8: The Genome

Figure 8.1
growth and acquisition

Our prototypical cell is now ready to begin its reproductive cycle of absence and return.

In its initial state, shown in Figure 8.1, our cell has an initial internal energy and a set number of contained chemical components. We mark that initial supply as ‘old’.

We now have two scientifically important but different ways of measuring the material components that our biological entity both needs and is composed of. We will sometimes want to refer to the DNA and general biochemistry of biological organisms. But we will sometimes be more concerned with their mechanical and gravitational mass. We therefore measure the stock of chemical components contained in our biological entity in two different ways:

  1. we measure the different types and quantities of chemical components in moles; and
  2. we measure the mass of chemical components, complete with its inertia in kilogrammes.

It is very important to appreciate that these two ways are in fact equivalent. The mole is based on the Avogadro constant, NA, which gives ‘amount’ a specific scientific meaning. Amount of substance, again measured in moles, refers directly to both (a) the mass, and (b) the numbers of whatever elementary particles make up the substance being investigated. So a mole is a certain number of elementary entities or types. We can always get the mass from knowing the type under discussion.

The elementary entities specified at any time could be be ions, atoms, molecules, electrons, photons, or whatever other substance is under discussion. If we take them to be atoms, then the Avogadro constant is defined as the number we find in 0.012 kilogrammes of carbon-12. The mass has been clearly stated.

The definition of moles used for carbon is now used, more generally, as a standard. The Avogadro constant is therefore the invariant constant of proportionality linking the amount of substance of whatever is under discussion to the numbers of components it contains; and so to their configuration, their composition, and their various modes of vibration and interaction. It is also linked to their mass. Once given a specified amount of substance, in moles, and a specified set of elementary entities, then all chemical elements and substances can be distinguished by their masses. The mole is therefore the scientific way to convert, at any time of our choosing, between the kilogrammes of elementary entities and components our cell contains, and the number of different kinds of atoms and molecules that make up both it and the population at any time.

When we have measured the mass of all the old components, and have also determined their molar count, then we know the chemical composition.

Now we are ready, our biological entity opens its entry orifice. It interacts with the surroundings. This is Stage I.

Our entity absorbs all its required resources from that environment. It attaches them with a single chemical bond. It is using its mechanical chemical energy.

Since the number of chemical components within the biological entity increases through the force of this mechanical chemical energy, both its internal energy and its entropy increase. However, since those absorbed components are all being removed from the environment, by the cell's use of its mechanical chemical energy; and since this is the best possible and ideal case; then that loss of components from the surroundings not only increases the cell's internal energy, it means that the entropy in those surroundings is decreasing by exactly that same and precise amount.

When we remove components from the surroundings using the force of this mechanical chemical energy, we decrease the entropy there because the number of potential molecular interactions and collisions within those surroundings decreases, while the potential number inside the entity increases. Since we can measure those incoming molecules—which we mark ‘new’—as both a quantity of mass, and a quantity of moles of components, we can always measure these entropy values.

Since the cell or entity's increase in entropy, through the acquisition of new components via its mechanical chemical energy, exactly matches the decrease in entropy happening in the surroundings (which loses those self-same components and resources, for they are removed), then the entropy in the universe at large (i.e. entity plus surroundings) remains exactly the same … which is the effect we wanted to achieve.

By the same token, when we use this mechanical chemical energy to increase the moles of molecular components inside our biological entity, we increase the potential number of molecular interactions and collisions it can undertake … which is the source of all chemical reactions. But we have also decreased the number of such chemical reactions, and so potential molecular collisions and interactions, that could have taken place in the surroundings. This is why we record both the moles and the mass of the chemical components moving back and forth.

In this best possible and ideal case, the numbers and the possibilities of the potential collisions, reactions, and possible interactions taking place inside and outside the cell match each other exactly; and the universe at large is left in an identical state. The total number of potential reactions and interactions remains the same. The actual number of chemical reactions that take place within the surroundings and within the cell of course changes according to where those molecules move. But the potential number in the universe remains indifferently the same, whether the substances move into the cell or not. An equivalent number of molecular interactions of some form or other could just as happily have taken place outside the cell, using those components, if they had not entered the cell. Everything—i.e. the cell plus its surroundings—therefore has the same potential to repeat this same process for an indefinite and infinite number of cycles.

At the end of this acquisition process, our prototypical cell has used its mechanical chemical energy to increase the moles or numbers of molecules at its disposal. It has done this by increasing in its mass. That has immediately increased the number of available molecular components, which is an increase in its internal energy. Some are old components that existed prior to the start of this cycle, whereas some are new components acquired in the currency of this particular cycle.

The population will open its entry orifice for its given period of time to absorb the amounts dictated by its DNA.

