Treasury Spread: Going to Zero!

Today's spread is above, the lowest is over half a century. I wrote on this a week ago and now it has just gotten lower. Here is another view:

This is a problem because it implies a very low to negative growth rate world wide. Despite the fact that we are still facing significant inflation in food, clothing, autos, fuel. This will have a massive impact on such things as pension funds who have anticipated unrealistic returns, well in excess of 7%. The State and Local Pensions are now drastically underfunded with no potential for escape. That perhaps is the next economic bubble.

The Wrong Question

It appears that Becker is not in any way concerned about the excessive increase in College Tuition. Posner makes a similar argument and I defer comment on that until later.

He begins his argument with:

Student loans have increased the supply of young persons who go to college. In a competitive higher education market-which describes the American situation where thousands of colleges compete for students- a greater number of college students induces increases in tuition. However, the increased supply of places for college students moderates the increases in tuition.

 Now this is a total nonsequitur. The increase in supply is really the result of "advertising" by Government and others to create a large pool of somewhat educated youth who can hopefully perform some useful function. For example, what good is a political science maj0or, none. Absolutely positively none. It can be said the same for an economics major, for as a "profession" they seem to all disagree with one another. Their field is more split than Greek theologians in the 4th century! Then how about a fine arts major, just where do we put them? You see it would be better to have trade schools, with electricians, plumbers, carpenters, and the like. You cannot outsource that, and there is a demand.

Now he continues:

Although students and their parents complain a lot about the rise in college tuition, since the early 1980s monetary and other benefits from college have risen even faster than tuition and other college costs. As a result, the rate of return on college education in the United States – benefits net of all costs- grew greatly during the past 30 years. The increased net return to college, despite the increase in tuition, explains why a larger, not smaller, fraction of young persons are going to college than did prior to the sustained rise in tuition.

 Benefits? What benefits. In the 60s engineers were in high demand. Now they are sourced with foreign nationals, even in defense programs. The benefits are de minimis if at all. Educational costs to starting salaries have exploded. In 1965 an engineer got $8.000-$10,000 per year salary, but tuition at MIT was $1,900. That was a 4:1 to 5:1 ratio. Now the starting may be $100,000 at the very best but tuition is $60,000. Not even 2:1! And that is for a real college educated person who can be put to work creating value. Not some English major who does not know where the bathroom is to be found. What is Becker basing his conclusions on. At least I have some facts.

Now the increase in costs are due to two factors; exploding Administrative costs and exploding maintenance costs.

Becker concludes with:

Young families with mortgages that exceed $100,000 under normal circumstances are not considered to be in dire economic straits, even though their homes can be taken if they fail to meet their mortgage payments, and they are only investing in more comfortable living arrangements. Young couples that contracted a similar level of debt when they were students have invested in raising their earning power, usually by a lot. So I find it difficult to comprehend why sizable mortgages are accepted while there are political and media outcries over comparable student loans that are based on usually highly productive investments in human capital.

 First, one can monetize a property with a mortgage, if one was prudent. Namely the $100,000 debt on a $150,000 property can be sold and paid off. One cannot so readily monetize an education. Especially if it is in Liberal Arts. Who wants a History major, a Philosopher, and especially an Arts major. Students, and I suppose their families, have a duty to look into the cash flow potential of a job based upon an education. Following your dream is utter nonsense unless you accept the costs, and with Federal loan guarantees the costs are on the rest of us. So go follow your dream some where else.

So what can one say of the Becker piece.

First it has no basis in reasonable economic thought. People make decisions, or should, based upon level of investment, risk and return. Take for example chemists. The field is collapsing. We really do not need more, due to technology. But does a student understand that? In my recent experience the answer is no.

Second, if there is a benefit to society for educated and productive people, note I combined the two attributes as one, then society may thus seek to invest in that. That is yet to be proven.

Third, what of the ever expanding bubble in higher education? Is there a too big to fail mentality there as well. Does the taxpayer have a duty to keep say the University of California system afloat, why not let if collapse. If the price equals the cost then the demand will drop.

Fourth, should there be truth in advertising. We force food companies to include calories. Should we force Universities to include average lifetime earnings for each degree?

Somehow Becker seems to be justifying the unjustifiable.

The question is not what value is there in an education, but why does it cost so much! Universities have been allowed free reign, assuming someone else would take up the tab. The problem is like so many other profligate usurpers of the public trust, we the taxpayers will bear the cost. It  ironically is that Quiet Generation, born before 1945, who paid their own way, then their children's and now their grandchildrens' way. The ones who are accused of getting too much Social Security and Medicare but who still work and pay into the system while taking what few pennies left to create a new generation of educated individuals. Those educated individuals may be able to then support the Baby Boomers who seem to be coming along now.

Genomic Complexity

There has been a great deal of work on genomic complexity of cancers and especially that of multiple somatic mutations in cancers.

As Berger et al state for prostate cancer:

We identified a median of 3,866 putative somatic base mutations (range: 3,192–5,865) per tumor; the estimated mean mutation frequency was 0.9 per megabase. This mutation rate is similar to that observed in acute myeloid leukemia and breast cancer but 7–15 fold lower than rates reported for small cell lung cancer and melanoma17–19. The mutation rate at CpG dinucleotides was more than 10-fold higher than at all other genomic positions. A median of 20 non-synonymous base mutations per sample were called within protein-coding genes. We also identified six high-confidence coding indels (4 deletions, 2 insertions) ranging from 1 to 9 base pairs (bp) in length, including a 2bp frameshift in the tumor suppressor gene, PTEN.

Similarly for melanoma the Nature discussion by Hayden states:

The team also confirmed some findings from earlier studies including the effect that sun exposure can have on the mutation rate of tumour DNA. Tumours from areas of the body that are not frequently exposed to sunlight had around 3 to 14 mutations every million base pairs, whereas one patient who was known to have had high levels of sun exposure had 111 mutations every million base pairs.

