamete") undergoes a large number of mitotic cell divisions at this time, resulting in a whole haploid individual. This is the case of male bees - drones that develop parthenogenetically, that is, from the unfertilized and therefore haploid eggs of the queen. The drone has no father! All cells in his body are haploid.
If you like, you can call it a gigantic enlarged sperm and, indeed, it is known that functioning as such is its only life task. However, this may not be a serious point of view. For this case is not an isolated one. There are plant families where haploid cells, which are formed during meiosis and are called spores, fall to the ground like seeds and develop into true haploid plants, comparable in size to diploid ones. Let's take a look at moss, which is often found in our forests. The leafy lower part is a haploid plant called gametophyte because at its upper end it develops genitals and gametes, which, by fertilization, produce a common diploid plant - a bare stem with a seed capsule at the top. This part of the plant is called a sporophyte, since by meiosis it produces spores that are in the capsule at the top. When the capsule opens, the spores fall to the ground and develop into a leafy stem. This process is aptly called generational rotation. You can, if you like, view the ordinary case of man and animals from the same point of view. But the "gametophyte" here is, as a rule, a very short-lived unicellular generation, a sperm or an egg cell. Our body corresponds to a sporophyte. Our "spores" are reserve cells from which a single-celled generation arises through meiosis.
Outstanding value of reduction division
An important and truly fate-determining event in the process of reproduction of an individual is not fertilization, but meiosis. One set of chromosomes comes from the father, one from the mother. Neither accident nor fate can prevent this. Each person receives exactly half of his inheritance from his mother and half from his father. The fact that one line often seems to be predominant is due to other reasons, to which we will move on later (gender itself, of course, is also the simplest example of such predominance).
But when you trace the origins of your inheritance back to your grandparents, the matter is different. Let me draw your attention to the set of chromosomes that came to me from my father, in particular to one of them, say, chromosome number 5. This will be an exact copy of either the number 5 that my father received from his father, or that number 5 which he received from his mother. The outcome of the case was decided (with a probability of 50:50 chances) in the meiosis that took place in my father's body in November 1886 and produced the sperm that a few days later became the cause of my birth. The exact same story could be repeated for chromosomes 1, 2, 3 ... 24 of my paternal set and mutatis mutandis for each of my maternal chromosomes.
Moreover, all 48 results are completely independent. Even if it were known that my paternal chromosome number 5 came from my grandfather Joseph Schrödinger, there would still be an equal chance for number 7 that it came either from him or from his wife Maria, née Bogner.
Crossing over. Localization of properties
But the role of chance in the mixing of grandfather and grandmother's heredity in descendants is even greater than it might seem from the previous description, in which it was tacitly assumed or even directly stated that certain chromosomes came as a whole either from grandmother or grandfather, in other words, that individual the chromosomes came undivided. In reality, this is not so, or not always so. Before dispersed in a reduction division, say, in the one that took place in the paternal body, every two "homologous" chromosomes come into close contact with one another and sometimes exchange significant parts with each other. Through this process, called "crossing over" (cross), the two properties located in the respective parts of this chromosome will be separated in the grandson, who will be similar to one of these properties to the grandfather, and the other to the grandmother.
The phenomenon of crossing over, being not too rare, but not too frequent, provides us with the most valuable information about the location of properties in chromosomes. To address the issue in its entirety, we would have to use some concepts that will only be given in the next chapter (e.g. heterozygosity, dominance, etc.), but since that would take us beyond the dimensions of this little book, let me just point to the most important point.
If there was no crossing over, then two characters, for which the same chromosome is responsible, would always come to the offspring together, and no individual could receive one of them without receiving the other as well. Two properties, determined by two different chromosomes, would either have a 50:50 chance of being separated from each other, or would always diverge in the offspring to different individuals, namely when these properties are located in the ancestor in homologous chromosomes, which never during meiosis does not go together.
These rules and relationships are violated by crossing over, the likelihood of which can be established by carefully recording the percentage of different combinations of traits in the offspring in wide crossbreeding experiments appropriately designed for this purpose. Analyzing the results of such crosses, they accept a convincing working hypothesis that the "linkage" between two properties located on the same chromosome is less often violated by crossing over, the closer these properties lie to one another. For then it is less likely that the break point will lie between them, while the features located closer to the opposite ends of the chromosome will be separated by each crossing over. (The same applies to the union in one chromosome of two characters located earlier in homologous chromosomes of the same ancestor.) In this way, one can expect to obtain from the "linkage statistics" a kind of "feature map" within each chromosome.
