Complexity of the DNA double helix -- -- introduction -- -- September 2006

A Mathematical Analysis of the DNA Double Helix

  Thomas J McCabe

  Copyright c, September 2006

How to read this

Don't worry about not understanding all of it.  See the direction, the motivation, and the spirit.  There is enough here to get mathematicians interested in genetics, and there's plenty to get geneticists interested in the possibilities of applied 
mathematics.  There is more than enough to get the general reader interested in the new breakthroughs in genetics and excited by the possibility that the underlying genetic machinery may be mathematically tractable.

Introduction

There is a seduction here.  It seduced me.  I hope it seduces you.

This is a story that interrelates two branches of study -- -- molecular biology and pure mathematics.  Molecular biology is about genes and the biological structure that holds them -- -- the DNA double helix.  The new science of molecular genetics has had momentous breakthroughs in the last several years: sequencing the human genome, identifying and locating over 30,000 human genes, identifying various morbid genes that lead to fatal diseases.  The breakthroughs in molecular genetics are happening every day; for example, today October 30, 2006 there was an announcement in the news that genetic have identified a 100 million year old honeybee and have sequenced the genome of current honeybees to understand their social 

behavior.  The breakthroughs in molecular genetics concerning our DNA and genes will be the defining event of the 21st century.  Many diseases presently fatal will have genetic prescriptions, lifespan will be extended, and a host of chronic disabling diseases will be both prevented and have more effective palliative treatments. More broadly the striking genetic similarly of many species is being identified, our evolutionary ancestry is being clarified, and the underlying genetic machinery common to all life will be fully understood and replicated.

The universality of DNA and genes, the common machinery of its cell division and protein synthesis, is stunning.  Every living species has such DNA and genes.  Likewise, every extinct species had its own DNA and genes.  The breakthroughs being made in genetics, as often as not, are pertinent to several species.  In fact, the similarities across species are striking -- -- the underlying mechanism for the splitting of cells and the protein synthesis of genes within each of many varied creatures is almost identical. The genome of a mouse is 99 per cent similar to a human; our genome is only 15 per cent larger than a mustard plant’s.

The structure of the DNA is intriguing; besides it’s universality as the code book for all living species it is also mathematically symmetrical and regular. There are two north-south backbones; one male, oriented north to south, one female oriented south to north. The horizontal latter has the four letter alphabet of the genes; which are encoded as bases, 

made up of four nucleotide chemicals: adenine, cytosine, thymine and guanine, usually denoted by the letters A,C,T, and G. The letters form base pairs that link together to form the rungs on the ladder of the DNA double helix. Genes are finite sequences of bases along each of the vertical backbones.

The other thread binding this story is of applied mathematics. Mathematics is called the purest of the sciences.  Mathematics requires no experimentation, or physical validation. Mathematics is not dependent upon a contemporary view of physics or chemistry, or astronomy. To mathematicians the classical life sciences and biology had seemed intractable; their processes seemed way to randomly chaotic and loose to admit of mathematical analysis.

Molecular biology has changed all that.  The DNA double helix is such a regular, stable, and rich structure that it can be thought of as mathematical object. Also the recent discoveries of the detailed process of cell replication and gene synthesis is so uniform, even across different species, and meticulous, that we can now apply mathematical concepts. The incredible recent genetic breakthroughs have demonstrated a universal regularity; the molecular biologists have opened the door for mathematicians.

This paper will present mathematical insights that systematize and simplify the way genes are produced from DNA. The mathematical concept we will use is a Vector Space -- a rigorous concept which has been developed over the course of many centuries. This paper will attempt to model the DNA double helix as such a mathematical Vector Space; if successful there will be many direct results. One of which will be a classification of genes into two camps -- -- basis genes and composite genes.  Vector Space analysis will provide a way to generate composite genes without the usual DNA protein synthesis -- -- composite genes will be shown to be linear combination of basis genes. Vector Spaces can potentially lead to alternate ways to generate genes and proteins; it could enable man made genetic drugs and medicines.