The relationship between sun exposure and mutation rates adds to the evidence for the role of sun exposure in melanoma development, says Laura Brockway-Lunardi, director of scientific programmes for the non-profit Melanoma Research Alliance in Washington DC, which helped to fund the work.

 We also note that these mutations may or may not be related in some sequence or pathway. We would also not that for the melanoma mutations the 3-14 for non sunlight exposed and the 111 for sunlight exposed is significant and causal. However we have also argued that such might also be the case for backscatter X ray scanning as now used by the US Government to an excessive degree.

Memorial Day 2012

Normandy, grave by grave. In memory.

Yield Curve, May 2012

The above is the yield curve at selected dates over the past 2 years. The curve yesterday is one of the lowest ever. The drop in the 30 year is almost a factor of 2. The advantages are clearly to lower borrowing, if one can accomplish the task, but the second is the pressure downward on fixed investments and the taxing of those on fixed incomes.

The above is another way to view it. Note how low we see the long term rates. Most likely driven by European fears. I suspect we may see another Recession before the Fall.

This is the 30 year to 30 day spread, the widest one would expect. It has reached an all time low!

This is the 10 year to 90 day spread, a typical metric, also at an all time low. The faith in any recovery has disappeared.

This is the same as above but we have combined them. Note the up tick on the 90 day but the down tick on the 10 year thus shortening the spread. This does not bode well for any recovery.

Ebb and Tide of Europe

Saw this on Zero Hedge, it tells a powerful tale. Beautifully done.

Ongoing PSA Debate

The current debate over PSA levels, testing and care continues. The NY Times has two articles yesterday on the Task Force Report.

Let me comment.

First the title was New Data on Harms of Prostate Cancer Screening.  The article was written by a woman, and yes that does mean something, but the title is basically false. The screening itself does de minimis harm unless there is something done improperly. Even saturation biopsy, 20 or more cores, can be performed in a properly prepped person with de minimis morbidity. Yes there are a few infections, and yes there is hematuria, and yes there is some minor nerve damage and discomfort,  but the alternative is rather terrifying. Colonoscopies have similar issues plus perforation of the colon. Is morbidity present, yes, to an overwhelming degree, in my opinion and experience, not really.


But one should read carefully the next to last paragraph:

xxxxx said that some men might look at the data on risks and benefits and decide that they still want to be tested, and nothing in the recommendations would prevent that. He also noted that federal legislation passed in the 1990s requires Medicare to cover the cost of P.S.A. testing, and that law will remain in effect unless Congress overturns it. Many insurance companies follow the lead of Medicare when it comes to reimbursement for health coverage.

 And the law will remain in effect unless Congress overturns it. Well, is that not what the Task Force is recommending. Let me remind the reader:

1. The Task Force is mainly concerned about the morbidity resulting from biopsies. That should be a decision made between the patient and their, in this case his, physician. Informed consent. It is not in the authority realm of the Task Force to tell me what discomfort level I should tolerate. If so then most likely no one would ever go to a Dentist as a child. However some discomfort to detect and remedy a PCa is much better than death from it.

2. It is true as we have argued that PCa comes in all shapes and sizes. And further as we have repeatedly reported and written on, PCa types are not yet identifiable. Does one have an indolent or aggressive form? In addition is there a cancer stem cell here we should try and find, perhaps. But we cannot and should not assume that since some are indolent we treat all people the same. Why not treat all women with breast lesions as DIC only, I rather not think so.

In the same edition of the Times there is a long discussion regarding preventive care. They state:


Could health care costs be reined in by improving access to preventive care? It’s an idea that appeals to policy makers and many public health experts, but the evidence for it is surprisingly hard to pin down. 

Is this not the same issue?

CBO and the Economy

The CBO has just issued a report looking at the impact of continued freeze in Congress, and the impact of such a Fiscal policy.

It states:

CBO estimates that the combination of policies under current law will reduce the federal budget deficit by $607 billion, or 4.0 percent of gross domestic product (GDP), between fiscal years 2012 and 2013. The resulting weakening of the economy will lower taxable incomes and raise unemployment, generating a reduction in tax revenues and an increase in spending on such items as unemployment insurance. With that economic feedback incorporated, the deficit will drop by $560 billion between fiscal years 2012 and 2013, CBO projects.

They conclude:

What Might Policymakers Do Under These Circumstances?

They could address the short-term economic challenge by eliminating or reducing the fiscal restraint scheduled to occur next year without imposing comparable restraint in future years—but that would have substantial economic costs over the longer run. Alternatively, they could move rapidly to address the longer-run budgetary problem by allowing the full measure of fiscal restraint now embodied in current law to take effect next year—but that would have substantial economic costs in the short run. Or, if policymakers wanted to minimize the short-run costs of narrowing the deficit very quickly while also minimizing the longer-run costs of allowing large deficits to persist, they could enact a combination of policies: changes in taxes and spending that would widen the deficit in 2013 relative to what would occur under current law but that would reduce deficits later in the decade relative to what would occur if current policies were extended for a prolonged period. 

Well someone must do something, but I suspect we will have to wait until after the election.

Prostate Cancer Screening, The Task Force

The USPSTF has issued its dictum on PCa screening with PSA. It states:

The USPSTF recommends against PSA-based screening for prostate cancer (grade D recommendation). 
 

This recommendation applies to men in the general U.S. population, regardless of age. This recommendation does not include the use of the PSA test for surveillance after diagnosis or treatment of prostate cancer; the use of the PSA test for this indication is outside the scope of the USPSTF. 

 It continues:

Men with screen-detected cancer can potentially fall into 1 of 3 categories: those whose cancer will result in death despite early diagnosis and treatment, those who will have good outcomes in the absence of screening, and those for whom early diagnosis and treatment improves survival. Only randomized trials of screening allow an accurate estimate of the number of men who fall into the latter category. There is convincing evidence that the number of men who avoid dying of prostate cancer because of screening after 10 to 14 years is, at best, very small. Two major trials of PSA screening were considered by the USPSTF: the U.S. PLCO (Prostate, Lung, Colorectal, and Ovarian) Cancer Screening Trial and the ERSPC (European Randomized Study of Screening for Prostate Cancer). 