This expectation was fully confirmed. In cases where a thorough check was carried out (mainly in Drosophila, although not only in her), it turned out that the studied characters really fall into as many separate groups between which there is no linkage, as there are different chromosomes (four in Drosophila). Within each group, a line map of features can be drawn, quantifying the degree of linkage between each pair of features in this group; therefore, there can be no big doubt that they are really located in the chromosome and, moreover, linearly, as the very rod-shaped form of chromosomes suggests.
Of course, the scheme of the hereditary mechanism, as it is described here, is still empty and colorless, even slightly naive. For we have not said what should be understood by a sign. To dissect into discrete "signs" an organism, which is essentially a single, "whole", seems incorrect and impossible. In reality, we only assert in each individual case that the pair of ancestors differed in a certain, well-defined relationship (say, one had blue eyes, and the other had brown eyes) and that the offspring were similar in this respect either to one or the other ancestor. In the chromosome, we localize the place of this difference. (We call it in technical language “locus” - or, if we think of the hypothetical material structure that forms its basis, “gene.”) In my opinion, the main idea is the difference in traits rather than the trait itself, despite on the apparent verbal and logical contradiction in this statement. The difference in traits is indeed discrete, as will be revealed in the next chapter when we talk about mutations and when the dry scheme presented above, I hope, will acquire more life and color.
Maximum gene size
We have just introduced the term gene for the hypothetical material carrier of a particular hereditary trait. We must now emphasize two points that will be of great importance for our study. The first point is the size, or rather, the maximum size of this medium; in other words, to how small a volume can we trace the localization of hereditary potencies. The second point is gene stability, deduced from the constancy of the "hereditary plan."
With regard to size, there are two completely independent ways of determining. One is based on genetic data (crossing experiments), the other is based on cytological data (direct microscopic observation). The first method is basically quite simple. Having established in the above way the location of a significant number of different characters (on a larger scale) within a certain chromosome (say, in the Drosophila fly), in order to obtain the required value, we only need to divide the measured length of this chromosome by the number of characters and multiply by the cross section. For, of course, we consider as separate features only those that are sometimes separated by crossing over and cannot be caused by the same (microscopic or molecular) structure. On the other hand, it is clear that our calculation can only give the maximum size, because the number of traits isolated by genetic analysis increases continuously as work goes on.
Another size estimate, although based on microscopic observation, is actually much less direct. Certain Drosophila cells (namely, the cells of the salivary glands) turn out to be gigantic for some reason, and this also applies to their chromosomes. In these latter, you distinguish a crowded pattern of transverse dark stripes crossing the thread. Darlington noticed that the number of these stripes (2000 in this case), although noticeably higher, is still of the same order of magnitude as the number of genes localized in the same chromosome on the basis of crossing experiments. He tends to view these stripes as actual genes (or boundaries between genes). Dividing the length of the chromosome, measured in a cell of normal size, by the number of stripes (2000), he finds the volume of the gene equal to a cube with a side of 300 A ?. Considering all the roughness of the calculations, we can assume that the same size is obtained by the first method.
Small numbers
A detailed discussion of the relationship of statistical physics to all the facts that I have stated (or, perhaps I should say - the relationship of these facts to the application of statistical physics in a living cell) will follow later. But let me draw your attention now to the fact that 300 (A)? - this is only about 100 or 150 atomic distances in a liquid or in a solid, so a gene, of course, contains no more than a million or several million atoms. According to statistical physics, which means - according to physics in general, such a number is too small (from the point of view of ηn to determine an ordered and regular behavior. It would be too small, even if all these atoms played the same role, as in a gas or a drop liquid, and the gene is almost certainly not just a homogeneous drop of liquid, it is probably a large protein molecule, where every atom, every radical, every heterocyclic ring plays an individual role, more or less different from that of any similar atoms, radicals or This is, at any rate, the point of view of such leading geneticists of our time as Halden and Darlington, and we will soon have to turn to genetic experiments that almost prove it.
