Can Arithmetic Treatment Most cancers? | Math ∞ Weblog

“I may even ask for an appropriation of an additional $100 million to launch an intensive marketing campaign to discover a remedy for most cancers, and I’ll ask later for no matter extra funds can successfully be used. The time has are available in America when the identical type of concentrated effort that break up the atom and took man to the moon must be turned towards conquering this dread illness. Allow us to make a complete nationwide dedication to realize this aim.”

President Richard M. Nixon (State of the Union Deal with, 1971)

This yr, 2011, is the fortieth anniversary of the Warfare on Most cancers. President Richard Nixon signed the Nationwide Most cancers Act on December 23, 1971 inaugurating the “Warfare on Most cancers.” Since 1971 the Warfare on Most cancers has consumed an astonishing $200 billion, with the annual finances of the Nationwide Most cancers Institute alone now at over $5 billion. That is akin to the annual fee of expenditure of the Manhattan Undertaking which invented the primary atomic bombs and nuclear reactors between 1939 and 1945, with many of the work and expenditure between 1942 and July 16, 1945, the date of the primary atomic bomb check generally known as Trinity, continued for forty years. The Manhattan Undertaking consumed about $20 billion in 2011 {dollars}, about $2 billion in 1940’s {dollars}. The Warfare on Most cancers is roughly comparable to 10 Manhattan Tasks. The outcomes have clearly been very disappointing. Since most cancers is among the main causes of demise, nearly everybody would nearly actually wish to see way more spectacular outcomes than achieved up to now.

The Warfare on Most cancers was impressed partly by the spectacular success of the wartime Manhattan Undertaking, the next improvement of the hydrogen bomb (1945-1952), and the then (1971) current spectacular success of the Apollo Program (1962-1969). This impressed not solely the Warfare on Most cancers however many different “new Manhattan Tasks” reminiscent of analysis into tokamaks and inertial confinement fusion gadgets for fusion energy. Just like the Warfare on Most cancers, most of those “new Manhattan Tasks” have yielded disappointing outcomes, actually nothing on the dimensions of the Manhattan Undertaking or the Apollo Program. As mentioned within the earlier article “The Manhattan Undertaking Thought of as a Fluke,” the Manhattan Undertaking seems to have been a fluke, atypical of main innovations and discoveries particularly within the success of the primary full system assessments: the Trinity check explosion on July 16, 1945 and the atomic bombings of Hiroshima and Nagasaki. Theoretical mathematical calculations and primitive numerical simulations appear to have been unusually profitable within the case of the Manhattan Undertaking in comparison with different breakthroughs. The Manhattan Undertaking was most likely fairly uncommon amongst main innovations and discoveries in different methods as properly, however that is much less clear. By way of funding ranges and the intense life and demise nature of the aim, the Warfare on Most cancers is among the closest analogs to the Manhattan Undertaking among the many many “new Manhattan Tasks” of the final forty years.

With the widespread availability of extraordinarily highly effective computer systems, there are rising makes an attempt to use arithmetic and computational strategies to biology and to most cancers. There’s a burgeoning subject of “quantitative biology,” which incorporates its personal part on the favored digital preprint server. In lots of respects, that is an try to copy the obvious success of theoretical mathematical calculations and early laptop simulations within the Manhattan Undertaking (1939-1945), the event of the hydrogen bomb (1945-1952), and the Apollo Program (1962-1969).

This text discusses the applying of arithmetic to the remedy of most cancers, the doable use of techniques of sensible medicine to carry out easy mathematical calculations to establish and kill most cancers cells, and presents a doable mechanism, developed by the writer a number of years in the past, to selectively destroy cells with irregular numbers of chromosomes (aneuploidy), one thing frequent in lots of types of most cancers.

What does forty years of failure imply?

Such lengthy intervals of repeated failure are frequent within the historical past of scientific and technological breakthroughs. Normally, this repeated failure has mirrored both a scarcity of basic data or an incorrect assumption or group of assumptions that was broadly, even universally, held. Whereas these two classes should not sharply outlined and blur collectively, typically a scarcity of basic data implies that the state of information was merely far too primitive to unravel the issue. An instance of this may be the failure of alchemists for 1000’s of years to remodel base metals into gold or produce an elixir of life, the 2 main objectives of each Western and Japanese alchemy. At the moment, we will with nice issue and at nice price convert base metals into gold and the elixir of life stays a distant dream. It’s clear looking back that the alchemical idea that metals had been a composition of mercury and sulphur was grossly in error as had been many different ideas of alchemy. Nonetheless, alchemists made many important technological advances together with strategies for creating alloys just like gold, gold and gold-colored coatings, and the invention of all kinds of helpful supplies. These successes, unappreciated at the moment, most likely gave the alchemists a false confidence of their theories and data.

The blurriness of the 2 classes is illustrated by asking what might need occurred if the alchemists had questioned and deserted the mercury-sulphur idea which in varied varieties was broadly held for a lot of centuries. Loosely, the mercury-sulphur idea of metals postulated that metals had been composed of mercury and sulphur in various proportions; gold being largely mercury, for instance. This idea is often attributed to the Islamic alchemist Jabir ibn Hayyan (born in about 721 in Tus, Iran, died in about 815 in Kufa, Iraq) also referred to as Geber in Latin.   Primarily based on present data, the alchemists would have needed to have deserted the mercury-sulphur idea and remoted a radioactive materials reminiscent of uranium or invented batteries and different electrical applied sciences resulting in particle accelerators to have had any hope of reaching their aim, each of which require performing very completely different experiments from those alchemists sometimes did. Batteries, particularly, might have been invented many centuries earlier than they got here into widespread use within the early nineteenth century.