The U.S. trial did not demonstrate any prostate cancer mortality reduction. The European trial found a reduction in prostate cancer deaths of approximately 1 death per 1000 men screened in a subgroup of men aged 55 to 69 years. This result was heavily influenced by the results of 2 countries; 5 of the 7 countries reporting results did not find a statistically significant reduction. All-cause mortality in the European trial was nearly identical in the screened and nonscreened groups. 

 The dissenting view stated:

Prostate cancer death was reduced by 21% in the screened compared with the control group and 29% after adjustment for noncompliance (5). The Task Force concluded that this decrease in prostate cancer–specific mortality amounted to few lives saved and did not outweigh … 

The recommendations of the USPSTF carry considerable weight with Medicare and other third-party insurers and could affect the health and lives of men at high risk for life-threatening disease. We believe that elimination of reimbursement for PSA testing would take us back to an era when prostate cancer was often discovered at advanced and incurable stages. At this point, we suggest that physicians review the evidence, follow the continuing dialogue closely, and individualize prostate cancer screening decisions on the basis of informed patient preferences.  

Now for our comments (see our draft book on PCa) :

1. We have discussed fatal flaws in our opinion in both studies relied upon. Simply they both used the old PSA threshold of 4 and did not include age dependency, percent free PSA and PSA velocity. In addition the European study had too great a time interval between tests.

2. No single PCa is alike. As we have been demonstrating for the past four years, the genetic makeup of PCa is complex and there are clearly certain specific markers for highly malignant PCa. By abandoning the test is throwing the baby out with the bathwater.

3. In my opinion this is a clearly age biased result, with the intent of removing care from the second highest cause of death amongst men. One wonders why!

4. Genetic makeup and family history are major drivers. PSA irregularities are one, along with PC3A testing, to ascertain PCa potential. Why eliminate it. The reason seems to be the cost of subsequent procedures, yet the Task Force argues it is the morbidity to the patient. Frankly morbidity in a competently performed procedure is less than a tooth extraction. Perhaps excess morbidity is more in the mind of the Task Force than reality.

What then is lost? We believe a great deal.

1. We are just beginning to understand the genetic makeup, just look at some of our recent postings, so that having the pool of data is indispensable. Having a genetic profile of multiple PCa would be the key to understanding the dynamics of PCa and its control.

2. What is the value of one life. If one has seen the agony of bone mets in a PCa patient, the results of DIC, and the loss of any dignity in the final days with catheter changes by a less than friendly "health care worker", the morbidity issue pales in comparison.

Hopefully we can find ways to work around this less than useful Government cost cutting "death panel" regulation. Welcome to our new world of health care!

SPOP and Prostate Cancer

SPOP is part of the Hedgehog signalling pathway[1]. The Hedgehog signalling pathway controls amongst other factors the formation of body segments in insects and in vertebrates the development of the neural tube, limbs and left-right asymmetry. In adult tissues Hedgehog is responsible for homeostasis, equilibrium between cells loss and gain while maintaining total mass and function. With an overactive Hedgehog pathway one sees excess cell proliferation and tumor growth[2]. We demonstrate that below:

Thus SPOP has a controlling mechanism for cell replication. Here Hedgehog attaches to Patched and the Patched inhibition of Smothered is eliminated allowing Smothered to start a transcription process enabling replication.

Now upon the activation of Smothered a set of processes are activated and one product is a protein called the zinc finger transcription factor Gli, which when mutually supported by SPOP allows movement to the nucleus as a transcription factor activating the DNA to transcribe[3]. We depict that below:

From Barbieri et al we have the following putative relationships:

 The authors argue that SPOP is a separate and significant marker for PCa. The pathway involved is somewhat understood and is a transcription driven pathway initiated by Hedgehog activation and Patched suppression with Smothered activation. From the NCI pathway databases we have a putative requirement that SPOP is needed to activate GLI for subsequent transcription and cell reproduction.

Specifically Barbieri et al state:

As demonstrated by a subsequent analysis of significantly more genomes, there are only a few truly recurrent non-synonymous mutations in PCa. The most common recurrent non-synonymous mutation in PCa involves SPOP. The SPOP gene encodes for the substrate-recognition component of a Cullin3-based E3-ubiquitin ligase. Mutations in SPOP in PCa were reported originally in two systematic sequencing studies. We have now identified the presence of recurrent mutations in SPOP in 6–13% of human PCas in multiple independent patient cohorts. 

Recurrent missense mutations are found exclusively in the structurally defined substrate-binding cleft of SPOP, and structural analysis suggests that these mutations will inactivate SPOP function by disrupting SPOP–substrate interaction.  

Further, we found that loss of SPOP function in prostate cell lines resulted in increased invasion and altered gene expression; evidence of this expression signature was identified in primary tumours harbouring SPOP mutation. 

Importantly, all SPOP mutations occurred in tumours that were negative for ERG rearrangement; these tumours displayed characteristic somatic copy number aberrations. Taken together, these findings support a distinct molecular class of PCa.

In a recent Nature Medicine article the same authors relate[4]:

Prostate cancer is the second most common cancer in men worldwide and causes over 250,000 deaths each year. Overtreatment of indolent disease also results in significant morbidity. Common genetic alterations in prostate cancer include losses of NKX3.1 (8p21) and PTEN (10q23), gains of AR (the androgen receptor gene) and fusion of ETS family transcription factor genes with androgen-responsive promoters. 