Persistence
Let us now turn to the second, very important question: with what degree of constancy do we encounter in hereditary characteristics and what should we therefore attribute to the material structures that carry them.
The answer to this can be given without any special research. The simple fact that we are talking about hereditary traits indicates that we recognize this permanence as almost absolute. For we must not forget that not a separate feature is transmitted from parent to child: an aquiline nose, short fingers, a predisposition to rheumatism, hemophilia, dichromasia, etc. It is convenient to isolate such features for studying the laws of heredity. But in reality, from generation to generation, without noticeable change over the centuries - although not over tens of thousands of years - the entire (four-dimensional) plane of the "phenotype" is transmitted, the entire visible nature of the individual. Moreover, in each generation, the transfer is carried out by the material structure of the nuclei of those two cells that are connected during fertilization. This is a "miracle"; there is only one even greater "miracle", although it is closely related to the first, but already related to another sphere. I mean the fact that we, whose existence is entirely based on the amazing play of this particular mechanism of heredity, still have the ability to learn so much about it. It seems to me that with regard to the first miracle, our knowledge can reach almost complete understanding. As for the second, it is possible that it generally lies outside the boundaries of human knowledge.
Mutations
"Hopping" mutations - the field of action natural selection
The basic facts that we have just put forward in support of the stability attributed to the gene structure may be well known to us and will not seem startling or convincing. But this time, the adage that exceptions prove the rule is indeed true. If there were no exceptions in the similarities between children and parents, we would be deprived not only of all the wonderful experiments that revealed to us the mechanism of heredity, but also of the grandiose, million-time experiment of nature, forging species by natural selection and survival of the fittest.
Let me take this last important problem as a starting point for presenting the relevant facts, again with an apology and a reminder that I am not a biologist.
We now definitely know that Darwin was wrong when he believed that the material on the basis of which natural selection operates are small, continuous, random changes, which necessarily occur even in the most homogeneous population. Because it has been proven that these changes are not hereditary. This fact is important enough to be briefly illustrated. If you take a crop of pure barley and measure the length of the awns from each ear, and then plot the result of your statistics, you get a bell-shaped curve.
In this figure, the number of ears with a certain awning length is plotted against the corresponding awning length. In other words, the known average spine length predominates, and deviations in both directions are encountered with certain frequencies. Now select the group of ears marked in black, with awns well above average length, but large enough to yield a new crop when sown in the field. In a similar statistical experiment, Darwin would have expected the curve to shift to the right for a new crop. In other words, he would expect selection to produce an increase in the mean awns. However, in practice, this will not happen if truly pure barley was used. The new statistical curve obtained for the selected crop will be quite similar to the first, and the same would happen if ears with particularly short awns were selected for sowing.
Selection fails because small, continuous differences are not inherited. They are obviously not due to the structure of the hereditary substance, they are random. But about 40 years ago, the Dutchman de Vries discovered that in the offspring of even completely pure-bred lines, a very small number of individuals appear - say, two or three in tens of thousands - with small, but "abrupt" changes. The expression "discontinuous" here means not that the changes are very significant, but only the fact of discontinuity, since there are no intermediate forms between unchanged individuals and a few changed. De-Vries called it a mutation. The essential feature here is precisely the discontinuity. It resembles physics to quantum theory - there are also no intermediate steps between two neighboring energy levels. A physicist would be inclined to call de Vries' mutational theory figuratively the quantum theory of biology. We will see later that this is much more than a figurative expression. Mutations actually owe their origin to quantum leaps in the gene molecule. But quantum theory it was only two years old when de Vries first published his discovery in 1902. No wonder it took a whole generation to establish a connection between the two!
They do reproduce, that is, they are perfectly inherited.
Mutations are inherited as well as the original unchanged traits. For example, in the first crop of barley discussed above, there could be several ears with awn sizes far beyond the range of variability, say, without awns at all. They could represent the De-Friesian mutation and therefore would indeed reproduce perfectly, that is, all their descendants would also be without awns.