In lots of instances, looking back, it’s clear that this pronounced lack of progress in fixing a scientific or technological downside was because of an assumption or group of assumptions that had been incorrect and broadly held. Certainly, usually the idea was one thing seen as self-evident, one thing “everybody is aware of,” apparent, firmly established by in depth proof, and so forth. Solely looking back is it “apparent” that the idea or assumptions had been in error and never properly supported by proof, expertise, or logic as most believed. Therefore, one ought to ask whether or not some broadly held, seemingly smart perception or group of beliefs, supported by “overwhelming proof” in trendy scientific jargon, in biology isn’t, in reality, flawed.

In precept, the Web and particular new applied sciences reminiscent of HTML or wiki’s ought to make it simpler for researchers to collaborate and to listing all assumptions, each said and unspoken, in a analysis subject and their interdependencies, together with hyperlinks to all supporting uncooked knowledge, experiments, and logical arguments: one thing like a Biology and Most cancers Assumptions Wikipedia, however extra rigorous than Wikipedia. Figuring out and evaluating assumptions may be finished way more systematically and completely with hypertext, databases, and different Web and laptop software program than was doable a couple of years in the past utilizing books, analysis papers, and convention shows.

Questioning assumptions, particularly assumptions “everybody is aware of,” is a social and political course of. In trendy Large Science, sure normally foundational assumptions are carefully related to excessive standing people and establishments and are routinely offered with few {qualifications} and even as incontrovertible fact past any rational questioning to the general public, enterprise leaders, and coverage makers: in Scientific American articles, PBS/Nova video applications, congressional testimony, personal casual discussions the place choices are sometimes truly made, and so forth.

In trendy scientific analysis, there’s pervasive rhetoric about “questioning assumptions” and “considering outdoors the field,” however this normally doesn’t apply to the foundational assumptions talked about above. This rhetoric normally refers to subsidiary assumptions reminiscent of which protein to make use of in a biology lab experiment and comparable non-threatening technical minutia. Certainly, many fields which have proven little or no sensible outcomes for many years, like most cancers analysis, are periodically swept by fads and fashions through which subsidiary assumptions are changed, modified, or added.

The dialogue of mathematical approaches to curing most cancers under usually assumes that trendy biology has it proper. A dialogue of assumptions that could be in error or unorthodox organic ideas is generally past the scope of this text, though the speculation that irregular numbers of chromosomes may play a extra necessary function in most cancers than usually thought is mentioned. This basic acceptance of present assumptions in biology is a vital qualification that readers ought to take into accout. At the least historic expertise with many “laborious issues” in science and expertise would counsel in any other case — that trendy biology is “lacking one thing” as physicists wish to say.

Present Mathematical Approaches

There are a selection of present makes an attempt to use arithmetic to the remedy or therapy of most cancers. Fairly a quantity are makes an attempt to make use of differential equations to mannequin the expansion and unfold of cancers and their response to numerous remedies and the immune system, pretty just like the work of Dr. Swanson and Professor Levy described intimately under.

A well-known instance is Dr. Kristin Swanson’s work on the College of Washington:

We specialize within the mathematical modeling of pathological biosystems – particularly, main mind tumors generally known as gliomas. We’re at present engaged on a number of collaborative tasks using each scientific and experimental imaging methods reminiscent of MRI and PET.

Our focus is on: 1) predicting patient-specific tumor development, 2) searching for patient-specific markers of tumor development, and, 3) figuring out predictors of response to remedy in particular person sufferers.

In plain English, that is an try to predict the expansion and unfold of sure mind tumors utilizing a mathematical mannequin, normally differential equations, with the intention to rigorously goal the spreading most cancers with radiation or different strategies.

One other well-known instance is the work of Professor Doron Levy on the College of Maryland, Faculty Park. From Professor Levy’s site:

Along with Peter Lee (Hematology, Stanford College) and Peter Kim (College of Utah) we have now been engaged on combining new experimental knowledge and mathematical fashions to develop new strategies for treating leukemia sufferers. The kind of leukmia that we have now extensively studied is power myelogenous leukemia (CML).

Our analysis emphasizes the function of the immune system within the development of the illness. By now it’s identified that almost all sufferers have an anti-leukemia immune response. It stays a thriller as of why this immune response is incapable of offering a ample response to the illness.

Our fundamental work on this subject was printed within the June 2008 concern of PLOS Computational Biology. On this paper we proposed to vaccinating CML sufferers utilizing their very own blood with the intention to increase their anti-leukemia immune response. Utilizing mathematical fashions we confirmed that the important thing concern is to time the most cancers vaccine primarily based on the dynamics of the immune response of the person affected person. A vaccination that’s offered to early or too late within the course of (i.e. after analysis and the initiation of drug-therapy) may have no noticeable impact. Our calculations counsel that such a process could in the end be used to remedy the illness. The work assumes that sufferers are handled with Gleevec (imatinib) ranging from the analysis of the illness. A timed vaccine could permit them to cease the drug remedy.

There are a lot of different makes an attempt to use comparable arithmetic to the remedy or therapy of assorted cancers together with work by Larry Norton at Memorial Sloan-Kettering Most cancers Middle, Lisette de Pillis at Harvey Mudd Faculty, Vito Quaranta and Alexander “Sandy” Anderson on the Vanderbilt Integrative Most cancers Biology Middle and the College of Dundee in Scotland, Franziska Michor at Memorial Sloan-Kettering Most cancers Middle, Sofia Merajver on the College of Michigan, Paul Macklin on the College of Southern California, and plenty of others.  An Web seek for “Arithmetic and Most cancers” will flip up many matches of this kind.

The writer isn’t too optimistic about these approaches, though they actually have advantage. Evidently one nonetheless would actually want one thing that might establish and both safely destroy or in some way render innocent the precise most cancers cells. Can arithmetic do that or help in doing this?

Good Programs of Medication

The present prevailing idea of most cancers is the oncogene or “most cancers gene” idea. That is seen as a incontrovertible fact by many molecular biologists. The present (2011) Director of the Nationwide Most cancers Institute, Dr. Harold Varmus, shared the Nobel Prize in Drugs with J. Michael Bishop for early work on this idea.