Recurrent somatic base-pair substitutions are believed to be less contributory in prostate tumorigenesis but have not been systematically analyzed in large cohorts. Here, we sequenced the exomes of 112 prostate tumor and normal tissue pairs. New recurrent mutations were identified in multiple genes, including MED12 and FOXA1. SPOP was the most frequently mutated gene, with mutations involving the SPOP substrate-binding cleft in 6–15% of tumors across multiple independent cohorts. 

Prostate cancers with mutant SPOP lacked ETS family gene rearrangements and showed a distinct pattern of genomic alterations. Thus, SPOP mutations may define a new molecular subtype of prostate cancer.

This just adds another gene in the mix for PCa. Namely they authors argue that it is a different type. We would still ask the same questions:

1. What is the issue regarding the presence or absence of a CSC stem cell in PCa.

2. When does this mutation occur.

3. What causes the mutation.

4. SPOP is not a true kinase so what type of blocking would be possible to mitigate the presence of a mutant.

References

1.     Barbieri, C. et al, Molecular genetics of prostate cancer: emerging appreciation of genetic complexity, Histopathology 2012, 60, 187–198.

2.     Barbieri, C., et al, Exome Sequencing Identifies Recurrent SPOP, FOXA1 and MED12 Mutations in Prostate Cancer, Nature Genetics (2012).

3.     Marks, F., et al, Cellular Signal Processing, Garland (New York) 2009.

4.     Pecorino, L, Molecular Biology of Cancer, Oxford (New York) 2008.

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[1] http://pid.nci.nih.gov/search/MoleculePage?molid=203488   and http://pid.nci.nih.gov/search/search_landing.shtml?atom_id=208460,208462&what=graphic&jpg=on and pathway at http://pid.nci.nih.gov/search/advanced_landing.shtml?what=graphic&svg=&jpg=true&xml=&biopax=&complex_uses=on&family_uses=on&degree=1&molecule=&pathway=hedgehog&macro_process=&source_id=5&evidence_code=NIL&evidence_code=IAE&evidence_code=IC&evidence_code=IDA&evidence_code=IFC&evidence_code=IGI&evidence_code=IMP&evidence_code=IOS&evidence_code=IPI&evidence_code=RCA&evidence_code=RGE&evidence_code=TAS&output-format=graphic&Submit=Go

[2] See Marks et al p 210-212.

[3] See Pecorino, p. 168-170.

[4] http://www.nature.com/ng/journal/vaop/ncurrent/full/ng.2279.html

Melanoma and Pathway Blocking

In a recent ASCO news release there is a report of blocking of BRAF and MEK in melanoma thus having the BRAF block the melanoma pathway and the MEK blocking the secondary squamous cell cancer pathway.

The release states:

Results from an expanded Phase IB trial show that combination therapy with two investigational targeted drugs – the BRAF inhibitor dabrafenib and the MEK inhibitor trametinib – stalls cancer progression and with a lower level of skin side effects than published studies of the current standard single-agent BRAFtargeted therapy, vemurafenib (Zelboraf), have shown. The analysis included patients with advanced melanoma who had a V600 BRAF mutation and who had no previous BRAF-targeted treatment. Approximately half of all melanomas harbor a V600E mutation in the BRAF gene; in those patients, the nearby MEK pathway is also highly active. While the approval of vemurafenib last year represented a major research achievement, most patients eventually develop resistance to the drug. It is hoped that simultaneously targeting the two active pathways – BRAF and MEK – will provoke a stronger anti-cancer response and prevent, or further delay, treatment resistance.

The result is not unexpected but it does presage a broader application of multiple pathway inhibiting profiles.

Social Justice and Catholics

Social Justice is a movement which argues that it is the Government's responsibility to provide others with what is perceived missing to establish what is perceived by them as an equity or to use the euphemism, a level playing field, and in reality an equality of outcome. ( To better understand this position it is worth reading my book on Individualism and Neo-Progressivism)

In the NY Times today some author states:

A broad, upbeat theme of social justice will be enough for Obama to reach persuadable Catholics, who can interpret the message in concert with their beliefs. The president might quote Pope John Paul II, who once said, “Radical changes in world politics leave America with a heightened responsibility to be, for the world, an example of a genuinely free, democratic, just and humane society.” They must hear the message often and at least 15 percent of the time in Spanish.

Now the interpretation of personal duty, rather than group duty, is a matter of concern regarding the treatment of others.  One could argue that the Sermon on the Mount was a call to personal duty, not a call to the Government of Rome to establish programs for the poor. The duty is individual, and individuals may group together to provide necessary services to those in need but the taxing and forced participation is questionable at best. Those who support Social Justice support a program of forced participation in satisfying needs perceived by a few but supported by the many.

In contrast the same people will force the Church to supply services that it objects to. Yet the Church would object to that force but ironically some of the same voices will press for the forced contributions under the rubric of social justice.

One wonders how one achieves what is sought for the doing of good deeds when one is forced to do so under the rubric of Social Justice. Is it the duty of Government or of the Church or of the individual.

The author continues:

What would a Catholic voter outreach program look like? The Roman Catholic Church doesn’t exactly let political operatives walk in the front door and set up shop, but there are several progressive Catholic organizations — Catholics United, Catholics in Alliance, Catholic Democrats — that the campaign could engage first to build a volunteer corps. Within each district office, the campaign could identify Catholic precinct captains to recruit Catholic door-knockers to reach out to their friends from church. Then there’s advertising. It would be more difficult to construct this architecture from scratch, but however it’s done, it’s a must: a positive social justice message could be what tips the balance toward re-election for the president.

 No, political operatives do not walk in the front doors, in fact one would suspect if they were allowed the tax benefit would be promptly revoked, albeit it appears not to be the case in other churches.

Catholics are individuals for the most part. With the general exception of the Sophists one finds in Jesuits, the arguments, if any, are limited. Catholics in this election will not be any block. If they ever were. Rome seems to have taken the position of admonishing Governments while leaving the individual free from any duty. I frankly find this difficult to rationalize with the teachings of th first seven centuries. Yet in many ways it was a response to Socialism and Communism, the concept of Social Justice.