Therefore, a mutation is definitely a change in the hereditary baggage and must be caused by some change in the hereditary substance. Indeed, most of the important experiments that revealed to us the mechanism of heredity consisted in a careful analysis of the offspring obtained by crossing mutated (and in many cases even multiple mutations) individuals with unmutated or otherwise mutated. On the other hand, by virtue of their ability to actually be passed on to descendants, mutations are also suitable material for natural selection, which can work on them and produce species, as described by Darwin, eliminating the unadapted and keeping the fittest.
In Darwin's theory, one only needs to replace its "small random variations" with mutations (just like in quantum theory, the "quantum leap" replaces "continuous energy transitions"). In all other respects, only very small changes were necessary in Darwin's theory, at least if I correctly understand the point of view held by most biologists.
Localization. Recession and dominance
Now we must consider some other important facts and ideas about mutations - again in a somewhat dogmatic form, without showing how these facts and ideas arose one after another from experimental data.
We would expect that a particular mutation is caused by a change in a particular region of one of the chromosomes. And so it is. It is important to state: we firmly know that this change occurs only in one chromosome and does not occur simultaneously in the corresponding "locus" of the homologous chromosome.
The fact that only one chromosome is affected is found when a mutated individual (often called a "mutant") is crossed with a non-mutated individual. For at the same time, exactly half of the offspring exhibits a mutant trait, and half - a normal one. This is exactly what should be expected as a result of the divergence of two chromosomes in a mutant in meiosis.
This figure shows a pedigree, where each individual (three consecutive generations) is represented by just a pair of chromosomes. Please note that if both chromosomes of the mutant were changed, then all children would have the same (mixed) inheritance, different from that of each parent.
But experimenting in this area is not as easy as it might seem from the above. The matter is complicated by the second important circumstance, namely, the fact that mutations are very often hidden. What does it mean?
In a mutant individual, the two "copies of the cipher code" are no longer the same; they represent two different "interpretations" or two "versions", at least in the place where the mutation took place. It may be helpful to point out straight away that, while tempting, it would be completely wrong to regard the original version as "orthodox" and the mutant version as "heretical." We must consider them, in principle, as equal, for normal signs in their time also arose through mutations.
Indeed, signs of a mutant individual like general rule, correspond to either one version or another, and this version can be both normal and mutant. The version followed by an individual is called dominant, the opposite is called recessive; in other words, the mutation is called dominant or recessive, depending on whether it manifests its effect immediately or not.
Recessive mutations are even more frequent than dominant mutations and are very important, although they are not immediately detected. To change the properties of an organism, they must be present on both chromosomes. Such individuals can be produced when two identical recessive mutants interbreed with each other or when a mutant interbreeds with itself. The latter is possible in hermaphrodite plants and even occurs spontaneously. Simple reasoning shows that in these cases about a quarter of the offspring will be mutant in appearance.
Introduction of some technical terms
For clarity, some technical terms should be explained here. What I call the "version of the cipher code" - whether original or mutant - is commonly referred to as "allele." When the versions are different, the individual is said to be heterozygous for that locus. When they are the same, as, for example, in non-mutated individuals, they are called homozygous. Thus, recessive alleles affect traits only in the homozygous state, whereas the dominant alleles produce the same trait in both homozygous and heterozygous states.
Color very often dominates lack of color (or whiteness). So, for example, peas will bloom white only when they have a "recessive allele responsible for white color"On both corresponding chromosomes, that is, when it is" homozygous for white "; he will then give pure offspring, and all his offspring will be white. But already one "red allele" (while the other white - "heterozygous individual") will make the flower red, and two red alleles ("homozygous individual") will make it exactly the same. The difference between the last two cases will become apparent only in offspring, when heterozygous reds will produce a certain number of white offspring, and homozygous reds will give pure offspring.
The fact that two individuals can be completely similar in appearance and, however, differ hereditarily, is so important that it is desirable to give this an exact formulation. The geneticist says that individuals have the same phenotype, but a different genotype. The content of the previous paragraphs can thus be summed up in a short but highly technical expression: the recessive allele affects the phenotype only when the genotype is homozygous.
We will use these technical expressions from time to time to remind the reader of their meaning when necessary.
Harmful effect of related crossing
Recessive mutations, as long as they are heterozygous, do not, of course, serve as material for natural selection. If they are harmful, as is often the case with mutations, they are nevertheless not discarded, because they are hidden.