Most cancers is now stated to be a whole bunch, even 1000’s of various illnesses. Whereas a medical physician or pathologist could establish one thing as “breast most cancers” or “pores and skin most cancers” or an identical basic class, at a molecular and genetic degree, “breast most cancers” is definitely many alternative illnesses. It’s thought that most cancers is brought on by the buildup of many mutations of many alternative oncogenes and tumor suppressor genes that management complicated networks of proteins that direct the expansion, functioning, and differentiation of cells. In biology, differentiation refers back to the course of by which cells “differentiate” throughout development into varied specialised kinds of cells reminiscent of neurons within the mind, blood cells, and so forth with completely different particular properties and features.

One sort of breast most cancers could have genes A,B,C, and D mutated whereas one other has genes W, X, Y, and Z mutated. Not solely this, however the cancers are regarded as regularly mutating and evolving within the physique, creating immunity to chemotherapy medicine for instance. Thus, there doesn’t appear to be a standard molecular goal that an anti-cancer drug can goal in the way in which that penicillin or different antibiotics can kill a variety of various micro organism, for instance. Because of this the newest favored idea in most cancers analysis and therapy has been “customized” focused medicine. If one can decide that affected person X has genes A, B, C, and D mutated, then in precept one can choose or produce a drug particular to this specific sort of most cancers with A, B, C, and D mutated. This, after all, requires creating not one or a couple of anti-cancer medicine, however a whole bunch and even 1000’s of anti-cancer medicine probably additional customized for every affected person.  See, for instance, this current article (“Focused medicine: the way forward for most cancers therapy?”, The Huffington Put up, June 9, 2011).

Personalised most cancers therapy has suffered a current excessive profile black eye with the retraction of a number of papers from a analysis group at Duke College and a entrance web page article within the Friday, July 8, 2011 New York Occasions (“How Vivid Promise in Most cancers Testing Fell Aside“, by Gina Kolata, The New York Occasions, July 8, 2011, web page A1). Most cancers analysis has lengthy been characterised by a sequence of analysis and therapy fads, with one surprise drug or therapy after one other closely touted for a time, adopted by disappointment, after which changed by a brand new surprise drug: interferon, interleukin-2, and plenty of others within the final forty years.

Nonetheless, medical medical doctors and pathologists going again to Hippocrates appear to have been in a position to establish a single illness as most cancers lengthy earlier than trendy genetic strategies. It could be that there are system degree options of most cancers cells that do establish them as most cancers cells. Conventional chemotherapy medicine had been designed to kill dividing cells on the speculation that most cancers cells divide quickly. Nevertheless, wholesome cells divide additionally and conventional chemotherapy has very restricted advantages if in any respect. Solely surgical elimination of a tumor earlier than it spreads — turns into metastatic in most cancers jargon — seems to have the ability to remedy most cancers utilizing the frequent sense definition of “remedy”. Whereas concentrating on cell division largely doesn’t work, concentrating on different system degree traits of most cancers may fit.

Many readers are most likely acquainted with the idea of nanotechnology and nanorobots, normally related to Okay. Eric Drexler. One can envision tiny robots, nanorobots, that enter the blood stream, analyze every cell in flip, and selectively kill the most cancers cells. The fabrication of such nanorobots is much past our present or close to future expertise. We’re nowhere close to implementing a pc central processing unit (CPU) or a robotic at a molecular degree. Even when we might, we have no idea the right way to program a nanorobot to acknowledge a most cancers cell and distinguish it from a traditional wholesome cell.

What we would have the ability to do, with nice issue, is produce a small system of interacting medicine/molecules that carry out some mathematical calculation within the cell and selectively kill cells recognized as most cancers cells or possible most cancers cells whereas leaving the conventional wholesome cells alone. It’s right here that arithmetic could also be of use. To realize success within the close to future, the easier the arithmetic the higher. Even engineering a single molecule reminiscent of genetically engineered insulin for diabetics is a frightening process at current. So a system of even a couple of molecules could be a considerable and troublesome enterprise.

There are some present makes an attempt to pursue this method, notably the Treatment Most cancers Undertaking related to Dr. Arnold Glazier, Dr. Emil Frei and others.   The Treatment Most cancers Undertaking accepts that the present fundamental assumptions of biology and most cancers analysis are appropriate. The notion is to establish an unchanging property of most cancers cells that may be focused by a system of sensible medicine. In particular phrases, this appears to discuss with concentrating on sure patterns amongst proteins which are regarded as related to sure basic properties, proliferation and invasivenes, of malignant most cancers cells. Dr. Glazier has written a ebook  and made some shows on his concepts.

The writer’s educated guess is that an method primarily based on a system of medication, maybe alongside the strains of the Treatment Most cancers Undertaking, is the probably method to supply an efficient remedy or therapy for most typical types of most cancers within the close to future.  (This dialogue is for academic and informational functions solely and isn’t an endorsement of the Treatment Most cancers Undertaking.) An necessary caveat is that such approaches usually assume that present organic assumptions and theories such because the somatic mutation idea of most cancers, the oncogene idea (a selected occasion of the somatic mutation idea) and the Central Dogma of Molecular Biology (DNA is the boss) are appropriate, making a remedy for most cancers “simply engineering.” Subsequent, this text presents a doable methodology to destroy cells with irregular numbers of chromosomes, a situation generally known as aneuploidy which is frequent in lots of cancers.

