Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Sunday, July 8, 2007

Cancer: A Mistep into Chaos Quicksand?

I spent much of this weekend pouring over two publications. The first, Probing Genetic Overlap Among Complex Human Phenotypes, was published in PNAS. Gene Expression has a nice post about the publication. While the paper itself focuses on genetic overlap between Autism, Schizophrenia, and Bi-polar Disorder, the scope of the work spans across over 150 diseases which were all compared in a pair-wise fashion. My personal interests in this work lie in their findings regarding Amytrophic Lateral Sclerosis which the authors included in their 200+ pages of supplementary materials. As I learn more about this work, I will share more about my understanding of the potential significance.


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The second publication I spent a lot of time attempting to wrap my feeble mind around this past weekend was a fascinating conceptual "modeling" paper written by Dr. Ivo Janecka, MD, MBA, PhD (that's a lot of letters...). As I mentioned in my post about Miuro, I am very much intrigued by chaos mathematics and non-linear dynamics. It is the most ambitious of my many amateur interests.

The introduction of Janecka's publication starts with a quote by Fritjof Capra saying:

"The more we study the major problems of our time, the more we come to realize that they cannot be understood in isolation. They are systemic problems, which means they are interconnected and interdependent."
It is a sentiment which many scientists share, but is very easy to lose site of when we attempt to make our research efforts more manageable. We try to linearize our experiments. We pretend that we can study individual variables. We forget that we are usually attempting to solve complex problems rather than answer simple binary questions. In the twenty-first century, living systems and their "problems" are proving to be more complex than any systems humans have ever tried to understand.

When I decided to pursue a career in life sciences, it was because I could not imagine that any other field of study could offer systems as beautiful and mysterious as life. I also could not imagine a field that could offer so much promise to help fellow humans once some of the mysteries were unlocked.

In this publication, Janecka offers a conceptual model for life systems. He describes life as a "non-linear dynamical system following the principles of organized complexity" with a "health territory" defined by the the systems ability to self-organize and self-adapt.

OK, so what does that mean? Let's take it one part at a time.


What is a non-linear dynamical system?

This is a system where small changes to early conditions can directly result in hugely different results at some later time. Many people have heard of the concept of a butterfly fluttering its wings on the North American west coast resulting in dramatic changes to huge tropical weather system on the east coast. Weather patterns are good examples of non-linear dynamical systems.


What is self-organization?

A system that self-organizes is one that will find a way to go back to "normal" after it has been disrupted. Imagine a beehive that is completely buzzing with activity. Now, imagine throwing a very small pebble at that beehive and disrupting the activity of the bees. For a few moments, the bees buzz away and circle the hive, only to go right back to the hive. The hive then appears almost exactly as it had before it had been disrupted. The system always approaches an organized baseline of activity.

Life, specifically human life, is very much the same. Our bodies work to self-organize. When we suffer lacerations, bleeding stops and the lesion closes/heals. This propensity to self-organize is catagorized by Janecka into a "zone of order".


What is self-adaptation?

Self-adaptation can be described as a systems flexibility to change based on information received from outside to the system. If you have ever attempted to play the guitar, you will know that it hurts at first. Fingertips become raw. Forearms become very sore. Over time, the muscles in the hand and forearm become much stronger and the fingertips become calloused and less sensitive to pain. The system is self-adapting to the information conveyed from the environment. If we could not adapt the environment around us and we didn't have flexibility to express a variety of phenotypes, our species could not survive. This flexibility is catagorized by Janecka within the "inner edge of chaos".

If life is a self-organizing and self-adapting system, then, Janecka reasons, it can be described as a pendulum swinging back and forth through the "zone of order" and the "inner edge of chaos".

When life swings too far into the "zone of order", it is at the expense of adaptability. This can result in detrimental rigidity as in the case of ECG cardiac signalling. Lack of chaotic fluctuations in cardiac electical signalling invariably indicates cardiac disease because of its lack of adaptability to variable conditions of stress and strain. Imagine if your heart couldn't beat faster when you needed to run. You wouldn't be able to get oxygen to your blood and muscles fast enough. It would be detrimental to you as a "living system".