Partly because mathematics is pure and not dependent on physical science it’s subjects tend to be abstract, obscure, and lifeless. Not here, the target of our mathematical analysis, DNA and gene generation, is life itself.  Every living thing, present or past, has DNA and genes -- -- so our subject is life universal. My finger tactile genes are being generated faster than I can type about the mechanism my finger DNA cells are using.  Your DNA has produced genes for your optic nerve faster than you can read about how it does this. This  is a mathematicians delight; our mathematical target is the most universal of life forms… the mathematical analysis of the DNA double helix … I hope you’re getting seduced.

The physical characteristics of DNA and genes are indeed mystical and seductive.

Size

Each Homo Sapiens has 500 billion cells.  Each cell has a nucleus containing 24 chromosomes that contain the DNA double helix.  Within each cell the information along the male and female strands of the double helix is rich enough to produce a complete clone --- not just of the cell itself, but a clone of the complete person.  If we spliced a human's DNA together and stood it end-on-end, it would stand about a six story-building high.

Speed

Each cell generates a new gene about every four seconds.  In the time it takes you to read this page your cells would have produced about 2 trillion new genes.

Omnipresence

Every living thing has DNA and genes.  Whales do. Microscopic life forms which could have an 8 million metropolis located on the head of a pin, indeed have DNA and genes.  Chimpanzees have 99.9% of the same genetic makeup that we do; we share 75 percent of our genetic makeup with a mouse.  For that matter the sea squirt, which Aristotle thought was a plant, has embryos which are strikingly similar to those of humans.

Symmetry

to be continued ……………..

Section IV Computer Science --- 2010

Identifying and Isolating software security risks   ............ just written. A neat application of both graph theory and set theory. Isolates a security flaw or bug. Works with incremental testing or gestalt batch testing. 

Presentation in Paris ----- March 9, 2010

This was the announcement of a talk I gave to the 'Club Qualimetrie' in Paris on March 9 2010. One of the topics was a new way to isolate a computer software threat with some new techniques I recently developed and in the process of publishing. The approach uses both graph theory and set theory to subset the exact fault edges along a entire end to end fault path. I am hoping and anticipate this will have a timely and significant impact on the current software security crisis.

This was the first time presenting this and it always amazes me how much I learn presenting new ideas --- all the reseach in the world seems incomplete until presenting it to practioners involved in everyday software nuts and bolts. Everone was excited and thought it a 'killer' app.

It was equally exciting to be with my gracious French associates who I now call friends. There were fascinating discussions with fellow French computer scientists of a different nationality --- so much alike yet so different. On these trips it's always me that learns the most ---- me the teacher! 

This trip and lecture I considered more of an artistic expression than a business trip --- unlike the many lectures I have given previously in Paris while I was a CEO making things happen. The fact is that my technology, company, and work has always been more about something I created, my art form;  my presentations are more about self-expression than tpical business issues. It was always that way and in fact that's what gave me the energy and drive to succeed. Instead of talking about the business bottom line I had a passionate enthusiasm for my mathematical breakthrough and how that could solve many of the problems. A business man talking of the bottom line is scant competition for an artist creating a top line ....  On this trip it felt energizing and liberating to fully embrace that spirit.


Irony would have it that my hotel and the presentation were in the Paris District of Montparnasse, south of the Latin quarter.  When Paris was the artistic center of the universe in the 1920s Montparnasse was the home of the 'lost generation', world renoun artist and philopsphrs ----John Paul Sartre, Henry Miller, Ernest Hemingway, James Joye -- -- a nurturing enclave of creative self-expression. I stayed several extra days and visited their haunts --- Luxenberg Gardens, cafes of Clôserie des Lilas, Le Dôme, La Rontonde.  The environment and culture was much more suited for artists than businessmen.

Paris has always had a unique charm and this trip was no exception.

Presentation in Beijing, June 2009

Here's the announcement:

Lecturing at the Chinese Space Agency was a fulfilling adventure.  A driver picked me up at 7:30 AM at the Beijing Great Wall Marriott for a talk beginning at 9:30 AM -- -- -- I wondered why so early?  With the Monday morning traffic and all the bicycles in a serious commute it took one hour just to circle around the Marriott and get pointed in the right direction.