The Selective Destruction of Cells with Irregular Numbers of Chromosomes

One frequent attribute of many cancers is an irregular variety of chromosomes, generally known as aneuploidy. That is usually an extra variety of chromosomes. A traditional wholesome human cell has forty-six (46) chromosomes. Most cancers cells usually have greater than forty-six chromosomes. This was found lengthy earlier than the fashionable genetic period. One historic idea, now out of favor, is that the irregular variety of chromosomes causes most cancers. This idea is normally credited to the German biologist Theodor Boveri. Essentially the most distinguished trendy advocate of the function of aneuploidy and chromosomes in most cancers is the extraordinarily controversial researcher Peter Duesberg who has printed some articles on his theories in most cancers analysis journals and a well-liked article in Scientific American in 2007 (“Chromosomal Chaos and Most cancers”, Scientific American, Might, 2007).  Numerous different researchers reminiscent of Angelika Amon at MIT have been investigating the function of chromosomes and aneuploidy in most cancers lately; references are given under.  The irregular variety of chromosomes or the opposite chromosomal anomalies usually seen in a variety of cancers could also be a system-level attribute of most cancers that may very well be focused regardless of the intense variation in gene-level mutations (part-level traits of most cancers).

Despite the fact that there are over one-million analysis papers on most cancers, it’s troublesome to get a transparent image of the function of aneuploidy in most cancers. Most trendy most cancers analysis is carried out inside the framework of the oncogene idea and an implicit assumption that the way in which to remedy or deal with most cancers is to focus on both a protein generated by a most cancers gene or the gene instantly. Chromosomal anomalies, each irregular numbers of chromosomes and the rearrangements of chromosomes which are frequent in lots of cancers, are normally mentioned as an apart to the putative most cancers genes. This translocation of chromosome X mutated the important thing most cancers gene ABC, or the duplication of chromosome X resulted in two copies of the important thing most cancers gene ABC.

It may very well be that killing most cancers cells with the flawed variety of chromosomes would don’t have any impact on the illness. It will merely lead to a most cancers with the right variety of chromosomes within the surviving most cancers cells. It might gradual the illness if the irregular variety of chromosomes is said to the malignancy of the most cancers cells. In one of the best case, it’d remedy the illness, if the irregular variety of chromosomes is both the reason for most cancers or important in a roundabout way to the malignant traits of the most cancers cells.

It could be doable to kill cells with an irregular variety of chromosomes utilizing a system of 5 molecules: a innocent precursor A, a supply catalyst S, a cell killer B, a drain catalyst D, and a neutralized cell killer C that the cell can safely digest or excrete.

The supply catalyst S is inactive till it bonds to a numerical or quantitative characteristic on the chromosomes such because the telomeres on the ends of the chromosomes or the centromeres on the middle. It turns into an energetic catalyst S* when it bonds to the chromosomes. Then the activated catalyst S* catalyzes the conversion of a innocent precursor A right into a cell killer B. The activated catalyst S* has a most throughput. If the focus of the precusor A is excessive sufficient within the cells, the catalyst S* will add the cell killer to the cell at a fee proportional to the variety of chromosomes within the cell.

The cell killer B is comparatively innocent in low concentrations. It must construct as much as a excessive degree to kill the cell. Up to now, it will occur in all cells. Nevertheless, if there’s a drain catalyst D that bonds to a numerical characteristic within the cell that’s the identical in each regular cells and irregular cells (most cancers cells) and turns into an energetic drain catalyst D* that removes the cell killer B by changing it to the neutralized cell killer C, then the focus of B may be engineered to rise to deadly ranges solely in cells with too many chromosomes.

A ==>S*==> B

B ==>D*==> C

This method of medication is sort of a bathtub with a number of working taps, one for every chromosome, and a single drain. If there are too many taps, chromosomes, the water degree, the focus of the cell killer B, will rise and overflow the bath. If there are the correct quantity, forty-six, or too few, lower than forty-six, taps, the drain can take away the water being added and the water degree by no means rises. The water degree stays nearly zero; the focus of the cell killer B is approach too low to hurt the cell.

One can kill cells with too few chromosomes (lower than forty-six) by swapping the roles of the drain and the supply. The drain catalyst bonds to the chromosomes. The supply catalyst bonds to the fixed numerical characteristic of the cells. Thus, if there are too few chromosomes, there should not sufficient activated drains to take away the cell killer B produced by the supply catalyst. The bath has one large faucet and plenty of small drains, one for every chromosome.

In precept, one might remove all cells with both too many or too few chromosomes by first treating the affected person with a system of medication that kills cells with too many chromosomes after which a system of medication that kills cells with too few chromosomes. Most cancers cells are often reported to have too many chromosomes, however typically too few can be reported.

A computational system of this kind would now (2011) be straightforward to implement utilizing mechanical parts just like the gears and comes utilized in conventional mechanical clocks, vacuum tubes and different conventional analog electronics parts, or an built-in circuit. The issue is that so simple as such a computational system is, this can be very difficult to implement utilizing our present potential to engineer proteins and molecular organic techniques within the cell.

This video reveals the construct up of cell killer B in a cell with seven (7) chromosomes the place the conventional variety of chromosomes is 5 (5). A smaller variety of chromosomes than forty-six is used for demonstration functions.  The cell membrane is represented by a sphere which begins to distort when the cell killer focus reaches the deadly degree.  The cell killer molecules are indicated by small inexperienced spheres that flip pink when the deadly focus is reached.  The membrane disintegrates, killing the cell, and the cell killer disperses.


This graph reveals the focus of the cell killer B as a perform of time:

Cell Killer Concentration

Cell Killer Focus


This video reveals the shortage of accumulation of cell killer B in a cell with 5 (5) chromosomes the place the conventional variety of chromosomes is 5 (5).


This video reveals the buildup of cell killer B in a cell with three (3) chromosomes the place the conventional variety of chromosomes is 5 (5). The sources and drains have been swapped as mentioned above to kill cells with too few chromosomes.


