11: Physiology and Metabolism

Figure 11.1
energy and an isentropic set

Once our cell has opened its entry aperture, it can further increase its internal energy. It can set about taking on and exploiting its quota of nonmechanical thermal, light, and chemical energy.

As our prototypical cell absorbs light, as shown in Figure 11.1, it steadily increases in its stock of nonmechanical chemical energy and so increases its internal energy. But since its temperature is not increasing, then it is doing work. Those work interactions allow it to undertake its set of perhaps photosynthetic, or other such, interactions. The previous set were also associated with movements across the boundary. However, they were all mechanical because they all involved changes in mass. They all increased the molecular stock. These ones are also involved with movements across the boundary, but do not involve changes in molecular stock. They are concerned entirely with internal changes.

The biological entity uses its available internal interactions to convert its absorbed solar and nonmechanical energy, through a set of work interactions, into a nonmechanical chemical energy. It selectively directs that nonmechanical chemical energy at all the new chemical components it absorbed earlier in the part of the cycle. In this best of all possible worlds it uses the behaviour pre-programmed in its DNA to convert the single chemical bonds between them into a set of different vibrations, which is in this case to form a set of double chemical bonds.

Thanks to the nonmechanical light energy that the entity is taking on, the new chemical components bind to each other more tightly. Since double bonds are more powerful than single ones, they are also shorter. The double chemical bonds thus draw those molecules closer together. The components therefore congregate, in chromosome-division like fashion, at the centre of the cell.

The quantity of nonmechanical energy held per each unit of mass is now increasing. The stock of nonmechanical chemical energy increases while the mechanical variety—and therefore the mass—remains the same.

The quantity of energy our population holds may now be increasing, but we have to pay attention to what is happening to its entropy throughout these proposed transformations.

The combination of the incoming nonmechanical energy and the chemical reactions it induces has a two-fold—but countervailing—effect on the cell's entropy. We are in exactly the same isentropic situation we were previously with the rock:

  1. The system's energy is increasing (but this time by converting the incoming nonmechanical radiant energy into equally nonmechanical chemical energy, rather than by converting the mechanical energy of a falling rock into the increased nonmechanical vibrations of a thermal molecular motion).
  2. The entropy is on the one hand INCREASING because the energy held by each component is increasing as some are surrounded by a set of double bonds (whereas in the previous case, the increased energy resulted in the molecules vibrating more rapidly and extensively, and so thermally, thus instead raising the temperature).
  3. But the entropy is simultaneously DECREASING because the bond length is decreasing and pulling the components closer together into a tighter configuration, and so into a decreased volume, and as a different mode of molecular vibrations.

Since the increase and the decrease in entropy exactly match each other, the entropy remains the same. Our prototypical cell therefore undertakes a transformation that successfully allows it to increase in its stock of nonmechanical chemical energy, but that nevertheless also keeps it in the same isentropic set throughout.

Since the system's entropy remains the same overall, then the entropy throughout the universe also remains the same. We have therefore taken on some nonmechanical energy and undertaken a set of metabolic and physiological reactions internal to the cell, while all the time keeping the entropy both internally and externally the same. This sequence of transformations, which is a net increase in the internal energy, is also now capable of indefinite and invariant repetition.

When our prototypical cell has completed all its internal interactions, it can close its entry aperture and stop taking on energy. We have had two consecutive stages in which the internal energy has increased, and we are now ready to move on to the next stage.

 

Every population will open its aperture for a given amount of time to take in a given quantity of nonmechanical energy, and all at a given rate as determined by its DNA and the environment.

We should also carefully note that it is possible for a biological organism to increase its nonmechanical energy while leaving its mass and its mechanical chemical energy and its entropy all constant, for none of these have changed.

We refer to this influx of nonmechanical energy that converts energy from one form to another, but without increasing the temperature, as the population's “Wallace pressure” or “energy flux”. It is named after Alfred Russel Wallace, co-discoverer of the theory of evolution, and who co-authored the first ever publication on natural selection with Charles Darwin.

A mathematical aside

The Wallace pressure is the nonmechanical chemical energy the population must absorb, per each unit of time, so it can continue with the cycle. We can measure it per each individual entity or member within the population at p watts or joules per second; and at P watts or joules per second for the entire population. And if there are n entities in the population, then they will each have an average individual Wallace pressure of = Pn watts. Again by the Biot-Savart law, it must follow a curved path in space and time and have a specific mean value, which is its centre of curvature. This is determined by the sum of all the contributions over the given interval. It is the average value , which is the characteristic source for the nonmechanical chemical energy over that interval. There is, again, both a total stock of nonmechanical energy, and a distribution characteristic of that spacetime curvature. Nonmechanical energy therefore comes complete with its rates of increase and/or decrease. As was also the case with the mechanical chemical energy, this sum and distribution of the nonmechanical chemical energy is a specified number of joules across both the population and the distinct entities, and is guaranteed unique by that interval and the law.

There is a further similarity. As was the case for the mass flux, M, of mechanical chemical energy, this incoming nonmechanical chemical energy flux or Wallace pressure has a positive divergence derived from P, while its overall volume is n. This divergence in nonmechanical energy is again a flux density, and is therefore given by ∇ • P = Pn = … once again highlighting the role played by this average individual value.

And as was once again the case with the mass flux of mechanical chemical energy, the divergence of the flux of nonmechanical chemical energy increases if either (a) the flux, P, increases; or (b) the population numbers, n, decrease as the flux either remains constant, or changes by some value other than the precise value of the average being currently maintained.

And by the the laws of chemical thermodynamics and the Gibbs and the Helmholtz energies—which again includes the Avogadro constant, the periodic table of elements, and all that they imply—if two populations differ in , then they are directing different quantities and intensities of nonmechanical energy at their genomes and so are undertaking different chemical reactions. They have different energies and entropies, and different amounts and distributions over their entities. They are therefore pursuing different paths both per each distinct entity, and as complete populations. Even if the mechanical energy of the chemical components concerned are the same, they are processing them differently and so their nonmechanical energies are driving those components along different pathways. They are exploring different possibilities with their similar genes and genomes. These differences would all be measured by their different Gibbs and Helmholtz energies, which directly incorporate the different entropies, transformations, and effects in the surroundings.