It follows that a very large number of unfavorable mutations can accumulate and not cause direct harm. But they, of course, are passed on to half of the offspring, and this applies both to humans and to livestock, poultry and other species, whose good physical qualities are of direct importance to us. Consider the case that a male individual (say, to be specific, myself) carries such a recessive deleterious mutation in a heterozygous state such that it does not manifest. Suppose my wife doesn't have her. Then half of our children (second row) will also carry it, and, moreover, again in a heterozygous state. If they all marry non-mutant partners (omitted from the diagram to avoid confusion), a quarter of our grandchildren will, on average, be affected in the same way.
No hazard of harmful manifestations will arise until such affected individuals marry each other. Then, as a simple calculation shows, a fourth of the children will be homozygous and show a harmful mutation. With the exception of self-fertilization (possible only in hermaphrodite plants), the greatest danger would be the marriage between my son and my daughter. Each of them has the same chances of being latently affected or unaffected, and therefore one fourth of such incestuous unions would be dangerous, since a fourth of the children from such a marriage would show a harmful sign. The level of danger for each individual child born in incest is thus 1:16.
Similar reasoning shows that the size of the danger is 1:64 for the offspring in the event of the marriage of my grandchildren, who are at the same time a cousin and a sister. It no longer seems so scary, and indeed, the last case of marriage is usually considered tolerable. But we must not forget that we analyzed the consequences of only one latent injury in one partner of a pair of ancestors (“me and my wife”). In reality, however, both of them quite possibly carry more than one latent flaw of this kind. If you know that you yourself carry a certain hidden flaw, you have to assume with a 1: 8 probability that your cousins \u200b\u200balso share it with you!
Experiments with plants and animals seem to indicate that, in addition to the comparatively rare defects of a serious nature, there are many smaller ones, the random combinations of which generally worsen the offspring from related crosses. Since we are no longer inclined to remove unsuccessful offspring in the cruel way that the Lacedaemonians used on the Taygeta Rock, we should pay especially serious attention to closely related marriages in a person for whom the natural selection of the fittest is mostly limited, and even more, is turned into his own opposite. The anti-selective effect of modern mass murders of healthy youths of all nationalities is hardly justified by considerations that in more primitive conditions war could have a positive value for selection, making it possible for the fittest tribes to survive.
General and Historical Notes
It seems surprising that recessive alleles in a heterozygous state are completely suppressed by dominant ones and do not produce any visible effect at all. It should at least be noted that there are exceptions to this. When a homozygous white snapdragon is crossed with a homozygous raspberry snapdragon, all immediate descendants are intermediate in color, that is, pink (and not crimson, as might be expected). The more important case of two alleles eliciting their action simultaneously occurs in blood groups, but we cannot go into more detail here. I would not be surprised if in the end it turned out that recessiveness can be of various degrees and that its detection depends on the sensitivity of the techniques used in the study of the "phenotype".
It may be appropriate here to talk about the early history of genetics. The backbone of the theory, namely the laws of transmission in subsequent generations of characters that distinguished parents, and in particular, the discovery of recessive and dominant characters, we owe to the world famous Augustinian abbot Gregor Mendel (1822-1884). Mendel knew nothing about mutations and chromosomes. In his monastery garden in Brunn (Brno), he experimented with garden peas, cultivating various varieties, crossing them and observing their offspring in the 1st, 2nd, 3rd ..., generations. You can tell that he experimented with mutants, finding them ready-made in nature. He published the results as early as 1866 in the Nalurforschender Verein in Brunn. No one seemed interested in the abbot's pursuits, and no one, of course, had the faintest idea that in the twentieth century his discovery would become a guiding star for an entirely new branch of science, perhaps the most interesting in our day. His work was forgotten, and it was not rediscovered until 1900, simultaneously and independently of each other, by Correns (Berlin), de Vries (Leiden) and Cermak (Vienna).