That is the Octave script that simulates the bath mechanism and was used to make the movies above. This script runs efficiently on a PC with Home windows XP (Service Pack 2) utilizing Octave 3.2.4.  GNU Octave is a free, open-source high-level interpreted language, primarily supposed for numerical computations that’s largely appropriate with MATLAB.

most cancers.m

perform [result, command] = most cancers(N_chromosomes, nsteps, bdisplay, lethal_level, cutoff, bTooFew, N_normal)
% [result, command] = most cancers( [N_chromosomes, nsteps, bdisplay, lethal_level, cutoff, bTooFew, N_normal ])
% N_chromosomes - variety of chromosomes in cell (default 50)
% nsteps - variety of time steps to simulate
% bdisplay - boolean flag to show simulation (default false)
% lethal_level - focus at which cells die (default 200)
% cutoff - variety of time steps for cell demise (default 10)
%          cell lives this many steps after the deadly focus is reached
% bTooFew - simulate course of to destroy cells with too few chromosomes
%           through the use of drains that connect to chromosomes and a supply someplace
%           within the cell. (default false)
% N_normal - variety of chromosomes in a traditional wholesome cell (default 46)
%            typically set to small values reminiscent of 5 for demonstration or debugging
% Returns:
%      consequence -- time sequence of focus of cell killer B
%      command -- ffmpeg command to create video of simulation
% Examples:
% [r, c] = most cancers(7, 20, true, 10, 10, false, 5);  % kill cell with greater than 5 chromosomes
% [r, c] = most cancers(3, 20, true, 10, 10, true, 5);   % kill cell with lower than 5 chromosomes
% Description:
% Primary Demonstration of Idea of Killing Most cancers Cells by Chromosome Counting
% "Bathtub Mechanism" (conceived by John F. McGowan, Ph.D.)
% That is an Octave script (see program/octave/). 
% N_chromosomes is the variety of chromosomes within the most cancers cell 
%(46 is the variety of chromosomes in a traditional, wholesome human cell).
% A (innocent poison precursor) =S=> B (poison) =D=> C (neutralized poison)
% A is innocent (ideally consumed orally or injected into bloodstream of affected person).
% S is supply on chromosome that catalyzes conversion of A to B
% B is poisonous at focus lethal_level (default 200)
% D is drain someplace in cell that catalyzes conversion of B to C
% C is innocent.  Cell can safely digest or excrete C molecules.
% The sources on the chromosomes convert sort A molecules to sort B molecules.
% The drain (someplace within the cell) converts sort B molecules to sort C molecules.
% Identical to a bath drain, the drain within the cell has a restricted throughput
% so if there are too many sources (too many chromosomes), the focus of
% the poisonous molecule B will increase till it reaches the lethal lethal_level degree and kills
% the cell.
% In most cancers, the most cancers cells are aneuploid, they've the flawed variety of
% chromosomes, normally too many.  If one can goal the variety of chromosomes in a cell
% one might be able to kill a variety of cancers utilizing a system of "sensible medicine".
% On this instance, the system of "sensible medicine" consists of the poison precursor A, the
% sources (S) which bind to websites on the chromosomes, and the drain (D).  The sources solely turn into energetic
% and in a position to catalyze the conversion of A to B after they bind to websites on the chromosomes.
% This doesn't require a posh Drexler fashion nanorobot or subtle sample recognition
% to establish the most cancers cells.
% The protein engineering is, after all, fairly difficult, however not essentially past current day
% or close to future capabilities.
% Precise remedy would most likely encompass infusing the supply and drain molecules (S and D) into the affected person.
% As soon as the sources and drains had connected to the cells (each wholesome and cancerous), the precursor A
% could be launched for a time till the most cancers cells die.
% From "Can Math Treatment Most cancers?" by John F. McGowan, Ph.D., at The Math Weblog
% Creator: John F. McGowan, Ph.D.
% (C) 2011 by John F. McGowan, Ph.D.
% E-Mail: [email protected]
concentration_a = 1.0;  % focus of precursor A molecules
concentration_b = 0.0;  % focus of cell killer B molecules
concentration_c = 0.0;  % focus of neutralized C molecules

if nargin  C)
		N_b += concentration_a * N_chromosomes;  % A =S=> B  (the sources on the chromosomes catalyze conversion of A to the cell killer B)
		delta_c = min(concentration_b, N);  % the drain D removes some cell killer B molecules (B =D=> C)
	N_b = max(0, N_b - delta_c);  % drain converts B molecules to innocent C molecules
	N_c += delta_c;  % replace variety of neutralized C molecules in cell (cell can safely digest or excrete these molecules)  
	concentration_c = N_c / quantity;  % compute focus of neutralized C molecules in cell
	concentration_b = N_b / quantity;  % compute focus of cell killer B molecules in cell
	if concentration_b >= lethal_level
		nsteps_lethal = nsteps_lethal + 1;
	if nsteps_lethal > cutoff
	% cell dies so focus of B begins to drop
	% membrane destroyed so molecule B disperses
		if nsteps_lethal == cutoff
			printf('CELL DIES AT STEP %d', i);
		N_b = ground(N_b / 2);
		concentration_b = N_b / quantity;
	conc = [conc concentration_b]; 	 % add new focus of B to time sequence
	% show the B molecules
	% use ffmpeg (for instance) to transform picture sequence to video (e.g. mp4)
	% ffmpeg -r 10 -i cancer_50_chromosome_percent03d.jpg cancer_50_chromo.mp4
	if bdisplay
		if nsteps_lethal 

In precept, the bath mechanism could also be tailored to selectively kill cells with any irregular amount of any mobile characteristic, reminiscent of for instance options on the outside membrane of the cell (through which case the proteins have to be trapped within the membrane floor). Thus, it could be tailored to concentrating on different numerical or quantitative abnormalities of malignant most cancers cells than the variety of chromosomes or the amount of chromosomal options reminiscent of telomeres.

The presentation on this article is clearly simplified. For instance, cells are multiplying and dividing. Throughout cell division, a cell goes by means of a interval the place it has two units of chromosomes earlier than it splits into two cells. Nevertheless, as long as the ratio of the sources to the drains is sufficiently fixed built-in over time, the bath mechanism will nonetheless work and selectively destroy the dividing cells with too many or too few chromosomes.