When I lecture these days I am struck by how young the attending computer scientists are, and the space agency employees were that and also a good deal shorter.  When I arrived and took a shuttle bus from the Beijig airport terminal B, the largest buiding n the world,  I stood next to a Chinese todler being held by her mother. She took one look at this big white giant and started to cry -- -- so even at 6' 1" I look like the Jolly White Giant to the Chinese.


There is a certain Chinese respect and reverence present even in modern careers like computer science that became apparent when I was interviewing for a local newspaper by two young female Chinese reporters after the presentation.  In the interview they started fielding light casual topics and I had the distinct impression they were building up for what they really want to ask -- -- -- and then it blurted out.  They asked ' why did you lose your generosity when you sold your company?.  They had complimented me on inventing the structured testing technology and growing a company to deliver it worldwide -- -- -- and then expressed their huge disappointment that I would sell the company and no longer lead -- 'losing my generosity'.


As I traveled throughout China I could see how the Chinee culture expects self dedication for the common good.  I happened to be traveling with a group of entrepreneurs and CEOs and we visited several Chinese cities --- Beijing, Qinghuangdao, Hangzhou, Haikou, Hong Kong .  Seeing their traditions and deeply rooted culture and history gave the refrain of 'losing my generosity'  more meaning.  They expect a good citizen to freely and joyfully contribute their gifts to Chinese society -- expressing their generosity.


Touring Chinese cities was a good opportunity to bounce some ideas off my fellow CEOs.  The discussions centered on finding a sweet spot after selling your business.  The other CEOs are obviously different but during the 14 days we toured China and Vietnam my sweet spot became clear. 


I am now back publishing and lecturing.  I may or may not regain 'my generosity' but I am sure having a good time.  Thank you Chinese.

Visiting Vietnam

Vietnam

Background -- -- I had been traveling with a group of CEOs visiting various cities in China from June 21, 2009 through June 29: Beijing, Qinghuangdao, Hangzhou, Haikou . We then proceeded on to Vietnam for four days.

I was excited just knowing we were going there --- Vietnam was a watershed event for my generation, especially for Vietnam era servicemen. The prospect of being called for the Vietnam war lasted for years and colored our youth with an anxious gray gloom --- Robin William's 'Good Morning Vietnam' captured the absurdity and gallows humor of the day. Vietnam was the seminal passage of my youth, and it was about to provide another seminal event.

Flying within China was exciting, particularly landing in a new city --- I always enjoy the cab ride from the airports to the cities. You get a glimpse of real life, not just a five-star hotel experience -- -- the trip from the airposts typically goes through some real neighborhoods and you get a sense of the way the native people live.

It was all that and much more flying into Hanoi. We were staying in the Hanoi Hilton no less, namesake of the infamous North Vietnamese prison camp.

I had been a captain in the United States Army. I was trained in the combat branch infantry and also was an intelligence officer in the Army security agency. I had attended the combat platoon leader training course in Fort Benning, Georgia during the months of March and April in 1967. Many of my infantry fellow officers had been in Vietnam already and most all of them upon graduation were assigned duty in Vietnam. I was extremely fortunate not to go. My thoughts often wandered back to my classmates in Vietnam.

As we flew into Hanoi on June 29 it brought back all the feelings of anxiety anybody in the service during the war had in the pit of their stomach. I also thought of the many US servicemen flying into Vietnam during the war -- -- and the incredible anxiety and angst they felt. Many never came back alive and many more were harmed for life. Even though it had been forty three years ago, I was surprised at the present intensity and strength of the feelings --- more than a sightseeing excursion Vietnam demanded homage as a hallowed ground, where many of my fellow servicemembers gave their life.

