[NKS and the evolution of genomes?] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

Pages:1


NKS and the evolution of genomes?

(Click here to view the original thread with full colors/images)


Posted by: Zac Cooper

Hi everyone,
This is my first post on the forum. I have been busy, since the 2006 NKS summer school, finishing my undergrad. at Humboldt State University and have thus not had much time to spend working on NKS. That being said, I've found it hard to get NKS out of my mind ... especially the potential to use NKS to gain insight on the process of genetic evolution. I've recently been turned on to Coalescent Theory by one of my professors and was wondering if anyone had any comments on possible ties between this theory and NKS.
Also, I was wondering if anyone knows of an easy way to inplement Markov Chain/Monte Carlo simulations using Mathematica. Currently I'm using a crude, brute force method (nested If statements).

Zac Cooper


Posted by: Todd Rowland

It depends on what you are implementing, but from your description, you should consider Nest. A Markov chain dynamics depends on the previous state, which is exactly what Nest and NestList do. In reducible cases there are faster methods a well.

Perhaps if you can explain Coalescent Theory in as clean and simple a manner as possible, that should suggest some NKS directions.


Posted by: Zac Cooper

Thanks for the reply Todd. The Nest/NestList functions seem obvious in hind sight. What exactly do you mean by reducible? I'm assuming you mean some sort of symmetry, but I'm not exactly sure what this means when talking about conditional probabilies.
As far as Coalescent Theory, I was sort of fishing for someone out there that knew more than I do because I'm still trying to figure it out myself. The basic idea is treating the evolution of genetic sequences as a bifurcating tree where every node has three branches due to the nature of DNA replication. Looking backwards in time (generations), the convergence of two branches (two closely related sequences differing by some single mutation) is seen as a coalescence of two 'related' sequences into a single ancestral sequence. In this way, sequences are compared and backtracked to a common ancestor.
This is all backed up by alot of Probabalistic/Statistical Mathematics that I have just begun to scratch the surface of. I know that many kinds of branching systems have been explored using NKS and I'm currently going back and re-reading these parts of the book but if anyone has suggestions of systems that might be relevent, I would appreciate it. Nice hearing from you Todd.

Zac Cooper


Posted by: Todd Rowland

Sounds like you are on your way of getting a clear picture. Looking forward to your future explanations.

A good example of a reducible system is one defined by a linear transition matrix: x[t]==A.x[t-1]

One could compute step by step, but it is possible to reduce the computation by noticing that x[t]==A^t.x[0] and then using the power trick to quickly compute the powers of A, e.g.,

A2=A.A==A^2
A4=A2.A2==A^4
A8=A4.A4==A^8
etc.

then A^t can be written as a product of these using the base 2 digits of t. The number of products that one needs to perform are about twice as many as the length of the base 2 digits.

As far as I know, there are many different ways a system can be reducible, and it usually involves some cleverness.


Posted by: Jesse Nochella

Hey Zac,

I found a video on google video that I think you would like to see. It is about cross-similar functional non coding DNA.

Ultraconservation and Living Fossils Mysteries of the Human Genome

What kind of system is like the one that the video is describing?