This text doesn't talk about the specifics of how the 5 completely different molecules within the system could be carried out, probably by modifying identified molecules. This can be finished in future articles or publications; the writer does have some concepts the right way to implement the system intimately. Astute biologists might even see the right way to implement some or the entire steps. It's possible that specialists from completely different sub-fields of molecular and cell biology can be wanted to efficiently implement the completely different components of the system. Please be at liberty to contact the writer you probably have some good concepts.


Arithmetic might be able to remedy most cancers by means of techniques of sensible medicine that carry out a comparatively easy calculation inside a cell or on the membrane of the cell and kill or neutralize cells which are or most likely are most cancers cells. There are some makes an attempt to develop a technique alongside these strains. It doesn't appear to be the mainstream method for the time being, which at present seems fascinated with customized therapy, one thing of a legacy of the Human Genome Undertaking and different gene-oriented analysis tasks.

The writer suspects that some frequent assumption or assumptions in biology and most cancers analysis are in error or incomplete. This can be mirrored not solely within the evident lack of sensible progress in most cancers but additionally within the largely failed makes an attempt to remedy or deal with many different illnesses in current a long time together with many of the illnesses at present recognized as autoimmune problems: Kind I diabetes, a number of sclerosis (MS), systemic lupus, rheumatoid arthritis (RA), and so forth. Relying on what assumptions could also be in error, all present approaches to curing most cancers could also be useless ends. If the unorthodox idea that irregular numbers of chromosomes truly trigger most cancers is appropriate or a much less drastic variant through which the irregular variety of chromosomes is crucial to the malignant nature of most cancers is appropriate, then a technique that targets cells with an irregular variety of chromosomes, reminiscent of the tactic outlined on this article, could also be profitable. It isn't clear which assumption or assumptions could also be incorrect or incomplete; many different potentialities exist.

It could be doable to make use of trendy Web and laptop software program to collaboratively construct an on-line database of biology and most cancers analysis assumptions, each said and unspoken, their interdependencies, supporting knowledge, and logical arguments to higher establish and reevaluate present assumptions. Questioning assumptions, significantly these which "everybody is aware of," is a social and political course of. It isn't in any respect clear that we have now the establishments and the psychological outlook amongst researchers essential to correctly reevaluate assumptions in most cancers or many different analysis fields. The rhetoric of "questioning assumptions" and "considering outdoors the field" is simple to seek out in trendy analysis. It isn't "speaking the discuss," however relatively "strolling the stroll" that's in query. Alternatively, most individuals and most most cancers researchers would absolutely wish to see main progress within the remedy or therapy of the illness, since everybody faces a considerable threat of dying from most cancers.

© 2011 John F. McGowan

Concerning the Creator

John F. McGowan, Ph.D. solves issues by creating complicated algorithms that embody superior mathematical and logical ideas, together with video compression and speech recognition applied sciences. He has in depth expertise creating software program in C, C++, Visible Primary, Mathematica, MATLAB, and plenty of different programming languages. He's most likely greatest identified for his AVI Overview, an Web FAQ (Continuously Requested Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has labored as a contractor at NASA Ames Analysis Middle concerned within the analysis and improvement of picture and video processing algorithms and expertise. He has printed articles on the origin and evolution of life, the exploration of Mars (anticipating the invention of methane on Mars), and low-cost entry to house. He has a Ph.D. in physics from the College of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Expertise (Caltech). He may be reached at [email protected].



Advised Studying/References

Some Questions on Immortal Cell Traces

The Immortal Cell [Paperback]

Gerald B. Dermer (Creator)

# Paperback: 212 pages

# Writer: Avery (January 1, 1995)

# Language: English

# ISBN-10: 0895295822

# ISBN-13: 978-0895295828

# Transport Weight: 12.8 ounces


A Conspiracy of Cells: One Lady's Immortal Legacy and the Medical Scandal It Induced [Hardcover]

Michael Gold (Creator)

# Hardcover: 170 pages

# Writer: State College of New York Press (January 1986)

# Language: English

# ISBN-10: 9780887060991

# ISBN-13: 978-0887060991

# ASIN: 0887060994

# Transport Weight: 12.8 ounces


The Immortal Lifetime of Henrietta Lacks [Paperback]

Rebecca Skloot (Creator)

# Paperback: 400 pages

# Writer: Broadway; Reprint version (March 8, 2011)

# Language: English

# ISBN-10: 9781400052189

# ISBN-13: 978-1400052189

# ASIN: 1400052181


The Tissue Organizing Subject Principle (TOFT) of Most cancers

Wiley-Blackwell (2011, April 14). Controversial TOFT idea of most cancers versus SMT mannequin: Specialists debate. ScienceDaily. Retrieved July 9, 2011, from­ /releases/2011/04/110415083217.htm

Ana M. Soto, Carlos Sonnenschein. The tissue group subject idea of most cancers: A testable substitute for the somatic mutation idea. BioEssays, 2011; 33 (5): 332 DOI: 10.1002/bies.201100025

The Society of Cells: Most cancers and Management of Cell Proliferation [Paperback]

Carlos Sonnenschein (Creator), Anne Marie Soto (Creator)

# Paperback: 154 pages

# Writer: BIOS Scientific Publishers; 1 version (January 1999)

# Language: English

# ISBN-10: 0387915834

# ISBN-13: 978-0387915838



Chromosomes, Aneuploidy, and Most cancers

This can be a assortment of references, hyperlinks, and abstracts of article on chromosomes, aneuploidy, and most cancers.