We arrived in Hanoi around six o'clock in the morning. The cab ride took three quarters of an hour, most of which was spent in the city stuck in rush hour traffic -- -- the likes of which I have never seen. It seemed like a roller derby of scooters and motorcycles crisscrossing in every direction. It seems we nearly got in an accident about every five minutes, just veering off at the last second. I sat up front next to the taxi driver so I could take it all in. It was so crazy that craziness became mood -- -- instead of fear, it seemed humorous and other worldly --- reminsent of the Vietnam era gallows humor --- 'Good Morning Vietnam,' humor as survival mechanism.

We crashed at the hotel for only a few hours and then took a three-hour limousine drive to Ha Long Bay. The limousine was so rickety and the driving so crazy that several CEOs attempted to tell our Vietnamese speaking driver to slow down. It was really interesting to see the small towns, rice paddies, water buffaloes walking free, roadside stands and the countryside of Hanoi. The poverty was striking -- there were several poverty driven customs that were surprising. For example caskets are reused after five years, the Vietnamese thought being that the spirit leaves the body within five years so the casket can be reused. I'm sure the real reason is the cost and I'm also sure there are other similar poverty necessitated customs.

About a dozen CEOs went on the Ha Long Bay trip and boarded a Vietnamese junk for a tour of the bay and an overnight stay. I slept alone on the open upper deck of the junk and enjoyed a

sense of vulnerability and adventure --- and the view of other Vietnamese junks with multicolored night lights reflecting off the still soft water beneath a gloroois Vietnamese sky. The beauty was enrapturing and accompanied with a tinge of guilt thinking of my fellow servicemen in Vietnam in a different, more difficult, era.

Next it was off to Saigon --- currently known as Ho Chi Men City. Another crazy taxi ride with water bug traffic -- -- several passengers got upset but I thought of it as a caricature of the city and the zany mantra 'Good Morning Vietnam.' Many of our CEOs were upset with a second class hotel and further irritated that the person who organized the China and Vietnam trip bailed out in the Saigon airport and went home to the USA. In the spirit of Vietnam of the 1960s I anticipated things would be crazy and found a certain wacky romance in the whole ordeal. I upgraded my room, the rest of the CEOs reluctantly stayed, and we proceeded with our tour of Saigon.

The War Remnants Museum was built by the North Vietnamese memorializing their victorious war. It was a different experience being an American in a museum built by our erstwhile victorious enemy. About half the people in the museum were Vietnamese and most of the other half were Orientals with a few Europeans. The only Americans present were fellow CEO American entrepreneurs in our group. It indeed felt strange and we caught the eye of several Vietnamese --- everybody was respectful if a bit tense.

There were many anti-American photographs, stories, testimonials, and American weapons and captured American fighter jets -- -- all of which we presented in a sinister way. Americans get a steady dose of the evils of the German Third Reich which I am sure is overly dramatized --- so I arrived expecting a dose of the same. The themes seem to be one half describing the horrors of war, and the other half describing the brutality of the American military.

As an American serviceman I thought about half of their characterization of the American behavior was fair. The shoe was on the other foot, and all although it was uneasy, I was glad to visit.

One striking Museum image I think of often, even now a year later, is the agent orange used in Vietnam. Hundreds of thousands of our Vietnam era veterans now suffer severe neurological damage because of agent orange. In Vietnam the suffering is tenfold -- -- it was in their country we dropped it. They had a separate enclosed theater with a movie showing the horrors of agent orange which would replay all day long. This is a horror the United States is truly responsible for, I don't think our Department of Defense has fully knowledged the damage suffered by our own veterans and I'm sure we have not reconciled what we did to the Vietnamese people.

We spent a lot of time walking downtown Saigon. There is a beautiful Notre to Dame cathedral built by the French contiguous to a beautiful Central Park area in a completely redeveloped downtown with upscale hotels and gourmet restaurants. We walked several hours for two days throughout the city and along the Saigon River.

The most poignant stops in the city were war related. The US Embassy, scene of the last Americans leaving by helicopter from Vietnam, the People's Palace was the headquarters for the South Vietnamese government now occupied by the current government, the US hospital, and the War Remnants Museum.