The need for mutations to be a rare event
So far we have directed our attention to deleterious mutations, which are perhaps more numerous; however, it should definitely be pointed out that we also encounter beneficial mutations. If a spontaneous mutation represents a small step in the development of a species, then it seems that the known change is "tested" blindly - with the risk that it may be harmful and in this case will be automatically eliminated. This leads to one very important point. To be suitable material for natural selection to work, mutations must be rare enough, as they actually turn out to be. If they were so frequent that there was a high probability that one individual would have, say, a dozen different mutations, the harmful ones would usually prevail over the beneficial ones, and the species, instead of being improved by selection, would remain unimproved or die. ... Comparative conservatism, resulting from high gene resistance, is very significant. An analogy to this can be seen, for example, in the operation of complex factory equipment at a plant.
In order to develop better methods, it is necessary to experience various innovations, even untested ones before. But in order to find out whether these innovations increase or decrease the output of the plant, it is important to introduce them one at a time, while other parts of the mechanism remain unchanged.
X-ray mutations
We must now consider a series of extremely witty genetic researchwhich will prove to be the most significant for our analysis.
The percentage of mutations in the offspring - the so-called mutation rate - can be increased many times over the natural mutation rate by illuminating the parents with x-rays or γ-rays. Mutations caused in this way do not differ in any way (except for a higher frequency) from those arising spontaneously, and it seems that every "natural" mutation can also be caused by x-rays. In large Drosophila cultures, many specific mutations are repeated over and over; they were localized on the chromosome, as described in § 16, and received special names. Were found so-called "multiple alleles", that is, two or more different "versions" or "readings" (in addition to the normal unmutated) in the same place in the chromosomal code. This means that there are not only two, but three or more changes in a given locus, and every two of them are located one to the other in the “dominance-recessive” relationship, when they are simultaneously in their respective places in two homologous chromosomes.
Experiments with mutations caused by x-rays give the impression that each separate "transition", say, from a normal individual to a given mutant, or vice versa, has its own individual "x-ray coefficient" indicating the percentage of offspring that mutate in a given special direction. if the parents received a single dose of x-rays before the birth of this offspring.
First law. Mutation is a single event
Moreover, the laws governing the frequency of occurrence of induced mutations are extremely simple and throw an extremely bright light on the whole question. I am following N.V. Timofeeva in Biological Reviews, vol. 9, 1934.
It is largely based on this author's own excellent work. The first law states:
1. The increase in the number of mutations is exactly proportional to the dose of rays, so that one can really talk (as I did) about the magnification factor.
We are so used to simple proportionality that we tend to underestimate the far-reaching consequences of this law. To assess them, we can remember that the value of a product, for example, is not always proportional to its quantity. Ordinarily, the fact that you have already bought six oranges can give the shopkeeper the impression that if you later decide to take a dozen from him, he may give it to you for less than twice the price of the first six. In the event of a crop failure, the opposite may happen. In our case, we conclude that the first half of the radiation dose, having caused, say, one mutation per thousand offspring, at the same time did not affect the rest of the offspring either in the direction of predisposition or in the direction of immunization against mutations. For otherwise, the second half of the dose would not cause again exactly one mutation in a thousand. Mutation, therefore, is not the cumulative result of successive illumination in small portions that would amplify one another. It should consist of some single phenomenon that occurs on one chromosome during exposure to x-rays. What is this phenomenon?
Second law. Localization of the event
The second law answers this, namely:
2. If you vary the quality of the beams (event wavelength) over a wide range from soft x-rays to fairly hard gamma rays, the ratio remains constant, provided you give the same dose in so-called r-units. In other words, the rate does not change if you measure the dose by the total amount of ions produced per unit volume, in a suitable standard substance, during the time the parents are exposed to the rays, and at the same place.
Air is chosen as the standard substance, not only for convenience, but also for the reason that the tissues of organisms are composed of elements of the same average atomic weight as air. The lower limit of the number of ionization or accompanying processes (excitations) in tissues is obtained simply by multiplying the amount of ionization in air by the density ratio. Thus, it is absolutely clear (and this is confirmed by a more detailed study) that a single phenomenon causing a mutation is precisely ionization (or a similar process) that occurs within a certain “critical” volume of the germ cell.
