On Relationship between X and Y chromosome evolution and PID control

First of all, I would like you to read my previous post on the graphical interpretation of the mechanisms of evolution of X and Y chromosomes.

These mechanisms clearly demonstrate the greater changeability of the X pool (in females) than the Y pool  (present only in males) – simply due to the fact that X chromosomes in females merge and branch (called fan in and fan out).

The next, in my opinion, interesting observation is drawn from the notions of mathematical analysis and dynamical systems theory. Here we have ideas of proportionality, integration, differentiation, on one hand, and notions of combinationality and sequentiality on the other.

If we look at the way how X-chromosomes evolve with fan-in mergers, we clearly see the features akin to proportionality and differentiality. The outgoing X pools are sensitive to the incoming X pools and their combinations. Any mixing node in this graph shows high sensitivity to inputs.

Contrary to that, the way of evolution of Y-chromosomes with NO fan-in contributions, clearly shows the elements of integration and sequentiality, or inertia, i.e. the preservation of the long term features.

So, the conclusions that can be drawn from this analysis are:

  1. Males tend to bring the integral or sequential (cf. sequential circuits in digital systems – with longer term memory) aspect to the overall process of evolution
  2. Females tend to bring the proportional/differential or combinatorial (cf. combinational circuits – with shorter term memory)
  3. The presence of both male and female genetics are essential for stability of the evolution and survival of the kind, much like the PID feedback control helps stability of dynamical systems, and much like the combination of combination and sequential circuits allow computer systems to operate according to their programs.

Again, I would be grateful for any comments and observations!

PS. By looking at the way how our society is now governed (cf. female or male presidents and prime ministers), you might think whether we are subject to differentiality/combinatorics or integrality/sequentiality and hence whether we are stable as a dynamical system or systems (in different countries).

Happy Days!

 

 

 

 

 

On the dynamics of evolution of Y and X chromosomes

It is a known fact that men inherit both Y and X chromosomes while women only X chromosomes.

As a corollary of that fact we also know that Y-chromosomes, sometimes synonymized with Y-DNA, are only inherited by the male part of the human race. This means that Y-chromosome inheritance mechanism is only forward-branching, i.e. Y-DNA is passed from one generation to the next generation “nearly” unchanged. As I am not an expert in genetics I cannot state precisely, in quantitative terms, what this “nearly” is worth. Suppose this “nearly” is close to 100% for simplicity.

Below is a diagram which illustrates my understanding of the mechanism of inheritance of Y-chromosomes.

This diagram is basically a branching tree, showing the pathways of the Y-DNA from one generation to the future generations of males. The characteristic feature of this inheritance mechanism is that it is Fan-out only. Namely, there is no way that the Y-DNA can be obtained by merging different Y-DNAs because we have no Fan-in mechanism.

Let’s now consider the mechanism of inheritance and evolution of X-chromosomes.The way how I see this mechanism is shown in the following diagram.

X-chromosomes are inherited by both males and females. But, as I understand, this happens in two different ways.

Each female takes a portion of X chromosomes from her father (let’s denote it as X1) and a portion of X chromosomes from her mother (denoted by X2), thereby producing its own set of chromosomes X2’ which is a function of X1 and X2. Similar inheritance is in the next generation where X2’’=f(X1’,X2’).

Each male, however, only inherits X chromosomes from his mother, as shown above, where X1’’=f(X2’).

At each generation, when the offspring produced has a female, there is a merge of X chromosomes from both parents. This means that the pool of X chromosomes as we go down the generations is constantly changed and renewed with new DNA from different incoming branches.

This mechanism is therefore both Fan-in and Fan-out. And this is not a tree but a directed acyclic graph.

What sort of conclusion can we draw from this analysis? Well, I draw many interesting (to me at least) conclusions associated with the dynamics of evolution of the genetic pool of males and females. One can clearly see that the dynamics of genesis of females is much higher than that of males. Basically, one half of a male’s genesis remains “nearly” (please note my earlier remark about “nearly”) unchanged, and only the other half is subject to mutation, whereas in females both halves are changed.

I can only guess that Y-chromosomes are probably affected by various factors such as geographical movements, difference in environment, deceases etc., but these mutations are nowhere near as powerful as the mergers in the X-pool.

In my next memo I will write about the relationship between the above mechanisms of evolution and PID (proportional-integrative-differential) control in dynamical systems, which will lead to some conjectures about the feedback control mechanisms in evolution of species.

I would be grateful if those whose knowledge of human genetics is credible enough could report to me of any errors in my interpretation of these mechanisms.