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Debra Malina, Ph.D., Editor

Why Does the Weeping Willow Weep? ReconceptualizingOncogenesis in Breast Cancer

Michael Baum, M.B., Ch.B.

Why is my flat-fronted, early-19th-century Geor-gian cottage considered so desirable in my partof northwest London, even though it lacks deco-ration or even a brightly painted front door? Itsattraction, unlike that of Baroque or Victorianarchitecture, has nothing to do with elaboratestucco or stained glass windows; rather, its re-lated to something integral in the proportions.The ratio between the height and width of aGeorgian town house is replicated in the pro-portions of the door and the windows and againat a smaller scale in the panels on the door andthe individual windowpanes. For reasons thatare obscure, the ratio of height to width of 1.62 called the golden ratio is intrinsicallybeautiful both in art and in nature. Is it possiblethat there is an evolutionary advantage of beauty,

or is the ratio the common currency of health inthe animal and plant kingdoms that has foundexpression in architecture and design since an-cient times? Of course this is a circular argumentlike the chicken-and-egg paradox.

If you look at the weeping willow tree in myfront yard and measure its branches and feath-ery hanging leaf clusters by extending your arm,holding up a pencil, and squinting one eye, youwill find that the ratio between the lengths ofproximal and distal branches at each bifurcationis the same as that of the length of the trunk to

the length of the first branches approxi-mately 1.62. That ratio also holds for second-,third-, and fourth-order branches. If you lookclosely, you can see that even the terminal leafcomplexes repeat this beautiful symmetry. Thissequence of a constant ratio is known as fractalgeometry. It is but a small leap of imaginationfrom botanical beauty to the idealized beauty ofthe human face. The ratio of length to breadthof an almond is a repeat of the golden ratio, and

we might extol the beauty of the celebrated por-trait head of Nefertiti by describing her eyes asalmond shaped.

But what interests me more than surfacebeauty is the aesthetics of the internal anatomyof the human body both in sickness and inhealth. The obvious place to start is the aptlynamed bronchial tree, where once again we seeperfect fractal geometry and golden ratios. Thesame applies to the vascular trees supplying mostof the organs and the collecting systems of ex-cretory or secretory glands. So what happens tothis ubiquitous symmetry in disease?

It is hard to convey a surgeons enthusiasmfor the study of pathology. Certainly I, and I sus-pect others, take an aesthetic as much as a scien-tific interest in the subject. The aesthetics can

be appreciated in the exquisite microscopicanatomy and molecular biology of the normalbreast before we examine the malignant trans-formation that turns this transcendental beautyinto life-threatening ugliness.

Broccoli, as well as resembling the bronchialtree, offers an almost perfect representation ofthe mammary ducts and glands at the time oflactation. The main difference, of course, is thatthe branches of the mammary gland are tubular.Imagine a treelike tubular structure and thenimagine taking transverse or random oblique cut

sections and magnifying them. If the structureis perfectly symmetric and the cuts are perfectlyhorizontal, you will see a plane scattered withsymmetrically positioned circular structures. Ofcourse, in real life the organs are not perfectlysymmetric and the pathologists cut is not per-fectly horizontal to the central tubes of thesystem. In fact, when you examine the breastcarefully, you will find as many as 12 ducts open-ing at the nipple. Each of these is the mouth of

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a treelike system for gathering milk at lactationfrom the glandular elements at the terminal endsof the system that look a little like the florets onthe surface of broccoli. You can now picture whatnormal breast tissue looks like under the micro-scope it appears as a collection of circles ofvarious diameters or as ellipses where the tubule

has been cut obliquely. You will also see clustersof tightly packed cells representing the glandularelements that secrete milk. Sometimes you willeven spot a tiny terminal tubule emerging fromthe lobule itself.

If you increase the magnification, you can seethe detail of the individual tubular structures. Inhealth they are quite banal one layer of simplecuboidal duct epithelial cells surrounded by asingle layer of spindle-shaped myoepithelialcells. If you increase the power of the simplelight microscope to its highest magnification,you will start seeing something of the extraordi-nary internal organization of these simple-looking cells. Just as many people become giddywhen contemplating the magnitude of outerspace and the expanding universe, I feel giddywhen considering the miniaturization at the otherextreme of the cosmic spectrum. The cell is en-closed by a membrane that looks like simplicityitself until you begin envisaging the comingsand goings of molecules and the recognitions ofchemical signals by specific receptors on the cell

surface that alert the interior mechanisms tospeed up or slow down. Beyond all that, andeven beyond the highest magnification of theelectron microscope, we can try to imaginewhats going on at the molecular level. The factthat such a complex and beautiful system retainsits integrity is a miracle; the fact that sometrivial molecular mismanagement can cause thewhole system to crash in spite of the robustrepair mechanisms and immune response to dis-eased tissues that exist in health and lead tothe death of its host should not be a surprise.

What is remarkable is the near-perfect fidelity ofthese complex structures, retained through thou-sands of divisions of their cellular units and thesharing out of the genome between the twodaughter cells at each event.

Surgeons and pathologists often describebreast cancers under the microscope as ugly-looking lesions. When they are distorted by thisugliness, the duct and lobular epithelium losetheir fractal geometry. When we grade these

cancers, the severity of the patients prognosis isdirectly proportionate to the ugliness of what wesee. Could it possibly be that one of the firststeps in malignant transformation is a mutationin the genes that control fractal geometry? Inother words, external symmetry might be a sur-rogate marker for internal symmetry, which is

no doubt determined by sequences on the humangenome that control fractal geometry. Loss offractal geometry is associated with malignanttransformation, but what is the direction of cau-sality? Is the ugliness the cause or consequenceof the malignant change, or is one a necessarybut insufficient trigger for the other?

As a young clinical scientist and surgeon, I wastaught that the natural history of breast canceris unpredictable, like the weather. As I maturedin my chosen field, I rebelled at what seemed tome a nihilistic attitude. Furthermore, the weatheris not so unpredictable now that meteorologistsuse chaos theory to refine their weather-forecast-ing precision.

Some 20 years ago, I saw one of the firstperformances of Tom Stoppards Arcadiaat theNational Theatre in London. In the third scene,set in a Georgian country house in 1809, Thoma-sina, a very precocious 16-year-old, asks her tutor,Gods truth, Septimus, if there is an equationfor a curve like a bell, there must be an equationfor one like a bluebell, and if a bluebell, why not

a rose? Do we believe nature is written in num-bers? Perhaps Thomasina would have gone onto discover chaos theory if only the computer hadbeen invented. As the story unfolded, I experi-enced a eureka moment it suddenly seemedclear to me that the natural history of breastcancer was unpredictable because wed been us-ing the wrong mathematics all this time. I soonrecruited Mark Chaplain, an exponent of chaostheory, and together with three Ph.D. studentswe set to work to try to explain the extraordinaryunpredictable pattern of recurrence of breast

cancer after surgery.In 1999, our group published an article that

challenged the linear mathematics conventionallyused to describe the natural history of breast can-cer and offered the heretical suggestion that theinitial peak of relapse occurrence between 2 and3 years after surgery was actually provoked by theact of surgery itself and that this pattern couldonly be modeled by using chaos theory.1We thenwrote a series of articles that strengthened that

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hypothesis and ultimately suggested that the in-flammatory response to surgery provoked theoutgrowth of latent foci of residual disease andthat this phenomenon might be inhibited by theadministration of antiinflammatory drugs in theperioperative phase.2,3Included in the first articlewas a formula developed by Chaplain and Ander-

son that if iterated and reiterated on a powerfulcomputer could produce remarkable animatedimages of angiogenesis and how it might beperturbed by one or two simulated mutations,as a result of which the blood supply to the breasttissue lost its beautiful fractal geometry.

Since then, Ive speculated that loss of fractalgeometry of the blood supply to human tissuesmight be an early step in oncogenesis, and per-haps many of the mutations we see in cancersmight be the results rather than the cause of thisearly phenomenon. It has already been suggest-ed that tissue hypoxia leads to loss of cell polar-ity, instability of the genome, and uncontrolledcell proliferation.4,5

In the front yard of my house are two orna-mental trees. One is Salix caprea pendula, the weep-ing willow described above, but the other is Salixmatsudana tortuosa, the corkscrew willow. The for-mer has beautiful fractal geometry, whereas thelatter is a complete mess and reminds me of thevascular system of a cancer as generated by theChaplainAnderson model. Searching the botani-

cal literature, I found an interesting article sug-gesting that the mutant corkscrew phenotype wasrelated to a dominant allele at a single locus andthat this mutation is associated with vascular

cell collapse within the trees structure.6If simi-lar mutations occur in the animal kingdom, per-haps we might start a new line of inquiry. Itshould not be beyond the wit of humans or evenmolecular biologists to search for similar genesto help us understand the geometry of normaltissue and their malignant phenotypes. This ap-

proach may lead to new insights about the treat-ment of cancer aimed at restoring both beautyand function to a diseased organ.

Disclosure forms provided by the author are available with thefull text of this article at NEJM.org.

I thank Lilian and Robert Slowe for having the foresight toplant the two willow trees 15 years ago.

From the Department of Surgery, University College London,and the Clinical Trials Group, Royal Free and University CollegeSchool of Medicine both in London.

1. Baum M, Chaplain MA, Anderson AR, Douek M, Vaidya JS.Does breast cancer exist in a state of chaos? Eur J Cancer 1999;

35:886-91.2. Baum M, Demicheli R, Hrushesky W, Retsky M. Does sur-gery unfavourably perturb the natural history of early breastcancer by accelerating the appearance of distant metastases? EurJ Cancer 2005;41:508-15.3. Retsky M, Demicheli R, Hrushesky WJ, et al. Reduction ofbreast cancer relapses with perioperative non-steroidal anti-inflammatory drugs: new findings and a review. Curr MedChem 2013;20:4163-76.4. Schwartz L. Cancer between glycolysis and physical con-straint. New York: Springer, 2004.5. Huang LE, Bindra RS, Glazer PM, Harris AL. Hypoxia-induced genetic instability a calculated mechanism underly-ing tumor progression. J Mol Med (Berl) 2007;85:139-48.6. Lin J, Gunter LE, Harding SA, et al. Development of AFLPand RAPD markers linked to a locus associated with twisted

growth in corkscrew willow (Salix matsudana Tortuosa). TreePhysiol 2007;27:1575-83.

DOI: 10.1056/NEJMms1505722

Copyright 2015 Massachusetts Medical Society.