Facebook and the Value Proposition

When looking at any business opportunity one looks at how value is created and how the company can monetize this value. Value is relative to the user. For example, Microsoft had substantial value creating capacity, and yes it cost to attain it. It was the word processor, spread sheet, and to some degree the operating system. Google had substantial value. It allowed access to information and it created and environment to share it and to monetize it via advertising.

I was a very early Facebook user at MIT, students drove the use. I have not used it for two years. It has no value and in fact it has a negative value. Why? Because it allows somewhat crazy comments from those to whom I was linked to create my profile. It had negative value. It also lacked privacy from my perspective. Thus I left.

So when looking at Facebook I see another AOL. And why AOL, because when in the mid 1990s while teaching at Columbia Business School I did a case on AOL and stated that in my analysis at the time it was at best declining in value. That was before the Time Warner acquisition. I see possibly the same here with Facebook. Yes it is a "social media" and yes it facilitates such communications. But is it of singular value to a person, a company? Time will tell.

Cancer Models:Prediction and Control

We will now consider what are the essential elements for modeling cancers. The first step is to re-establish the goals of a model and then its structure. Finally we will lead into the interrelationship between a model and the data which is used to justify it.This work is detailed in a recent White Paper.

Many authors have developed models concerning pathways and also cancer. The books by Klipp et al and that of Szlassi et al are excellent overviews of the area with significant detail. The Klipp et al book is a truly superb discussion regarding pathways and modeling alternatives. The books by Bellomo et al and Wang are directed specifically at cancer modeling but unfortunately they lack adequate pathway dynamics to be of substantial use. Yet they are the only books available within the focused area.

At the core, we want a model which reflects the following qualities:

1. Based Upon Reality: The model must at its core be based upon the known reality. It must conform with what we currently know and understand. Namely it must reflect in its core the elements which we consider critical and the temporal and spatial dynamics of those elements. The model must be based upon a tempero-spatial system of measurable quantities ;linked in some kinetic manner using reasonably well understood processes.

2. Predictability: Any modeling must, if it is to have any credibility, have the ability to predict, to say what will happen, and then to have that prediction validated. Although the ability may be statistical in nature the statistical confidence must be justifiable. We know all too well that many things are correlated, yet not causal, and not predictable.

3. Measurable: One must be able to measure and then predict the quantities which make up the model. Many of the modeling systems include proteins but they react in some zero-one format. We know in reality that we have concentrations, or better yet specific numbers of proteins, produced in a cell. Yet we cannot yet measure the number of each of these proteins. We all too often can at best measure their presence or absence. However, is it not the case that it is the excess or the low density of some set of proteins which shift reactions, and that reactions are often concentration dependent.

4. Modellable: We want a system which can be modeled. It must reflect the measurable quantities in space and time and the tempero-spatial dynamics of them, using techniques that we can then use for prediction and validation.

In this paper we examine and analyze several models of cancer. Specifically we look at intracellular, extracellular and full body models. We attempt to establish a linkage between all of them. Many researchers have looked at the gene level, the pathway level and the gross flow of cancer cell level, namely whole body. Connecting them has been complex to say the least.

But herein we look at the pathway level and a whole body level and demonstrate the nexus, physically, and from this we argue that one can construct both prognostic tools as well as methodologies to deal with metastasis.

The following graphic lays out the flow of development and its implications as we detail them herein.

 The key question we ask is just what is it we are modeling in cancer cell dynamics. Let us consider some options:

Intracellular Gene Dynamics:

This type of model focuses on the genes, and their behavior. It is basically one where we examine the gene type and its product.

Intracellular Protein Dynamics:

This type of model falls in several subclasses. All begin with protein pathways and the “dynamics” of such pathways. But we have two major subclasses; protein measures and temporal measures. By the former we mean that we can look at the proteins as being on or off, there or not there, or at the other extreme looking at the total number of proteins of a specific type generated and present at a specific time. By the latter, namely the temporal state, we can look at the proteins in some static sense, namely there or not there at some average snapshot instance, or we can look at the details over time, the detailed dynamics. In all cases we look at the intracellular dynamics only.

Let us consider the two approaches.

i. On-Off: In this approach the intracellular relationships are depicted as activators or inhibitors, namely if present they allow or block an element in a pathway. PTEN is a typical example, if present it blocks Akt, if absent it allows Akt to proceed and enter mitosis. p53 is another example for if present we have apoptosis and if absent we fail to have apoptosis. These are simplistic views. This is a highly simplistic view but it does align with the understanding available say with limited microarray techniques. This is an example of the data collection defining what the model is or should be.

ii. Density: This is a more complex model and it does reflect what we would see as reality. The underlying assumptions here are:

a. Genes are continually producing proteins via transcription and translation.

b. Transcription and translation are affected at most by proteins from other genes acting as repressors or activators. There are no other elements affecting the process of transcription and translation. Not that this precludes any miRNA, methylation, or other secondary factors. We shall consider them later. In fact they may often be the controlling factors.

c. The kinetics of protein production can be determined. Namely we know the rate at which transcription and translation occur in a normal cell or even in a variant. That is we know that the production rate of proteins can be given by a typical creation differential equation.

Here we have production rates dependent on the concentration of other proteins. The processes related to consumption are not totally understood (see Martinez-Vincente et al). We understand cell growth, as distinct from mitotic duplication, but the growth of a cell is merely the expansion of what was already in the cell when at the end of its mitotic creation. In contrast, we understand apoptosis, the total destruction of the cell, we also understand that certain proteins flow outside the cell or may be used as cell surface receptors, but the consumption of these is not fully understood. Yet we can postulate a similar destruction differential equation.

This is based upon the work of Martinez-Vincente et al which states[1]:

All intracellular proteins undergo continuous synthesis and degradation. This constant protein turnover, among other functions, helps reduce, to a minimum, the time a particular protein is exposed to the hazardous cellular environment, and consequently, the probability of being damaged or altered. At a first sight, this constant renewal of cellular components before they lose functionality may appear a tremendous waste of cellular resources.