I had hoped to meet a Vietnamese who had been in the war. It happened on July 4 at 4am taking a taxi to the airport for our 6:05am departure to Hong Kong ---- the driver had been in the South Vietnamese Navy. I explained my background and interest and he was excited to meet me and very cordially escorted us to see the war related sites mentioned above. he was obviously pro-American and mentioned working closely with the U.S. Navy during the war. It was interesting that he was in the war for the duration -- -- he had spent eight years fighting in the Mekong Delta --- our servicemen had a one-year tour and then they would rotate 'out of country.'

I asked what happened when the US military left Vietnam in 1974 when after about one year the North Vietnamese communists overran the country-- -- I was specifically asking how they treated military personnel and what it was like. This was the one question the cabby would not answer ---- there was an awkward silence and I realized he couldn't fully answer the question due to the political climate, so I let it go. I found out later that hundreds of thousands of people were murdered and military offices above the grade of Captain were rounded up and mysteriously disappeared. Ironically much of this sad detail was filled in by my local barber who was at the US Embassy when the last US helicopter flew off. She told me of the many people sacrificed when the Communists took over and the terror of living under the communist regime.

I found what I had been looking for -- -- the driver was of my generation and he likewise asked me many questions about the US military and our domestic reaction to the war. We connected with a certain kinship and it broadens my empathy for those who sacrificed during the war, to include the many Vietnamese who paid a heavy price. It was a wonderful warm reunion and I hated to arrive at the airport. We hugged and exchanged affectionate and respectful salutations.

I was the only ex-serviceman in a group of touring CEOs and had a very different take on Vietnam than my colleagues. Their main focus and interest was of the thriving Vietnamese

economy and their sense of the war was only as a distant historical footnote. For me it was witnessing a path not taken -- -- many of my contemporary infantry comrades paid the ultimate price in Vietnam. The Vietnam era memories and strong emotions were palpable and still affect how I see the world.

You can't return home again

.  

Returning home again can hold many surprises and prosaic moments. The comfort of familiar faces, the warmth of childhood scenes, relishing fond memories, and most poignant of all – reconnecting with friends of old. Going home again is a strange admixture of the certainty of the past with surprises of unexpected change. Old friends are the best example of this – – the comfort of a shared youth you know so well and a conversation with a nostalgic warm flow are interrupted by turns of fate you never imagined.  We somehow project an idealized fate for early friends and are taken aback by unexpected surprises while filling in the lost years.

Catching up on old acquaintances, getting filled in on the story of people's lives – – here's where many surprises lay hidden. Discovering significant life success from 'kids' you thought were headed for a dead-end, and the other way around. The high school classroom stars that took a wrong turn – – stories of alcoholism, families abandoned, chasing after waning youth.  Stories of long ago friends, shared from the perspective of old men, recalibrating a mutual starting point in our mutual youth and fast forwarding life stories.

My trips back home brought a palpable comfort --the feeling that all's good, being back home where things are safe and you are taken care of. Rediscovering the long lost sense that someone is taking care of you, momentarily easing back home where life is provided for, feeling a freedom of spirit protected by home's safety net. A feeling unutterable by words, but present none the less. A sense of returning from a long lonely trip to home where super viligence is out of place, letting down your guard. As if your parents reincarnated to the perfect nurturing age --- setting you free again to explore without danger -- going out to play and return when the street lights go on --- to a loving home where all is taken care of.  Isn't this the way it's supposed to be, the safe harbor after the long journey, we return home, the warm womb of home where all is well, to tell the story of our adventure.

There's a historical perspective the return trip brings, a framing of one's life story, on a canvas bordered by where we started and where we are now.  Hearing early buddies confirm our sense our history’s beginning juxtaposed to where we are now --- seeing the contrasts, synergy, the preordination.  Seeing the storyline of our life unfolded from the beginning. Making sense of our life story, looking for its poetry, our path in hindsight seeming more like destiny than the random meandering it felt like. The unspoken agenda being played out is valuing and honoring our respective life paths. The homecoming gift here is that only close early friends can co-narrate this retrospective –especially close friends that shared dreams.