Yuen, Karen Wing Yee(Oct 2010) Chromosome Instability (CIN), Aneuploidy and Most cancers. In: eLS. John Wiley & Sons Ltd, Chichester. https://www.els.internet [doi: 10.1002/9780470015902.a0022413]



Most cancers Analysis


Revealed OnlineFirst December 1, 2009; doi: 10.1158/0008-5472.CAN-09-2802 Most cancers Res December 15, 2009 69; 9245

Most cancers Stem Cells and Aneuploid Populations inside Growing Tumors Are the Main Determinants of Tumor Dormancy

1. Anjali P. Kusumbe, and

2. Sharmila A. Bapat material/69/24/9245.summary

Human Molecular Genetics

Constitutional aneuploidy and most cancers predisposition†

1. Ithamar Ganmore,

2. Gil Smooha and

3. Shai Izraeli*

+ Creator Affiliations


Sheba Most cancers Analysis Middle, Sheba Medical Middle, Tel-Hashomer, Ramat Gan; Sackler College of Drugs, Tel-Aviv College, Tel Aviv, Israel

1. *To whom correspondence must be addressed at: Pediatric Hemato-Oncology, Practical Genomics and Childhood Leukemia Analysis Part, Sheba Medical Middle, Tel Hashomer 52621, Israel. Tel: +972 35303037; Fax: +972 45303031; Electronic mail: [email protected]

* Obtained January 19, 2009.

* Accepted February 17, 2009.

* © The Creator 2009. Revealed by Oxford College Press. All rights reserved. For Permissions,


Hum. Mol. Genet. (2009) 18 (R1): R84-R93. doi: 10.1093/hmg/ddp084 material/18/R1/R84.brief



Identification of aneuploidy-selective antiproliferation compounds. Tang, Y-C., Williams, B.R., Siegel, J.J., and Amon, A. (2011). Cell. 144(4):499-512.


Mol Cell Biol. 2009 September; 29(17): 4766–4777.

Revealed on-line 2009 July 6. doi: 10.1128/MCB.00087-09.

PMCID: PMC2725711

Copyright © 2009, American Society for Microbiology

Lack of GATA6 Results in Nuclear Deformation and Aneuploidy in Ovarian Most cancers †

Callinice D. Capo-chichi,1,2 Kathy Q. Cai,2 Joseph R. Testa,2 Andrew Okay. Godwin,2 and Xiang-Xi Xu1,2*

Sylvester Complete Most cancers Middle, Division of Drugs, and Division of Obstetrics and Gynecology, College of Miami College of Drugs, Miami, Florida 33136,1 Ovarian Most cancers, Human Genetics, and Tumor Cell Biology Packages, Fox Chase Most cancers Middle, Philadelphia, Pennsylvania 191112

*Corresponding writer. Mailing tackle: College of Miami College of Drugs, Rm. 417, Papanicolaou Constructing, 1550 NW tenth Ave. (M710), Miami, FL 33136. Cellphone: (305) 243-1750. Fax: (305) 243-5555. E-mail: [email protected]

Obtained January 19, 2009; Revised February 23, 2009; Accepted June 25, 2009.

This text has been cited by different articles in PMC.

* Different Sections?

o Summary




o Supplementary Materials



A distinguished hallmark of most human most cancers is aneuploidy, which is a results of the chromosomal instability of most cancers cells and is assumed to contribute to the initiation and development of most carcinomas. The developmentally regulated GATA6 transcription issue is often misplaced in ovarian most cancers, and the lack of its expression is carefully related to neoplastic transformation of the ovarian floor epithelium. Within the current examine, we discovered that discount of GATA6 expression with small interfering RNA (siRNA) in human ovarian floor epithelial cells resulted in deformation of the nuclear envelope, failure of cytokinesis, and formation of polyploid and aneuploid cells. We additional found that lack of the nuclear envelope protein emerin could mediate the implications of GATA6 suppression. The nuclear phenotypes had been reproduced by direct suppression of emerin with siRNA. Thus, we conclude that diminished expression of GATA6 results in a compromised nuclear envelope that's causal for polyploidy and aneuploidy in ovarian tumorigenesis. The lack of emerin would be the foundation of nuclear morphological deformation and subsequently the reason for aneuploidy in ovarian most cancers cells.


[Proc Amer Assoc Cancer Res, Volume 45, 2004]

Mobile, Molecular, and Tumor Biology 89: Mouse Fashions of Prostate and Gastrointestinal Cancers

Summary #4310

The function of the Bub1 gene in aneuploidy and most cancers development

Danaise V. Carrión, Marie Lia, Joerg Heyer, Patrick McDonald, Weijia Zhang, Kan Yang, Martin Lipkin, Ronan O’Hagan, Lynda Chin and Raju Kucherlapati

Harvard Medical College-Companions Middle for Genetics and Genomics, Boston, MA, Albert Einstein Faculty of Drugs, Bronx, NY, Strang Most cancers Prevention Middle, Rockefeller College, New York, NY, Dana-Farber Most cancers Institute, Boston, MA

Human colorectal tumors may be categorised on the premise of their genomic stability. Some CRC tumors present chromosomal instability (CIN) that's manifested by irregular chromosome numbers whereas others present microsatellite instability. The trigger for microsatellite instability is taken into account to consequence from mutations in DNA mismatch restore genes however the genetic foundation for CIN isn't properly understood. We hypothesized that CIN may consequence from mutations in genes concerned within the mitotic checkpoint. Bub1 is a gene concerned in mitotic checkpoint. Mutations in Bub1 have been recognized in CRC tumors, thus making this gene a superb candidate to be concerned in CIN and in colorectal most cancers. To look at the function of Bub1 in carcinogenesis and chromosomal instability, we generated mice that carry a null mutation on this gene. Mice which are heterozygous for a null mutation in Bub1 are regular. When the heterozygotes had been intercrossed, we failed acquire any homozygous offspring suggesting that Bub1 homozygosity results in embryonic demise. Bub1–/– embryos had been detected at E3.5 however not at E8.5. We examined chromosome segregation in Bub1+/– and wild sort (WT) ES cell strains. At completely different passages the Bub1+/– line confirmed the next proportion of aneuploid cells. To verify this commentary FISH evaluation was carried out in blood cells of WT and Bub1+/– mice utilizing probes for chromosomes 9 and 17. Modest chromosomal instability was noticed within the Bub1+/– samples analyzed. Bub1+/– mice are fertile and inclined to develop tumors very late of their lives. When Bub1+/– mice had been bred to Apc1638N and Msh2 mutant mice, there was no distinction within the incidence or multiplicity of tumors suggesting that the genomic instability offered by Bub1 heterozygosity is inadequate to considerably lower the tumor latency or enhance the incidence of tumors within the double mutants. Taken collectively, these outcomes counsel that the Bub1 gene is crucial for regular survival; and that heterozygosity of the gene results in a gentle chromosomal instability phenotype. This diploma of chromosomal instability doesn't considerably have an effect on the phenotype of Apc1638N and Msh2–/– mutant mice. material/summary/2004/1/994-d


Developments Cell Biol. 2005 Might;15(5):241-50.