What is this critical volume? It can be established from the observed mutation frequency by the following reasoning: if at a dose of 50 thousand ions per 1 cm 3 the probability of mutating in a given special direction for each separate gamete located in the irradiated space is only 1: 1000, the volume - the "target" into which it is necessary to "hit" the ionization for this mutation to occur - will be only 1/1000 of 1/50 000 cm 3, that is, in other words, one fifty millionth cm 3. The numbers here are not accurate and I have included them for illustration purposes only. In the actual calculation, we follow M. Delbrück (in the joint work of him, N.V. Timofeev, and K.G. Zimmer). The same work will serve as the main source for the presentation of the theory in the next two chapters. Delbrück comes to a volume of only about ten average atomic distances in a cube and thus containing only 103 atoms. The simplest interpretation of this result boils down to the fact that there is a sufficient probability of this mutation occurring if ionization (or excitation) occurs no further than at a distance of about 10 atoms away from a certain place in the chromosome. We will discuss this in more detail later.
End of introductory snippet.
One of the most famous physicists of the twentieth century Erwin Rudolf Joseph Alexander Schrödinger ( german Erwin Rudolf Josef Alexander Schrödinger ) was born on 12 August 1887 in Vienna and died there on 4 January 1961. At the same time, Schrödinger was by no means a stay-at-home, his life for years was nomadic and hectic. He worked in Zurich, Stuttgart, Berlin, Oxford and Dublin. After leaving Vienna shortly after the end of the First World War, Schrödinger returned to his hometown only in 1956, at the zenith of his fame.
Schrödinger was one of the founders of quantum mechanics. He received the Nobel Prize in Physics in 1933. He was a member of a number of world academies of sciences, including the USSR Academy of Sciences (1934).
Schrödinger made a number of fundamental achievements in the field of quantum theory, which formed the basis of wave mechanics: he formulated wave equations (stationary and time-dependent Schrödinger's equations), showed the identity of the formalism he developed and matrix mechanics, and developed the wave-mechanical perturbation theory. Schrödinger offered an original interpretation of the physical meaning of the wave function. In addition, he is the author of many works in various fields of physics: statistical mechanics and thermodynamics, physics of dielectrics, color theory, electrodynamics, general relativity and cosmology; he made several attempts to build unified theory fields.
Moreover scientific interests Schrödinger were not limited to physics. In the book What is Life ?, presented in our edition, Schrödinger turned to the problems of genetics, looking at the phenomenon of life from the point of view of physics. He also paid great attention to the philosophical aspects of science, ancient and oriental philosophical concepts, issues of ethics and religion.
Book "What is Life?" (1944) is based on lectures given at Trinity College Dublin in February 1943. These lectures and the book were inspired by an article by Nikolai Timofeev-Ressovsky, Karl Zimmer and Max Delbrück, published in 1935 and transmitted to Schrödinger by Paul Ewald in the early 1940s. The article is devoted to the study of genetic mutations that arise under the influence of X-ray and gamma radiation and for the explanation of which the authors developed the target theory. Although the nature of heredity genes was not yet known at that time, a look at the problem of mutagenesis from the point of view atomic physics revealed some general patterns this process. The work of Timofeev - Zimmer - Delbrück was taken by Schrödinger as the basis for his book, which attracted wide attention of young physicists. Some of them, under her influence, decided to study molecular biology.
Schrödinger was also interested in philosophy. However, it was only after his arrival in Dublin that he was able to devote sufficient attention to philosophical issues. From under his pen came a number of works not only on the philosophical problems of science, but also of a general philosophical nature - "Science and Humanism" (1952), "Nature and the Greeks" (1954), "Mind and Matter" (1958) and "My View to the world ”, the work he completed shortly before his death“ My view of the world ”is presented in this edition. Schrödinger paid special attention to ancient philosophy, which attracted him with its unity and the importance that it could play for solving the problems of our time. Schrödinger also looked to the heritage of Indian and Chinese philosophy. He wanted to look at science and religion, human society and the problems of ethics from a unified position; the problem of unity was one of the main motives of his philosophical work. In works that can be attributed to the philosophy of science, he pointed to the close connection between science and the development of society and culture as a whole, discussed the problems of the theory of knowledge, participated in discussions on the problem of causality and modification of this concept in the light of new physics. In his works, Schrödinger consistently defended the possibility of an objective study of nature.