Posted by: Garrett Neske

Genomics is a very tricky subject. Only 1.5% of the human genome consists of exons that code for mRNA, rRNA, or tRNA. Around 24% consists of intervening sequences that are spliced out during RNA processing, as well as regulatory regions. If this were all the genome were about, the data would be relatively easy to analyze. But the astounding aspect of the human genome is that 74% of it does not encode anything. What's more, 44% of the human genome is composed of sequences known as transposable elements that "jump" from one part of the genome to the other, seemingly in a random fashion. It is the non-coding, or "junk" DNA that many suspect to have played a role in molecular evolution. The genetic recombination that results from such "jumping genes" provides an interesting stage for evolution. But this still begs the question, why is so much of the human genome composed of non-coding DNA in the first place? Is it evolutionarily advantageous? If so, then why do bacteria have incredibly economical genomes composed nearly exclusively of coding and regulatory sequences? Also, if "junk" DNA truly is an artifact of evolution, then shouldn't the human genome, the human being among the most evolutionarily derived of organisms, be larger than that of the tsetse fly (which has more than twice the DNA of a human) or the "lowly" Amoeba dubia (which has 200 times more DNA than the human genome!)?
I very strongly suspect that there is another reason for the high degree of non-coding DNA in the human genome. I believe the reason is that the genetic code itself is evolving. While the genetic code is nearly universal, save for a few organisms such as Paramecium and organelles such as mitochondria and chloroplasts, I really don't see any particular evolutionary advantage for the same molecular language to have been spoken throughout biological history. The genetic code consists of codons (three nucleotides of an mRNA) that encode amino acids, the building blocks of proteins. What if all that non-coding DNA, at one point in evolutionary time, actually did code for protein, but no longer does due to evolution of what combination of nucleotides actually does code for protein. This needn't seem like some genetic Babel story leading to utter chaos, for I do not see any reason why the evolution of the language of molecules should in fact be deleterious.
Since this is a forum on NKS, I'd better discuss the implications of this idea in NKS research. From what little of NKS I've been exposed to so far, it seems that the main point is to examine the evolution of simple programs from a set of rules. But what if these rules themselves evolved? What if there were some "meta cellular automaton" whose evolution gave rise to new rules for "conventional cellular automata?" While my little theory (has anyone else held this idea before?) regarding the evolution of the genetic code will always remain suspect, the idea of a "meta" generative system, I believe, can be studied from a pure NKS standpoint.
Any thoughts on these ideas?

-Garrett Neske


Posted by: Tony Smith

This would be a complete aside, except that it is symptomatic of the kind of cross-domain patterns that keep cropping up in complex systems of the kind NKS seeks to emulate.

1.5% encoding, 24% regulatory and 74% unexplained (for humans, with high interspecific variation) looks way too close to 4% baryonic matter, 22% dark matter and 74% dark energy.

And it might not be too hard to come up to similar percentages with respect to three comparable categories of human-produced information.

I suspect the deeper truth is that interesting things can only happen as a quantitatively minor byproduct of a much larger self-sustaining production system, and that principle may need to influence NKS search strategies.


Posted by: Zac Cooper

Jesse, Thanks for the video. I watched some of it but I have a couple of tests this week that have me busy at the moment. Due to this, it will take me a couple of days to give you a good reply. One thing I would like to throw out there, in regards to junk DNA, is that one possibility for the selective purpose of 'junk' DNA is it acting in some sort of a buffer capacity against random mutation. I initially got this idea from a conversation I had with Eric Shultz (sp?) during summer school. This essentially allows for many mutations without deleterious effects on the organism. Prokaryotes, on the other hand, have much less 'junk' but there strategy for survival and/or proliferation is much more suited to quikly evolving genomes.


Posted by: Sean Lynch

Erik Schultes
http://www.wolframscience.com/summe...s/schultes.html


Posted by: Garrett Neske

There are those who believe that a possible purpose for all of the non-coding DNA in the genomes of more derived eukaryotes lies in its capacity to serve as a molecular stage for evolution. For instance, these individuals would argue that the non-coding DNA allows for certain degrees of freedom for beneficial mutations to take place. I believe that there is a problem with this argument, for it falls into what Gould and Lewontin have referred to as the "adaptationist paradigm," assuming that natural selection is always working toward some optimum and that inventing little adaptive stories is a safe bet for uncovering the likely selective pressures on an organism. Natural selection is blind. It cannot forsee that evolution of the genome would somehow be beneficial, so I do not suspect that non-coding DNA exists because natural selection has "allowed it to do so." Natural selection works with what it has. If it's bad, it's phased out. If it's good, it's retained, but it is not the best solution, nor is it working toward the best solution.

Going back to my argument about the evolution of the genetic code itself, perhaps the evolution of genomes can be seen from the following NKS perspective: Evolution constitutes a search the space of efficient and non-efficient programs (i.e. genetic codes) and retains the history of this search in the genome in the form of non-coding DNA. Indeed, in this space, there is no one optimally efficient genetic code since many are likely to be computationally equivalent, as Wolfram would suggest.