Aurora kinases, aneuploidy and most cancers, a coincidence or an actual hyperlink?

Giet R, Petretti C, Prigent C.


CNRS UMR6061 Université de Rennes 1, Groupe Cycle Cellulaire, Equipe Labellisée LNCC, Université de Rennes 1, IFR140 GFAS, Faculté de Médecine, 2 Avenue du Pr Léon Bernard, CS 3417, Rennes cedex, France.


As Aurora kinases are overexpressed in a lot of cancers, and ectopic expression of Aurora generates polyploid cells containing a number of centrosomes, it has been tempting to counsel that Aurora overexpression provokes genetic instability underlying the tumorigenesis. Nevertheless, examination of the proof suggests a extra complicated relationship. Overexpression of Aurora-A readily transforms rat-1 and NIH3T3 cells, however not main cells, whereas overexpression of Aurora-B induces metastasis after implantation of tumors in nude mice. Why do polyploid cells containing irregular centrosome numbers induced by Aurora not get eradicated at cell-cycle checkpoints? Does this phenotype decide the origin of most cancers or does it solely promote tumor development? Would medicine towards Aurora relations be of any assist for most cancers therapy? These and associated questions are addressed on this assessment (which is a part of the Chromosome Segregation and Aneuploidy sequence).



[PubMed - indexed for MEDLINE]


Professor Angelika Amon (MIT)


The Cell Cycle and Most cancers, Angelika Amon, June 7, 2006 (Video of Presentation to a Common Viewers)

Exploiting most cancers cells' weaknesses

Staff identifies potential medicine that improve stress brought on by too many chromosomes.

Anne Trafton, MIT Information Workplace

Quantity 144, Difficulty 4, 18 February 2011, Pages 499-512

doi:10.1016/j.cell.2011.01.017 | The best way to Cite or Hyperlink Utilizing DOI

Cited By in Scopus (7)

Permissions & Reprints


Identification of Aneuploidy-Selective Antiproliferation Compounds


$ 31.50

References and additional studying could also be accessible for this text. To view references and additional studying you will need to buy this text.

Yun-Chi Tang1, Bret R. Williams1, Jake J. Siegel1 and Angelika Amon1, Corresponding Creator Contact Data, E-mail The Corresponding Creator

1 David H. Koch Institute for Integrative Most cancers Analysis and Howard Hughes Medical Institute, Massachusetts Institute of Expertise, Cambridge, MA 02139, USA

Obtained 4 August 2010;

revised 22 November 2010;

accepted 17 January 2011.

Revealed on-line: February 10, 2011.

Accessible on-line 10 February 2011.

Referred to by: Focusing on Aneuploidy for Most cancers Remedy

Cell, Quantity 144, Difficulty 4, 18 February 2011, Pages 465-466,

Eusebio Manchado, Marcos Malumbres

PDF (141 Okay) |


Aneuploidy, an incorrect chromosome quantity, is a trademark of most cancers. Compounds that trigger lethality in aneuploid, however not euploid, cells might due to this fact present new most cancers therapies. We've recognized the power stress-inducing agent AICAR, the protein folding inhibitor 17-AAG, and the autophagy inhibitor chloroquine as exhibiting this property. AICAR induces p53-mediated apoptosis in main mouse embryonic fibroblasts (MEFs) trisomic for chromosome 1, 13, 16, or 19. AICAR and 17-AAG, particularly when mixed, additionally present efficacy towards aneuploid human most cancers cell strains. Our outcomes counsel that compounds that intrude with pathways which are important for the survival of aneuploid cells might function a brand new therapy technique towards a broad spectrum of human tumors.


Modeling the Aneuploidy Management of Most cancers

Li, Yao and Berg, Arthur and Wu, Louie R. and Wang, Zhong and Chen, Gang and Wu, Rongling (2010) Modeling the Aneuploidy Management of Most cancers. BMC Most cancers, 10 . Artwork. No. 346. ISSN 1471-2407



PDF - Revealed Model

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Background: Aneuploidy has lengthy been acknowledged to be related to most cancers. A rising physique of proof means that tumorigenesis, the formation of latest tumors, may be attributed to some extent to errors occurring on the mitotic checkpoint, a serious cell cycle management mechanism that acts to stop chromosome missegregation. Nevertheless, up to now no statistical mannequin has been accessible quantify the function aneuploidy performs in figuring out most cancers. Strategies: We develop a statistical mannequin for testing the affiliation between aneuploidy loci and most cancers threat in a genome-wide affiliation examine. The mannequin incorporates quantitative genetic ideas right into a mixture-model framework through which varied genetic results, together with additive, dominant, imprinting, and their interactions, are estimated by implementing the EM algorithm. Outcomes: Underneath the brand new mannequin, a sequence of hypotheses assessments are formulated to elucidate the sample of the genetic management of most cancers by means of aneuploid loci. Simulation research had been carried out to research the statistical conduct of the mannequin. Conclusions: The mannequin will present a device for estimating the results of genetic loci on aneuploidy abnormality in genome-wide research of most cancers cells.