Rx: Sand piles and Cancer

In 2001, I read Mark Buchanan’s wonderful book “Ubiquity” and became introduced to the concept of “critical states universality” through the “sand pile” game devised by physicists Per Bak, Chao Tang and Kurt Weisenfeld. They created a computer game in which grains of sand fall slowly and in a single file, and as the pile grows and becomes unstable, a single grain of sand can set off an avalanche that causes the collapse of the mountain. The grain of sand that set off the avalanche is no different than the other grains already in the pile. Rather, it is the pile that has become hypersensitive and unstable; a peculiar self-organization that gets pushed away from equilibrium and becomes prone to sudden and cataclysmic changes; the “tipping point”. This state is called a “critical state” and seems to develop in the sand pile on its own through self-organization. ‘Self-organized criticality’ has been found to underlie events as disparate as earthquakes, forest fires, stock market crashes, and mass extinction of species.

I was thinking about the application of these universal laws to cancer, especially the parallels between self-organization in sand piles and the initiation of leukemias through self-organization in bone marrow cells when I received a call from a patient who wanted to consult me from London. His name was Per Bak. Per was suffering from the bone marrow disorder called myelodysplastic syndrome (MDS) which happens to be my specialty. Since he was too sick to be transferred to the US, over the next few weeks, I was able to get him connected with the right specialists in London, where he began his chemotherapy, eventually undergoing a bone marrow transplant. There were many days when Per would call me with his latest results or ask me to help interpret what the hematologists had told him, and after our professional consultation was over, we invariably ended up discussing the issues of critical states and power laws. Many things became clear to me for the first time during these trans-Atlantic conversations. Per was ever so gracious and kind while explaining some of the more complicated aspects of his work. Following interminable and depressing weeks in the hospital, I finally received the good news from Per’s wife Maya:

Per is coming home today! His white count was over seven yesterday when the GCSF was stopped. We took a long walk in a nearby park. He is amazingly well.

I had been wondering why after spending almost $200 billion since 1971 on the war on cancer, 150,000+ experimental studies on mice and publication of ~1.5 million papers, we are still not sure about the roots of cancer. “A workable theory of cancer has to explain both why it is predominantly a disease of old age, and why we do not all die from it. A 70 year old is roughly 100 times as likely to be diagnosed with a malignancy as a 19 year old is. Yet most people make it to old age without getting cancer.” This is what W. Wayt Gibbs says in his excellent review “Untangling roots of cancer”. He summarized four prevailing views of how cells turn malignant. “For decades, the most widely accepted view of how cancer begins has been that mutations to a handful of special genes eliminate tumor suppressor proteins and activate oncoproteins. More recently, three alternative theories have gained currency. One modifies the standard paradigm by postulating a dramatic increase in the accumulation of random mutations throughout the genomes of pre-cancerous cells. Two other theories focus on the roles of aneuploidy: large scale aberrations in the chromosomes.”

Each possibility described by Gibbs traces the root of cancer to either the gene or the chromosomes within the nucleus. Because cancers universally begin in a single cell, explanations regarding origins naturally concentrate upon identifying an intracellular event as the initial cause. After reading about the phenomenon of self-organized criticality, I began to wonder about events preceding the intra-cellular gene-chromosome cataclysm which could bring about a malignant transformation.

Per was gaining strength after the transplant.

Dear Dr. Raza,

I am writing to update you on how Per is doing. First, the good news: a bone marrow test at day 30 showed 100% donor cells, which were normal! His blood counts have also been fine: the most recent is platelet over 100, neutrophils 4.5, Hb has been up and down but he hasn’t required transfusions since discharge after the transplant. All the white counts are normal except for lymphocytes (0.18). I find the change almost miraculous! Also he doesn’t have GvHD, at least nothing that the doctors have mentioned.

That’s all,


The precursors of blood cells exist in the bone marrow as “stem cells”. At any given time, only a small number of bone marrow stem cells are actively cycling to produce blood cells, the rest are in a quiescent state. The activities of the stem cells are controlled by cells of the bone marrow microenvironment or “stromal cells”. The dose of the signal stem cells receive is critical, and depends on the distance between the two cells. This distance can be perturbed as we age. In a healthy adult, roughly half the marrow is occupied by cells while the other half is fat. With increasing age, this fat:cell ratio increases so that it is not unusual to find the cellular compartment reduced to 30% in a 70 year old individual. The spatial re-organization may be sufficient to disturb the normal physiologically graded cell-cell signaling in the marrow. Even a very slight resulting proliferative advantage in a given stem cell distanced from its controlling stromal cell would gradually lead to an unchecked expansion of its clone. If this abnormal situation continues, then the marrow can eventually become predominantly “monoclonal” or populated by the daughters of one cell. As the number of monoclonal cells grow, the system may begin to move away from equilibrium, and towards self-organization and a “critical state”. Obviously, monoclonality does not by itself mean that a malignant transformation in one of the daughter cells is inevitable. Rather, monoclonality may predispose to the development of malignancy. Once a critical state has been achieved, the system is now prone to sudden and cataclysmic changes. This is the order of events:

  • Aging frees up more space in the marrow
  • Decrease in inhibitory signals (distance) that keep normal “stem cells” from continuous proliferation
  • Increase in clonal expansion of a stem cell
  • Monoclonal state
  • Self-organization and recession from a state of Equilibrium
  • Critical State Universality
  • System now predisposed to sudden and violent change
  • Accumulation of events such as single gene mutations or aneuploidy during cell division may be sufficient to “tip” the system towards a malignant transformation
  • Cancer

Support for this hypothesis comes from several observations. For example, practically every malignant cell in patients with chronic myeloid leukemia is marked by a translocation between chromosomes 9 and 22 which is known as the Philadelphia chromosome in honor of the city where the discovery was made. Some years ago, it was demonstrated that clonal expansion and a monoclonal state preceded the appearance of the Philadelphia chromosome (Fialkow). The incidence of monoclonality increases in direct proportion to advancing age; as many as 40% females over age 60 show monoclonal born marrow function (Gilliland). Interestingly, not only are almost all cancers monoclonal, but their precursor states called dysplasias are also monoclonal. Thus, dysplastic states affecting the bone marrow (MDS), cervix, liver, esophagus and stomach are all monoclonal. MDS is what Per had started with; a dysplastic state of the marrow which can evolve to acute leukemia or prove fatal by itself through an increasing profundity of the lowered blood counts. One of the saddest conversations I had with Per was several months after his bone marrow transplant. Just when everything appeared to be stabilizing, he developed one of the known and dreaded complications of the transplant procedure; severe pulmonary damage. After many rounds of therapies, some bordering on the heroic, Per finally knew that he was not going to make it. In that last telephone conversation I had with him, he talked about his young child and beloved wife. He did not want to be a pulmonary cripple and burden them any further.

Once a system follows critical state universality, it is impossible to predict the course it is going to have. The very diagnosis of cancer represents the end of a complex chain of events, where nature (stem cell) interacted with nurture (environmental influences) at multiple steps in unpredictable and often accidental ways. What are the therapeutic consequences of this hypothesis? Targeting the cancer cell alone may only be palliative rather than curative. The microenvironment which predisposes towards self-organization of any residual clonal cells needs to be targeted as well if a cure is to be achieved.

Dear Dr. Raza,

I am writing with some sad news. Per has been in Copenhagen since April, and the last three months confined to hospital. His lung function has been worsening and he has been having ongoing infections, as well as sometimes bleeding in his gut. A few days ago he decided to stop all treatment except palliative like oxygen and morphine, and is not expected to live very long. Even though his oxygen requirement is low (2 liters) he feels very incapacitated and cannot get out of bed without enormous strain.

I am going to Copenhagen now to be with him through this sad time.

With warm regards,

And after a few more increasingly painful e-mail exchanges, this:

10-01-2002 Subject: Valediction
My Dear Maya,

I was deeply disturbed to read your note. While it was good to know that Per is still alive, it is also very sad that he is essentially waiting to die. The emotional burden on all concerned is of an unspeakable nature. I should know as I just lived through a very similar situation. My best advice under the circumstances is to make him as comfortable as possible, and that is all. This may sound a bit heartless to you, but given the irreversible nature of his current problems, I think the decision made by his physicians for only providing comfort care is the right one. I hope you are not upset that I agree. This does not mean you and the rest of the family should not try to give him as good a quality of life as possible within these confines. Spending time with him, talking to him and making him feel loved are all natural parts of that.

Please keep me informed and give him my best regards,
Dr. Raza

Dear Dr. Raza,

I was saddened to hear that you had also lost your husband in this slow and deliberate way. After thinking about what you wrote, and talking some more with his doctors I am eventually coming around to going along with the plan that Per has made to die, even though it seems, as you wrote, heartless. I have always tried to give Per hope and encouragement in what were some desperate situations, so it is hard to know when to stop. I had some doubts because there are people who can live reasonably fulfilling lives, even when they are on oxygen support. But it seems clear that for Per that situation was unacceptable.

He has been resting peacefully and sleeping more and more.

With warm regards,

Shortly thereafter, a highly creative mind was laid to rest forever, and it reminded me of Alexander Pope’s moving eight lines where he looks poignantly towards death, and back to the arduous years of creating his rhyme:

Years following years, steal something everyday,
At last they steal us from ourselves away;
In our own Frolicks, one Amusements end,
In one a Mistress drops, in one a Friend:
This subtle Thief of Life, this paltry Time,
What will it leave me, if it snatches my Rhime?
If ev’ry Wheel of that unweary’d Mill
That turn’d ten thousand Verses, now stands still.

[Note: The article as written was approved by Dr. Maya Paczuski, and her emails are used with her permission.]

Suggested Reading:

  • Mark Buchanan. Ubiquity: Why catastrophes happen. Three Rivers Press, New York. 2000.
  • W. Wayt Gibbs. Untangling the roots of cancer. Scientific American. Vol 289 (1): 2003.
  • Per Bak. How Nature works. Oxford University Press, 1996.
  • Gary D. Gilliland. Nonrandom X-inactivation patterns in normal females: lyonization ratios vary with age. Blood.88(1):59-65, 1996.
  • Azra Raza. Consilence across evolving dysplasias affecting myeloid, cervical, esophageal, gastric and liver cells: Common themes and emerging patterns. Leukemia Research 24(1):63-72, 2000.