However, it is well justified considering the detrimental consequences that the accumulation of damaged intracellular components has on cell function and survival. Furthermore, protein degradation rather than mere destruction is indeed a recycling process, as the constituent amino acids of the degraded protein are reutilized for the synthesis of new proteins.

The rates at which different proteins are synthesized and degraded inside cells are different and can change in response to different stimuli or under different conditions. This balance between protein synthesis and degradation also allows cells to rapidly modify intracellular levels of proteins to adapt to changes in the extracellular environment. Proper protein degradation is also essential for cell survival under conditions resulting in extensive cellular damage. In fact, activation of the intracellular proteolytic systems occurs frequently as part of the cellular response to stress. In this role as ‘quality control’ systems, the proteolytic systems are assisted by molecular chaperones, which ultimately determine the fate of the damaged/unfolded protein.

Damaged proteins are first recognized by molecular chaperones, which facilitate protein refolding/repairing. If the damage is too extensive, or under conditions unfavorable for protein repair, damaged proteins are targeted for degradation. Protein degradation is also essential during major cellular remodeling (i.e. embryogenesis, morphogenesis, cell differentiation), and as a defensive mechanism against harmful agents.

We have also discussed this process with regards to the function of ubiquitin, which marks proteins for elimination. As Goldberg states[2]:

Proteins within cells are continually being degraded to amino acids and replaced by newly synthesized proteins. This process is highly selective and precisely regulated1, and individual proteins are destroyed at widely different rates, with half-lives ranging from several minutes to many days. In eukaryotic cells, most proteins destined for degradation are labelled first by ubiquitin in an energy requiring process and then digested to small peptides by the large proteolytic complex, the 26S proteasome.

Indicative of the complexity and importance of this system is the large number of gene products (perhaps a thousand) that function in the degradation of different proteins in mammalian cells. In the past decade, there has been an explosion of interest in the ubiquitin–proteasome pathway, due largely to the general recognition of its importance in the regulation of cell division, gene expression and other key processes1. However, the cell’s degradative machinery must have evolved initially to serve a more fundamental homeostatic function — to serve as a quality-control system that rapidly eliminates misfolded or damaged proteins whose accumulation would interfere with normal cell function and viability.

Also we refer to the recent review work of Ciechanover which details the evolution of this understanding[3].

In contrast the proteins are consumed and thus the negative sign. In toto we have a combined equation as a total balance of proteins. This assumes we have a production mechanism for each of the proteins, namely their genes and the activators and repressors as required.

d. Pathway Dynamics must be meaningful. Let us consider the pathway as shown below. This is a typical melanoma pathway we have shown before.

Now let us consider PTEN blocking BRAF and Akt. Now physically it is one molecule of PTEN needed for each molecule of BRAF and PI3K. But what if we have the following: n(PTEN)n(PI3K).

Here we have PTEN blocking some but not all the BRAF and PTEN blocking all the PI3K. At least at time t. Do we have an internal mechanism which then produces even more PTEN? One must see here that we are looking at the actual numbers of PTEN, real numbers reflecting the production and destruction rates. We know for example that if we have a mutated BRAF then no matter how much PTEN we have an unregulated pathway.

Now it is also important to note that this “model” and approach is distinct in ways from classic kinetics, since the classic model assume a large volume and concentrations in determining kinetic reaction rates of catalytic processes. Here we assume a protein binds one on one with another protein to facilitate a pathway.

Thus knowing the dynamics of individual proteins, and knowing the pathways of the proteins, namely the temporary adhesion of a protein, we can determine several factors:

1.     The number of free proteins by type

2.     The pathways activated or blocked

3.     The resultant cellular dynamics based on activated pathways.

It should be noted that we see pathways being turned on and off as we produce and destroy proteins. There is a dynamic process ongoing and it all depends on what would be a stasis level of proteins by type. The question is; are cells in stasis or are they in a continual mode of regaining a temporary stasis?

This also begs the question, that if as we have argued, that cancer is a loss of stasis due to pathway malfunction, then can this be a process of instability in the course of a normal cell? Namely is there in the dynamics of cell protein counts, unstable oscillator type modes resulting in uncontrolled mitotic behavior. Namely can a cell get locked into an unstable state and start reproducing itself in that state, namely an otherwise normal cell.

e. Total intracellular dynamics can be modeled yet the underlying processes are still not understood and the required measurements are yet to be determined.

Intercellular Dynamics:

Here we look at the intercellular dynamics as well, not just as a stand-alone model. By this methodology we look at intercellular communications by ligand binding and the resulting activation of the intracellular pathways. We must consider both the intercellular signalling between like cells but also between unlike, such a white cells perhaps as growth factor inhibitors and the like. We also then must consider the spatiodynamics, namely the “movement” of the cells, or in effect the lack of fixedness or specificity of function. This becomes a quite complex problem.

There are two functions we examine here:

a. Intercellular binding or adhesion: E cadherin is one example that we see in melanocytes. Pathway breakdown may result in the malfunctioning of E cadherin.

 The above demonstrated E cadherin in melanocyte-keratinocyte localization. The bonds are strong and this stabilizes the melanocyte in the basal layer. If however the E cadherin is compromised then the bond is broken, or materially weakened, and the melanocyte starts to wander. Movement for example above the bottom of the basal layer and upwards is pathognomonic of melanoma in situ. Wandering downward to the dermis becomes a melanoma. Thus the pathways activating E cadherin production is one pathway essential in the inter-cellular dynamics.

b. Ligand production and receptor production: Here we have cells producing ligands, proteins which venture out of the cell and become signalling elements in the intercellular world. We have the receptor production as well, where we have on the surface of cells, various receptors, also composed of cell generated proteins, which allow for binding sites of the ligands and result in pathway activation of some type. For example various Growth Factors, GF proteins, find their way to receptors, which in turn activate the pathways. Wnt is an example of one of these ligands which we have shown above.