Posted by: janos

I always thought that "junk" DNA is part of a mechanism to manipulate coding DNA via the Lamarkian effect, where Lamarkian effect means that the individul life experiment - events during lifetime - are stored back into the DNA. It means that evulution is not blind at all, but rather it is a learning process and with the change back in junk DNA it tries to guess or influence the future. Of course I have no clue what the actual process is, but if I am looking the DNA just from pure control mechanical point of view it is hard to belive that such a complex piece of apparatus in a much more complex environment would not participate in a feedback cycle.
So in this context I think it is not just crossover and mutation that takes place, but rather a self regulatory base-flipping that relates to the impulses coming from the central nervous system of the individual as distilled life experience. A recent Nature article showed that just the mother touch/caress can induce heavier neuron growth in a newborn brain. I am positive that similar "environmental" feedback mechanisms can also affect junk DNA. Then from there on the epigenetical effects of junk DNA will have a say on future generations or in extreme case even on the affected individual.

J‡nos


Posted by: Garrett Neske

It is true that there is a certain degree of interaction between the genome and the environment. This interaction, however, does not ordinarily arise from the creation of new DNA bases, but from the differential expression of different sections of a genome. A cell of the iris in the eye, for example, is different from a liver cell not because these two very different cell types have different genomes, but because different sections of their genomes are expressed. Thus, there is very little, if any, Lamarkian nature to the genome; it is a fundamental tenet of molecular and developmental biology that different cell types arise from differential gene expression, not the modification of the genome per se.
Evolution by natural selection *is* blind, a point agreed upon by any biologist. From a purely biological standpoint the process is described as descent with modification, with the modifications being well-suited to the environment, but not at all optimal. From an NKS standpoint, the process is described as a search through the space of simple programs, many of which are equivalent in computational sophistication. But for both of these views, there is no deterministic path taken for either the "modification" or the "search."


Posted by: Chris Humphrey

Environments don't cause life; complexity does. Complexity also causes atom formation, and hence by extension; environments. Complexity refers to organizational properties that are inherent in this universe. Therefore, it can be said that complexity causes both environments and organisms.

- Judith Rosen comments on her father's work


Posted by: Chris Humphrey

[Quote]
Chaos and Complexity

One of the themes straddling both biological and physical sciences is the quest for a mathematical model of phenomena of emergence (spontaneous creation of order), and in particular adaptation, and a physical justification of their dynamics (which seems to violate physical laws).

The physicist Sadi Carnot, one of the founding fathers of Thermodynamics, realized that the statistical behavior of a complex system can be predicted if its parts were all identical and their interactions weak. At the beginning of the century, another French physicist, Henri Poincare`, realizing that the behavior of a complex system can become unpredictable if it consists of few parts that interact strongly, invented "chaos" theory. A system is said to exhibit the property of chaos if a slight change in the initial conditions results in large-scale differences in the result. Later, Bernard Derrida will show that a system goes through a transition from order to chaos if the strength of the interactions among its parts is gradually increased. But then very "disordered" systems spontaneously "crystallize" into a higher degree of order.

First of all, the subject is "complexity", because a system must be complex enough for any property to "emerge" out of it. Complexity can be formally defined as nonlinearity.

The world is mostly nonlinear. The science of nonlinear dynamics was originally christened "chaos theory" because from nonlinear equations unpredictable solutions emerge.

A very useful abstraction to describe the evolution of a system in time is that of a "phase space". Our ordinary space has only three dimensions (width, height, depth) but in theory we can think of spaces with any number of dimensions. A useful abstraction is that of a space with six dimensions, three of which are the usual spatial dimentions. The other three are the components of velocity along those spatial dimensions. In ordinary 3-dimensional space, a "point" can only represent the position of a system. In 6-dimensional phase space, a point represents both the position and the motion of the system. The evolution of a system is represented by some sort of shape in phase space.