Likewise, when life swings too far past the "inner edge of chaos", the system loses its ability to self organize. This can be observed in cases of cancer where a subsystem of cells within the complete living system loses the ability to regulate expenditure of resources. In cancer, most cellular resources are allocated to reproduction instead of differentiation and functionality. The cancer cells replicate in exponential self-similar chaos fractal patterns like the common Mandelbrot geometic patterns of Merkel cell carcinomas.

Janecka suggests that many untreatable human diseases can be catagorized as pendulum swinging too far in either direction of the self-organizing/self-adapting systems. A swing in either direction plunges the living system into a stage of accelerating entropy ontil the system completely unravels at death. He goes on to suggest that scientists and clinicians could use the model to evaluate what needs to happen to a diseased patient to best bring them back to their healthy balance of order and chaos. In the case of cancer, Janecka proposes that efforts be made to re-educate the cancer cells to move back toward efficient energy consumption. Teach the cancer cells to differentiate again instead of reproduce. Re-balance the system.

The concept is fascinating and I look forward to following up on researcher who reference this publication.






Sunday, July 1, 2007

Doing the Robot to a Chaotic Beat

Omnome is dedicated to talking about three broad subjects and how they intersect at the point of human application; technology. The subjects are:
  • Biology
  • Physics
  • Mathematics
So far, we have talked a LOT about biology, a little about physics, and not at all about math. Honestly, it bothers me that I haven't written about math at all. Mathematics is what ties all of this together. Mathematics, by one definition, is the study of quantity, structure, space, and change. That covers a great deal since most scientific study can catagorized as the study of quantity, structure, space, and change.

In any case, I am going to introduce math to Omnome by talking about a little Japanese robot named Miuro that has a few functions. First and foremost, Miuro is a music player that can play music from an iPod or from a WiFi connection. Secondly, though, Miuro can dance. Ok, so I have watched the video, and I find Miuro's dancing to be rather lame and nondescript. It basically rolls around with a few shimmies to the beat of the music it is playing. See the video below:



Like I said, kind of lame and non-descript, right? However, the interesting thing about Miuro is that it doesn't actually have pre-programmed dance patterns. I remember very distinctly the first time I found myself almost uncontrollably tapping my feet as a young child listening to a song that came on the radio in the car. I had never learned any dance moves, yet my brain picked up a pattern in a song that made me decide to tap my feet in time with one of the song's cadences. Miuro is designed to do the same thing.

Miuro has software rooted in mathematic chaos theory that allows it to decide how to react to the music. So what is chaos theory and how would it allow a robot to "decide" anything? The study of chaos in mathematics is the study of systems with more than one changing variable that seems random, but is very much dependent on the initial conditions. Weather patterns are chaotic systems as are Earth's magnetic fields and human economies. Basically, any system that can change exponentially as a result of numerous variables in time can be considered a chaotic system. Most things still to be discovered in most fields of study will somehow be tied to these very complex systems.

So Miuro is a robot that has software that is designed to change its movement unpredicably based on: 1) The motion it is already carrying out and 2) the many musical tracks recorded in a given song 3) Where it is dancing. Any of these many variables will make Miuro decide how it wants to bust a move. Most artifical intelligence (AI) researchers believe that AI break-throughs will be ushered in via harnessing of chaotic decision making models somewhat like the Miuro model.

So this is a humble introduction to the world of Chaos Mathematics and/or Non-linear Dynamics. These are subjects of much interest to me. Unfortunately, I know very little about them right now. I am a sub-amateur student of them. I hope to change that over the coming years. I hope you, my readers, can teach me a little bit about the subjects. I hope to broach the subjects with regards to genetics, proteomics, physics, weather, disease epidemiology, and much more in the future.