There’s a magic conversational ‘peek a boo’ going on here --- we each vacillate between our customary adult personality but revert way back to silly adolescence by our teenage view of our friend. It’s ‘now you see me, now you don’t’, the inner child resurrected and disappearing again.  Belly laughs and exuberance fill the air, gifts we soulfully miss as adults,  that’s reserved only for the young --- but here we cheat our old age and laugh like kids again -- a ‘peak’ into our former innocence – home again, young again. For moments we forget age and we’re right there where we started --- what a gift. George Bernard Shaw said 'youth is wasted on the young'; there's no waste here, this gifted glimpse into our youth is celebrated and savored.

Our peek-a-boo conversation with a two-headed personality gives a rare glimpse into who we really are. My reconnection with home and friends happened well after my retirement, and my close childhood friends likewise were retired. Each had already decompressed from a career personality --- the veneer we wore to be successful was wearing off.  As an entrepreneur I had to belly up to high risk and assume responsibility for a company, and I always assumed that the ‘take charge’ mentality I had grown into was a gift.  The Zen of this homecoming adolescent behavior sheds our pretenses, to open and see our real authentic personality.

Who are we really?  The take charge entrepreneur who only focuses on opportunity, or the mischievous child who fixates on humor? The hyper vigilant high risk taker, or the cavalier story telling dilettante?

We are both. The long years looking only upward at a career latter stifled the inner child, and now he peeks out, a bit unsure of himself, both joyful and fragile. The rebellious silly inner child seems at diametric odds with the driven entrepreneur businessman – but in truth, the early rebellion was the seed of an offbeat vision the enabled the entrepreneur.  

My Biography

Thomas J. McCabe, founder of McCabe Software, author, inventor, entrepreneur, speaker -- is internationally known for his development of software metrics that bear his name. As Founder, CEO, and Chairman of McCabe Software, Tom grew the company and three European subsidiaries to a critical mass of 175 people based on his original research.   In 1999 he was appointed to lead the Washington DC chapter of the Chief Executive Officers (CEO) Club, a group consisting of founders and entrepreneurs.  Tom also actively speaks across the country and overseas on software development as well as on entrepreneurship. 

He gave a talk in Beijing to the Chinese Space Agency in June 2009 on using the McCabe metrics on the Chinese moon landing project. In December 2009 he gave a presentation to Greek CEOs in Athens on entrepreneurship; during 2009 he made presentations to various industry leaders like Qualcomm in San Diego. He gave a talk in Paris in March 2010 announcing a new mathematical breakthough to isolate computer viruses.

In 2009 Tom McCabe’s publication on software complexity was chosen as one of the retrospective 23 highest impact papers in computer science by the ACM-SIGSOFT. Tom was the 1998 recipient of the fourth international Stevens Award and presented the Stevens Lecture on Software Development Methods on March 10^th in Florence, Italy. He also testified before congress in the hearing entitled, “Year 2000: Biggest Problems and Proposed Solutions” in June of 1998.  CNN Headline News aired a segment featuring Tom McCabe where he was interviewed on the Year 2000 in 1998. Tom has recently given presentations to the faculty and student body at the University of California Polytechnic, the University of Connecticut, and the Citadel on entrepreneurship. 

Tom currently is on the boards of several US and European companies. He is leading a project to apply mathematical complexity analysis to the DNA double helix. He has authored a paper which applies mathematical analysis to biological emergent intelligence.

Tom McCabe’s landmark research appears in “Design Complexity Measurement and Testing” which was published in 1989 in Communications of the ACM.  Other publications include “Software Complexity” with Arthur Watson, CrossTalk, 1994; “Combining Comprehension and Testing in Object-Oriented Development” with Arthur Watson, Object Magazine, 1994; “Testing an Object-Oriented Application” with Lori Dreyer, Albert Dunn, and Arthur Watson, The Journal of the Quality Assurance Institute, 1994; “An Engineering Approach of Software Maintenance” with Eldonna Williamson, CASE Outlook, 1992; Tips on Reengineering Redundant Software” with Eldonna Williamson, Datamation, 1992; and “Reverse Engineering, Reusability, Redundancy:  The Connection”, American Programmer, 1990.