The shapes that chaotic systems produce in phase space are called "strange attractors" because the system will tend towards the kinds of state described by the points in the phase space that lie within them.

The program then becomes that of applying the theory of nonlinear dynamic systems to Biology.

Inevitably, this implies that the processes that govern human development are the same that act on the simplest organisms (and even some nonliving systems). They are processes of emergent order and complexity, of how structure arises from the interaction of many independent units. The same processes recurr at every level, from morphology to behavior.

Darwin's vision of natural selection as a creator of order is probably not sufficient to explain all the spontaneous order exhibited by both living and dead matter. At every level of science (including the brain and life) the spontaneous emergence of order, or self-organization of complex systems, is a common theme.

Koestler and Salthe have shown how complexity entails hierarchical organization. Von Bertalanffi's general systems theory, Haken's synergetics, and Prigogine's non-equilibrium Thermodynamics belong to the class of mathematical disciplines that are trying to extend Physics to dynamic systems.

These theories have in common the fact that they deal with self-organization (how collections of parts can produce structures) and attempt at providing a unifying view of the universe at different levels of organization (from living organisms to physical systems to societies).





Catastrophe Theory

Rene' Thom's catastrophe theory, originally formulated in 1967 and popularized ten years later by the work of the British mathematician Erich Zeeman, became a widely used tool for classifying the solutions of nonlinear systems in the neighborhood of stability breakdown.

In the beginning, Thom, a French mathematician, was interested in structural stability in topology (stability of topological form) and was convinced of the possibility of finding general laws of form evolution regardless of the underlying substance of form, as already stated at the beginning of the century by D'Arcy Thompson.

Thom's goal was to explain the "succession of form". Our universe presents us with forms (that we can perceive and name). A form is defined, first and foremost, by its stability: a form lasts in space and time. Forms change. The history of the universe, insofar as we are concerned, is a ceaseless creation, destruction and transformation of form. Life itself is, ultimately, creation, growth and decaying of form.

Every physical form is represented by a mathematical quantity called "attractor" in a space of internal variables. If the attractor satisfies the mathematical property of being "structurally stable", then the physical form is the stable form of an object. Changes in form, or morphogenesis, are due to the capture of the attractors of the old form by the attractors of the new form. All morphogenesis is due to the conflict between attractors. What catastrophe theory does is to "geometrize" the concept of "conflict".

The universe of objects can be divided into domains of different attractors. Such domains are separated by shock waves. Shock wave surfaces are singularities called "catastrophes". A catastrophe is a state beyond which the system is detroyed in an irreversible manner. Technically speaking, the "ensembles de catastrophes" are hypersurfaces that divide the parameter space in regions of completely different dynamics.

The bottom line is that dynamics and form become dual properties of nonlinear systems.

This is a purely geometric theory of morphogenesis, His laws are independent of the substance, structure and internal forces of the system.

Thom proves that in a 4-dimensional space there exist only 7 types of elementary catastrophes. Elementary catastrophes include: "fold", destruction of an attractor which is captured by a lesser potential; "cusp", bufurcation of an attractor into two attractors; etc. From these singularities, more and more complex catastrophes unfold, until the final catastrophe. Elementary catastrophes are "local accidents". The form of an object is due to the accumulation of many of these "accidents".


Glossary of terms by Dan Winter




Fractal (fractality/fractal attractor): when the small part of a pattern contains a miniature of the whole pattern, it is said to be self-embedded, or recursive. This kind of symmetry among waves, permit the long, to cascade right into the same pattern in the short wave, creating a cascade or vortex or attractor. This IS Ability to Embed;
Embedability (Idealized Recursion): The ability of a short wave to embed or nest non destructively in a larger one. Similar to Fractality. See how this is IMMERSIVE, in the sense it allows one biological oscillator to enter another. To begin the process is SELF RE-Entry, optimized by PHI, the Golden Mean..




Forum Sponsored by Wolfram Research

© 2004-2008 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. | Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings