From molecules and cells to ourselves and our discontents
Each of us is but the aggregate consequence of the enormous number of fundamentally discrete events that occur among the many molecules, genes, and cells of which we are comprised. For more than a decade, our group has used this viewpoint to try to make sense of multicellular organization and its diseases.
The things of which we are made – cells, molecules, genes, nucleotides, atoms, electrons, protons, photons, etc. – are fundamentally discrete things. They always come as integers, and never as fractions. There may be 1, 3, or 1,000,000,003 cells in an anatomical structure, or 1, 3, or 1,000,000,003 insulin-like growth factor II molecules bound to a cell, but never 1.333 molecules or cells. The fact that the things of which we are made are fundamentally discrete means that the microscopic events that occur among these things must inevitably be either/or, events. For example:
- Either a specific molecule of insulin growth factor II has bound to a specific molecule of insulin growth factor receptor, or it hasn’t.
- Either there’s been an A->T mutation at codon 6 of a β-hemoglobin gene, thus giving rise to sickle cell disease, or there hasn’t been such a mutation.
- Either codon 6 in a β-hemoglobin gene has bound a transfer RNA molecule, leading to the synthesis of a β-hemoglobin mRNA molecule, or it hasn’t.
- Either a cell is alive or it’s dead.
- Either a cell is dividing or it isn’t.
- Either a cancer cell has spread away from the site in which it was born, giving rise to lethal metastatic disease, or it hasn’t.
It follows that the biology we see at our macroscopic scale is inescapably the result of the many fundamentally discrete, either/or, events that occur at the microscopic scale. We call this approach Binary Biology.
Mathematically, our work in binary biology has concerned the use of the fundamentally discrete, either-or quality, of the microscopic events that occur within cells and among cells to build equations and other mathematical tools for capturing the macroscopic features of biological systems. Such an approach has:
- Revealed that the simple partitioning of mitotic signaling molecules among cells is enough to account for the creation (at predictable times, to predictable sizes, and to predictable shapes) of the tissues, organs, and anatomical structures that arise during the development of multicellular organisms (1).
- Made it possible to develop a practical arithmetic for understanding how mutations lead to pre-malignant growth and cancer (1).
- Made it possible to derive mathematical equations to accurately predict risk of death for individual cancer patients, and the impact of various treatment choices on that risk of death (9,10,11,16).
- Made it possible to derive mathematical equations for determining whether mutations are a necessary at the time of the spread of cancer cells (they are not) (7).
- Made it possible to develop a practical mathematics for analyzing, in a computer, how chemotherapy interacts with cancer, so as to identify optimal treatment strategies for such agents (1).
- Made it possible to develop mathematical techniques that can predict the impact of various usages of cancer screening tests, such as mammography, on the cancer survival rate (5,6,8,10,12,13,14,15).
Experimentally, our work in binary biology has concerned the analysis of several dozen plasma proteins that are made by the liver for export into the blood. Using immunofluorescence microscopy to color these plasma proteins in the cells in which they are made, we could see that each protein is produced in a separate subpopulation of the liver’s cells (1,2,3). The most abundant protein, albumin, is made by about 1% of the liver’s cells, and the abundance of the cells producing the other proteins parallels the liver’s overall output of each protein. It also appears that once a liver cell decides to turn on a plasma protein gene, it stays turned on even after the cell divides into two. This can be seen in the finding that not only are there single cells in the liver producing a single plasma protein, there are also little clonal clusters of cells each producing a single plasma protein.
Apparently, the liver achieves the trick of cellular diversity by switching on each plasma protein gene randomly. Each albumin gene appears to have about a 1-in-100 chance of being turned on, and that causes albumin to be produced by about 1% of the liver’s cells. We found direct evidence that the activation of plasma protein genes is random (as opposed cells producing albumin because they were “told” to turn on a plasma protein gene) by taking advantage of the fact that every cell has at least two copies of each autosomal gene. Using antibodies that react with only one genetic type of albumin, we could see that when a cell is producing albumin from the gene it got from one parent, it isn’t producing it from the albumin gene it got from the other parent (1,2,3). If the cell had been following some sort of “instruction” to turn on its albumin genes, it would certainly be making albumin from both genes.
Curiously, the random quality seen in the activation of individual plasma protein genes is an inevitable quality of all genes, for the simple reason that genes are just very large molecules (1). This may surprise us, because we don’t often get to see the activation of individual genes, as we can do by looking at gene expression in the individual cells in the liver; we usually grind up a lot of cells, and all of the molecular granularity gets homogenized. Unlike our macroscopic world, which appears to be smooth and predictable, the molecular world is nothing but either/or, either/or, either/or, either/or, either/or.
The immunofluorescence method visualizes for us an essential (indeed the essential) quality of cells: cells are machines for sensing the discrete, either/or nature of the microscopic events that occur among the molecules that are within us. The cells of the liver, indeed all cells, have very few genes (2 copies of each autosomal gene for cells with a single nucleus, and 4, 6, or 8 copies for cells that have several nuclei). Because of this, the cells of the liver can take advantage of the molecular granularity of the individual giant molecules we call genes to create the dozens of specialized cells in the liver producing individual plasma proteins. Furthermore, there’s lots of evidence that this isn’t a skill unique to the liver. Indeed there are many hints in the literature that this is precisely how we create the cellular variety that makes multicellular life possible (1).
The role of cells as machines for sensing the discrete, either/or nature of microscopic events can be seen in another aspect of multcellularity: control of growth. We can see this by calculating how many growth factor molecules are at work in signaling a cell. Such a calculation is fairly straightforward, if we have information on growth factor concentration, affinity, number or receptors, etc. The surprising result is that, in many instances, there are very few such ligand molecules at work in signaling individual cells (1). Indeed, sometimes there are not even as many bound growth factor molecules as there are cells. For the growth factor IGF II, for example, at the ordinary physiological concentration of 10 11mol/L, there is just one molecule of the growth factor bound for every six cells with receptors for this ligand. Thus, if it takes but a single molecule of IGF II to make a cell divide, then the discrete allocation of IGF II among cells gives every cell a 1-in-6 chance of dividing. In fact, by modeling this discrete allocation of the molecules that control growth, it can be seen that this is enough to account for how the tissues, organs, and anatomical structures of the embryo grow to predictable sizes and shapes at predictable times (1)
Whether cells reach down to sense the granularity of the molecules that are genes, or the molecules that do other things, such as control cell division (i.e. IGF II) their ability to span the worlds of the microscopic and macroscopic makes it possible for cells to amplify the discrete events that occur at the molecular scale up into the discrete either/or behaviors that cells display, and then, because cells are small and abundant, to amplify the these either/or events up to the macroscopic scale that we inhabit. For the liver, this makes it possible for us to carry out the ordered synthesis of the many plasma proteins that we need to live. For us, this makes it possible for us to carry out many of the ordered processes that we need to live (1,2,3,4).
Reviews of binary biology
- Michaelson, J. The Role of Molecular Discreteness in Normal And Cancerous Growth. Anticancer Research
- Michaelson, J. Cell Selection in the Genesis of Multicellular Organization Lab Invest. 69: 136-150 1993.
- Michaelson J. The significance of cell death. In: Apoptosis (Eds Cope F.O., Tomlei, L.D.)
- Michaelson J. Cell selection in development. Biological Reviews 1987; 62:115-139.
Applications of binary biology to the practical understanding and management of cancer
- Michaelson J, Reducing Delay in the Detection and Treatment of Breast Cancer. Adv Imag Onc In Press 2007
- Michaelson J, Mammographic Screening: Impact on Survival in CANCER IMAGING Ed: M.A. Hayat in press 2007
- Michaelson JS, Cheongsiatmoy JA Dewey F, Silverstein M, Sgroi D Smith B. Tanabe KK, The Spread of Human Cancer Cells Occurs with Probabilities Indicative of A Non Genetic Mechanism British Journal of Cancer 93:1244-1249 2005
- Blanchard K, Weissman J, Moy B, Puri D, Kopans D, Kaine E, Moore R, Halpern E, Hughes K, Tanabe K, Smith B Michaelson J, Mammographic screening: Patterns of use and estimated impact on breast carcinoma survival Cancer 101, 495-507 2004
- Michaelson JS, Silverstein M, Sgroi D, Cheongsiatmoy JA, Taghian A, Powell S, Hughes K, Comegno A, Tanabe KK, Smith B The effect of tumor size and lymph node status on breast carcinoma lethality. CANCER 98:2133-43 2003
- Michaelson JS, Satija S, Kopans DB, Moore RA, Silverstein, M, Comegno A, Hughes K, Taghian A, Powell S, Smith, B Gauging the Impact of Breast Cancer Screening, in Terms of Tumor Size and Death Rate Cancer 98:2114-24 2003
- Michaelson JS Silverstein M, Wyatt J Weber G Moore R Kopans DB, Hughes, K. Predicting the survival of patients with breast carcinoma using tumor size CANCER 95: 713-723 2002
- Michaelson JS Satija S, Moore R Weber G Garland G Phuri, D. Kopans DB The Pattern of Breast Cancer Screening Utilization and its Consequences CANCER 94:37-43 2002
- Michaelson JS Using Information on Breast Cancer Growth, Spread, and Detectability to Find the Best Ways To Use Screening to Reduce Breast Cancer Death Woman's Imaging 3:54-57 2001
- Michaelson, JS, Kopans, DB, Cady, B. The Breast Cancer Screening Interval is Important. Cancer 2000 88:1282-1284
- Michaelson, J, Halpern, E, Kopans, D. A Computer Simulation Method For Estimating The Optimal Intervals For Breast Cancer Screening. Radiology
- www.CancerMath.net Contains web-based calculators for predicting cancer outcome, and technical manuals on the underlying mathematics, which is based on using binary biology to derive mathematical expressions for answering practical questions about cancer.