But most of all, Schrödinger became famous for his thought experiment, named after the scientist - "Schrödinger's cat". Schrödinger's article "The Current Situation in Quantum Mechanics" (1935) described the experiment as follows:
“You can also build cases in which burlesque is enough. A certain cat is locked in a steel chamber along with the next hellish machine (which must be protected from the direct interference of the cat): inside the Geiger counter there is a tiny amount of radioactive substance, so small that only one atom can decay in an hour, but with the same probability it can and do not disintegrate; if this happens, the reading tube is discharged and the relay is triggered, releasing the hammer, which breaks the cone with hydrocyanic acid. If you leave this whole system to itself for an hour, then we can say that the cat will be alive after this time, as long as the atom does not decay. The very first decay of an atom would have poisoned the cat. The psi function of the system as a whole will express this by mixing or smearing a living and a dead cat (sorry for the expression) in equal proportions.
It is typical in such cases that the uncertainty, initially limited by the atomic world, is transformed into macroscopic uncertainty, which can be eliminated by direct observation. This prevents us from naively accepting the “blur model” as reflecting reality. In itself, this does not mean anything unclear or contradictory. There's a difference between a blurry or defocused photo and a cloud or fog shot. ”
According to quantum mechanics, if no observation is made over the nucleus, then its state is described by the superposition (mixing) of two states - a decayed nucleus and an unresolved nucleus, therefore, a cat sitting in a box is both alive and dead at the same time. If the box is opened, the experimenter can see only one specific state - "the nucleus has disintegrated, the cat is dead" or "the nucleus has not disintegrated, the cat is alive."
The question is: when the system ceases to exist as a mixture of two states and chooses one specific one? The goal of the experiment is to show that quantum mechanics is incomplete without some rules that indicate under what conditions the collapse of the wave function occurs, and the cat either becomes dead or remains alive, but ceases to be a mixture of both.
Since it is clear that a cat must be either alive or dead (there is no state that combines life and death), this will be the same for the atomic nucleus. It must be either disintegrated or not disintegrated.
Simply put: according to quantum mechanics, if no observation is made over the nucleus of an atom, then its state is described by the mixing of two states - a disintegrated nucleus and an unresolved nucleus, therefore, a cat sitting in a box and personifying the nucleus of an atom is both alive and dead at the same time. If the box is opened, then the experimenter can see only one specific state - "the nucleus has disintegrated, the cat is dead" or "the nucleus has not disintegrated, the cat is alive." Schrödinger's experiment showed that from the point of view of quantum mechanics, the cat is both alive and dead, which cannot be. Hence, quantum mechanics has significant flaws. The question is: when does the system cease to exist as a mixture of two states and chooses one specific one? The goal of the experiment is to show that quantum mechanics is incomplete without some rules that indicate under what conditions the collapse of the wave function occurs, and the cat either becomes dead or remains alive, but ceases to be a mixture of both. Since it is clear that the cat must necessarily be either alive or dead (there is no state intermediate between life and death), then this will be the same for the atomic nucleus. It must necessarily be either disintegrated or non-disintegrated
In this book, we present two milestone works by Schrödinger: "What is life?" (1944) and My View of the World (1961).
This book is called Erwin Schrödinger's philosophical testament. It outlines the worldview of a natural scientist who has had a significant impact on the development of modern physics.
Everything is possible exactly until a choice is made.
Imagine that you have a box with a radioactive core and a container of poisonous gas. The probability that the nucleus will disintegrate and trigger the mechanism that opens the container is 50%. If you put a cat in this box and close it, the Schrödinger paradox will arise. According to quantum mechanics, if no observation is made over the nucleus, then its state is described by the mixing of two states - a disintegrated and non-disintegrated nucleus, therefore, a cat sitting in a box is both alive and dead at the same time.
For those who want to know more, for those who dare to find out what exactly is the paradox of Schrödinger's theory, for those who want to know what life is from the point of view of physics, the great scientist wrote his last and best work.
The work was published in 1944 by Algorithm publishing house. On our site you can download the book "The Quantum Cat of the Universe" in fb2, rtf, epub, pdf, txt format or read online. Here you can also, before reading, refer to the reviews of readers who are already familiar with the book and find out their opinions. In the online store of our partner, you can buy and read a book in paper form.