It can also be argued that as ligands are produced and as the “flow” throughout the intercellular matrix, we can obtain effects similar to those in the Turing tessellation models. Namely a single ligand may be present everywhere but density of ligands may vary in a somewhat complex but determinable manner, namely is a wavelike fashion.

This is akin to the Turing model used in patterning of plants and animals[4]. Namely the concentration of a ligand, and in turn its effect, may be controlled by

Total Cellular Dynamics

In this case we would want a model which reflects the total body spatiotemporal dynamics This type of models is an ideal which may or may not be achievable. In a simple sense it is akin to diffusion dynamics, viewing the cancer cells as one type of particle and the remaining body cells as another type. The cancer cells have intercellular characteristics specific to cancer and the body cells have functionally specific characteristics. Thus we could ask questions regarding the “diffusion” of cancer cells from a local point to distant points based upon the media in between. The “rate” of such diffusion could be dependent upon the local cells and their ability for example to nourish the cancer cells as well. In this model we could define an average concentration of cancer cells at some position x and time t and we would have some dynamic process as well.

This is a diffusion like equation and is a whole body equation. Perhaps knowing what the rate of diffusion is on a cell by cell basis may allow one to determine the most likely diffusion path for the malignancy, and in turn direct treatment as well.

This is of course pure speculation since there has been to my knowledge any study in this area. Except one could imagine a system akin to PET scans and the like which would use as input the surface markers from a malignancy and then the body diffusion rates to plot out in space and time the most likely flow of malignant cells and thus plan out treatment strategies. Although this model is speculative we shall return again to it in a final review of such models since it does present a powerful alternative.

This concept of total cellular dynamics is in contradistinction to the intercellular transport. In the total cellular dynamics model we regard the model as one considering the flow of altered cells across an existing body of stable differentiated cells.

We may then ask, what factors drive cancer cells to what locations? One may putatively state that cancer cells will follow the path of least resistance and/or will proceed along “flow lines” consistent with what propagation dynamics they may be influenced by.

Total Cellular Dynamics: An Example

The concept of a model of Total Cellular Dynamics is somewhat innovative. It focuses on the movement of the cancer cells throughout the body. We will consider three possible possibilities:

1. No Stem Cells

2. Stem Cells but Fixed at Initial Location

3. Stem Cells which are mobile.

In Case 1 all malignant cells are clones of each other at least at the start. As the malignant cells continue through mitosis additional mutations are likely so that after a broad set of mitotic divisions we have a somewhat heterogeneous set of malignant cells, some more aggressive than others. As with most such cancer cells they also produce ligand growth factors which stimulate each other and result in the cascade of unlimited growth and duplication.

In Case 2 we assume that there was a single cell which mutated and that this becomes the CSC. The CSC replicates producing one CSC for self-replication and TICs which migrate. We assume that the CSC may from time to time actually double, but not at the mitosis rate of the base. Furthermore we assume the CSC sends out growth factors, GF, to the TICs. The GF flow outward in a wave like manner from the somewhat position stabilized CSCs to the TICs which are mobile and both diffuse and flow throughout the body. The GF must find the TICs which become a distant metastasis.

In Case 3 in contrast to Case 2, we assume mobile CSC and thus the CSCs also flow according to some set of rules.

Total Cellular Dynamics Models

Now depending on the case we assume we can model the flow of cancer cells according to some simple dynamic distributed models[5]. Thus we could have[6] a partial differential equation of the type found in McGarty (see White Paper).

This provides diffusion, flow, and rate elements. The rate term, the F term, is a rate of change in time at a certain location and time specific. It is the duplication rate at that specific location due to the normal mitotic change. The last term may be both pathway and environment driven.

Now this description has certain physical realities.

Here above we describe the three factors in terms of their effects and their causes. The three elements of the equation; diffusion, flow, and growth, are the three ways in which cancer cells move. We can summarize these as below:

Factor	Diffusion	Flow	Growth
Physical Effect	Cancer cells begin to diffuse due to concentration effects.	Cancer cells are “forced” to move by a flow mechanism driven them in a direction along flow lines.	Cancer cells begin to go through mitosis and cell growth.
Genetic Driver	Movement is due to the loss of location restrictors such as E cadherin found in melanocytes and restricting their movement.	Flow lines may be developed by means of metabolic needs of the cell in search of the nutrients required for growth. This may be a combination of angiogenesis as well as a Warburg like effect.	Growth factor ligands attach to the surface of the cell. Flow of such ligands and their production may be influenced by a Turing flow effect thus accounting for complexity of location of growth.
Impact	Slow migration in local areas.	Cells have lost functionality and move to maximize their nutrition input to facilitate growth.	Cancer cells may find optimal areas for proliferation based upon factor related to ligand density.

Now consider the following graphic as a human body,

 

We have a D, E, F, for each gross portion of the body. We also have a model as specifically below in the Table:

Organ	D Diffusion	E Flow	F Production
Epidermis	0.5	0.01	0.7
Dermis	0.4	0.02	0.5
Cutis	0.3	0.05	0.2
Blood	5.0	0.5	0.01
Brain	0.1	0.01	0.2
Liver	2.0	0.2	0.3
Lung	3.0	0.3	0.4
Kidney	1.5	0.4	0.5
Bone	2.5	0.5	1.0

The above numbers are purely speculative. But if we can ascertain them then we get a solution of p(x,t) in time. Note that here we have a two dimensional space. Thus we have the above constants applying only to this artifactually spatial model. Distance is measured in terms of movement across the interfaces. For simplicity we assume that all other space is impenetrable by any means. This we have production, flow and diffusion in each area.

 Note that in the above we have laid out the x and y coordinates such that we have blood flow in the center, namely the metastasis flows via blood, and then enters organs as shown. The “location” of the organs are distances. Note also the origin of the malignancy is at (0,0).