The prototypical cell has now finished using its mechanical chemical energy to acquire its components, again at the direction of its DNA. Once its internal energy has suitably increased, it closes the entry orifice, and we are ready for the next step.

We should carefully note that since its entropy increases when its mass increases, we can track its entropy from its mass, and so from its usage of its mechanical chemical energy which is its force and energy exerted in the surroundings.

We refer to this use of mechanical chemical energy to intake material chemical components and resources and increase the internal energy as the population's "Mendel flux", "Mendel pressure", or "mass flux". It is named after the Austrian monk Gregor Mendel who discovered the fundamental laws of heredity.

A mathematical aside

As a mathematical aside this mass flux—which is more strictly a flux of the mechanical form of binding chemical energy—is the quantity of chemical components the population must absorb, per each unit of time. We can measure it at m kilogrammes per second for each individual entity or member within the population. Although this flux is stated in kilogrammes per second and so appears to be a statement of mass; since it in fact refers to chemical components and to the fact that a specific amount of energy must be used to bind them, then it is in actuality a measure of the intensity with which that specifically mechanical variety of chemical energy is being used to increase the entity's stock of internal energy.

The Mendel pressure or mechanical chemical energy flux of a mass of chemical components is M kilogrammes per second for the entire population. And please again note that it is the chemical energy aspect of the internal energy that is important. Its declaration as ‘kilogrammes per second’, and an apparent reference to mass, is just a way to measure that energy's current impact through the entirely mechanical effects its moles of molecules are having on the surroundings.

If there are n entities in the population, then we can attribute an average individual mass flux, or Mendel pressure of mechanical chemical energy, of m̅ = Mn kilogrammes per second to each of them. This is therefore a characteristic and distinctive feature of the population. It is accompanied by a characteristic distribution—a typically Maxwell distribution—of mechanical chemical energy amongst the n entities.

And also by the Avogadro constant and the periodic table of elements, if two populations have a difference in , then the entities within them immediately hold different numbers of moles of different chemical components, and so are composed of different molecules. They therefore have different genes and different internal energies, and will organize or distribute those moles and kilogrammes of chemical components amongst themselves in different ways, making different chemical pathways available to themselves. Two populations with different ’s therefore have entities that are each using different rates, intensities, and quantities of mechanical chemical energy, and so are composed of different chemical compounds. If two populations with the same have a different population flux M, then that is entirely because the numbers, n, in each are different. The populations are different sizes … and that is their only difference. They do not differ in type.

But if two populations differ in their , then their entities are each composed of different numbers of different molecules. The two populations may also have different sizes, but they definitely have different types. They have different numbers of moles per each entity, which therefore have different kilogrammes of different chemical components and compounds. They are using those different quantities of mechanical chemical energy in different ways. Their DNA, their genes, and their entire genomes must therefore all be different.

We can also note that since this first stage in the circulation of the generations the entity is undergoing has a net incoming mass flux or Mendel pressure, then this is a positive divergence of that mechanical chemical energy. And not only is it a positive divergence, but since the flux total is M, while the volume through which it is entering is simply the set of n entities, then the divergence in this mass flux of mechanical chemical energy is that population and mechanical chemical energy's flux density. The divergence is therefore the average individual mechanical chemical energy, and is given by ∇ • M = Mnm̅ > 0.

And this is extremely interesting. It is worth taking careful note of the following two circumstances concerning this divergence:

  1. There is a positive correlation between the mass flux and the divergence, for M is the numerator. So if DNA programming or any other factor increases the Mendel pressure or the mass flux of mechanical chemical energy, then the divergence or flux density of that mechanical chemical energy increases commensurately. This is also a record of the moles of chemical components making up, and commanded by, that DNA, both individually and over the whole population.
  2. There is, however, an inverse correlation between the divergence and the population numbers, n, which is the denominator. Therefore, the divergence or flux density of mechanical chemical energy will also increase if the numbers ever decrease, while leaving the population's flux volume the same. The divergence can only remain unaffected if the flux volume decreases by exactly the average value when the numbers decrease, so also leaving the distribution the same. In other words, any entities lost must have exactly the average value, , or the divergence over the rest changes.

And since, by the Helmholtz decomposition theorem—which is the fundamental theorem of the vector calculus—a divergence is one of the two properties that uniquely identify any flux, then this again highlights the role played by the population's average individual mass, , along with its characteristic distribution of its mechanical chemical energy. If two populations have the same divergence in their flux of mechanical chemical energy at every point across the circulation of the generations, then they are the same population with the same internal energies, busy handling the same moles of chemical components, i.e. on a molecular and genomic scale, in the same ways; and again at each moment.