Now we can relate the constants to the pathway distortions which are part of the malignancy as well.

The question is how do we determine these constants so that we may verify the model. Let us assume we can do so via examination of prior malignancy, not an obvious task but one we shall demonstrate. One must be cautious also to include in the determination pathway factors for each malignancy and its state and stage. Thus the three constants will be highly dependent upon the specific genetic makeup of the initial malignancy.

Turing Tessellation

In 1952 Alan Turing, in the last year and a half of his life, was focusing on biological models and moving away from his seminal efforts in encryption and computers. It was Turing who in the Second World War managed to break many of the German codes on Ultra and who also created the paradigm for computers which we use today. In his last efforts before his untimely suicide Turing looked at the problem of patterning in plants and animals. This was done at the same time Watson and Crick were working on the gene and DNA. Turing had no detailed model to work with, he had no gene, and he had just a gestalt, if you will, to model this issue. Today we have the details of the model to fill in the gaps in the Turing model.

The Turing model was quite simple. It stated that there was some chemical, and a concentration of that chemical, call it C, which was the determinant of a color. Consider the case of a zebra and its hair. If C were above a certain level the hair was black and if below that level the hair was white.  As Turing states in the abstract of the paper:

"It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system.

The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis.

The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading."

Now, Turing reasoned that this chemical, what he called the morphogen, could be generated and could flow out to other cells and in from other cells. Thus focusing on one cell he could create a model across space and time to lay out the concentration of this chemical. He simply postulated that the rate of change of this chemical in time was equal to two factors; first the use of the chemical in the cell, such as a catalyst in a reaction or even part of the reaction, and second, the flow in or out of the cell. The following equation is a statement of Turing's observation.

It allows one to solve for a concentration, C, as a function of time and space. It requires two things. First is the diffusion coefficient to and from cells and second the functional relationship which shows how the chemical is used within a cell.

Determining the Coefficients

The question now is how does one link the coefficients in the models. For example if we believe that diffusion D depends on E cadherin concentration, namely as E cadherin decreases then D increases we may postulate a simple linear relationship between diffusion constants and protein concentrations, where the constants are to be determined. We know that the more E cadherin the stickier is the cell and the less diffusion that occurs. Thus the above is at the least a first order approximation. In a similar manner we can relate F to PTEN and p53.

This is merely suppositional. But we do know the following:

1. The genes which are expressed for adhesion and replication are known.

2. We know the pathways for these genes

3. We know the intracellular models controlling these genes.

4. We know that functionally an excess or paucity of a gene has a certain effect.

5. We know that in general in small amounts the world is linear.

6. We know that we can use regression techniques based upon collected data to determine coefficients in a general sense.

Thus we have a fundamental basis to express the relationships for all gross constants in terms of linearized versions of the protein concentrations.

Now we have related intracellular concentrations, which themselves may be temporally and spatially dependent, to the total parameter values for the flow of cells throughout the body. We may also want to relate these to organ specific parameters as well.

Thus what we have achieved is as follows:

1. Model relating intracellular and whole body.

2. Methodology to determine the constants.

3. Methodology to go from patient data to prognostic data.

4. Methodologies to establish possible treatment methodologies. Namely what gene controls will result in what whole body reactions.

We can now summarize this models we have considered. First we should emphasize that for the most part those working in the field have developed pathway models which exhibit a non-temporal mode, it is some steady state model, and the model assumes a protein to protein connection, as if there were a single protein molecule produced and that the interacting proteins were there or not. Part of the simplicity of the models is determined by the limits of what can be measured. We have herein attempted not to limit the results by what can be accomplished currently but has extended the model to levels which assist in a fuller representation of reality. However even here we may very be falling short.

For we have deliberately neglected such things as miRNA, methylation, and the stem cell paradigm just to name a few.

We combine all four methods in a graphic below. We summarize the key differences and differentiators. Currently most of the analytical models focus on pathways. This can generally be supported by means of microarray technology and even rough estimates of relative concentrations may be inferred by such an approach.

 The risks we see even in the above models is the absence of exogenous epigenetic factors and the inclusion of a stem cell model. The latter issue is one of major concern. For example if we have true cancer stem cells, CSC, then we have a proliferation of differing cell types. The use of microarrays is for the most part and averaging methodology, not a cell by cell methodology. If we collect cells from say a melanoma tumor. how much of that is a CSC and how much a TIC. And frankly should we identify CSCs only and perform our analysis on those cells alone.

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1.      Martinez-Vincente, M., et al, Protein degradation and aging, Experimental Gerontology 40 (2005) 622–633.

 2.      Goldberg, A., Protein degradation and protection against misfolded or damaged proteins, NATURE, Vol 426, 18/25 December 2003.

 [3] Ciechanover , A, Intracellular Protein Degradation: From a Vague Idea through the Lysosome and the Ubiquitin-Proteasome System and onto Human Diseases and Drug Targeting, Rambam Maimonides Medical Journal, January 2012, Volume 3, Issue 1

[4] Turing, A., The Chemical Basis of Morphogenesis, Phil Trans Royal Soc London B337 pp 37-72, 19459.

 [5] See Andersen p 277 of Bellomo et al for an variant on what we are proposing here. The Andersen model is somewhat similar but lacks the detail we present herein. Also there is in the same volume a paper by Pepper and Lolas focusing on the dynamics of the lymphatic cancer system, p 255. Bellomo, N., et al, Selected Topics in Cancer Modeling, Birkhauser (Boston) 2008.

[6] McGarty, T., Stochastic Systems and State Estimation, Wiley (New York) 1974.

1.     Szallasi, Z. System Modeling in Cellular Biology: From Concepts to Nuts and Bolts. MIT Press (Cambridge) 2006.

1.     Klipp, E., et al, Systems Biology, Wiley (Weinheim, Germany) 2009.