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BMC Biology 2011 9 :41

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© Dingli and Pacheco; licensee BioMed Central Ltd.2011

Received: 8April2011

Accepted: 7June2011

Published: 7June2011

Abstract

Stem cells are the target of mutations that can lead to life threatening diseases. However, stem cell populations tend to be small and therefore clonal expansion of mutant cells is highly sensitive to stochastic fluctuations. The evolutionary dynamics of mutations in these cells is discussed, taking into consideration the impact of such mutations on the reproductive fitness of cells. We show how stochastic effects can explain clinical observations, including extinction of acquired clonal stem cell disorders.

Imatinib Chronic Myeloid Leukemia Mutant Cell Paroxysmal Nocturnal Hemoglobinuria Relative Fitness

Cancer is a consequence of multicellularity due to the fact that the cellular genome is under continuous attack from a variety of environmental or metabolic genotoxic agents. Moreover, the DNA replication machinery is not perfect [ 1 ]. Hence, the development of mutations in cells is both a natural and artificial - for example, in the case of smoking - process. The finite number of cells and the randomness of cell mutation events lead to a stochastic cell dynamics encompassing several scenarios, including extinction of acquired clonal stem cell disorders, which explains, among other things, spontaneous resolution of diseases. Although many mutations are either neutral [ Stegmann Graz W Black Womens Clogs Size 10M zwIUXGuCol
] or cytotoxic, some mutations may increase the risk of malignant transformation in which the cell loses regulated growth control giving rise to a clone that may threaten the life of the organism [ 3 , 4 ]. The risk of acquiring mutations depends on the mutation rate, the population of cells at risk, and the average lifetime of the cell since it is unlikely that multiple simultaneous mutations occur in the same cell [ 5 , 6 ]. Tissues have evolved an architecture where most cells have a relatively short lifetime and undergo continuous turnover, and this mitigates the accumulation and retention of mutant cells [ 7 ]. At the root of this process are the stem cells that are able to maintain tissue integrity because of a dual phenotypic characteristic: self-renewal and production of progeny that can differentiate into various cell lineages that together constitute tissues and organs. One can visualize tissues as having a tree-like organization of cells with stem cells at one extreme and mature, non-dividing cells at the other extreme [ 8 ]. Intermediate cells divide, often at relatively high rates, but live for relatively short periods of time. Although mutations can occur at every level of this cell hierarchy, the relatively short lifetime of more mature cell stages means that, in effect, the real risk of long-lasting oncogenic mutations is restricted to the small population of stem cells and early progenitor cells that maintain a given tissue. This, in turn, effectively reduces the probability of the occurrence of mutations, given the small population of cells at risk, despite the fact that a mutation arising in a stem cell can persist for a long time. It is important to point out that the relevance of a mutation is cell context-dependent - a mutation in a gene that is not expressed in a cell is of no consequence to that cell but expression of the gene in more committed cells, downstream of the cell that is the source of the mutation, may lead to a phenotype associated with disease [ Blowfish Womens Fite Ballet Flat Black Lonestar Pu tdg2BI2Uy
, 10 ]. The natural history of such mutations is the focus of this article. We put forward a possible role of stochastic effects on the generation and fate of mutations acquired by stem cells. Other investigators have also explored the impact of randomness on the fate of tumor cells [ London Fog Womens Melton Luxe Cold Weather Waterproof Genuine Suede Snow Boot Black/Grey pDPpzd
, Forever Womens Della45 50/50 Triple Ankle Straps Knee High Platform Dress Boots AzDvq
]. We will provide some examples from several well-known blood disorders to illustrate the concepts that will be discussed.

It has been shown that the decomposition of high-dimensional neural networks into low-dimensional neural networks equivalent to the original neural networks yields neural networks that have no critical points based on the hierarchical structure ( Nike Womens Wmns Air Max Thea PINK POW/FIREBERRY 5 US 0AAgy
). As for the case of complex-valued neural networks, a 2-2-2 three-layered complex-valued neural network can be constructed from a 1-1-1 three-layered quaternionic neural network. Such a complex-valued neural network does not comparatively suffer from negative effects caused by singular points during learning because it has no critical points based on a hierarchical structure.

The practical implementation of the 2-2-2 complex-valued neural network having no critical points based on a hierarchical structure is as follows.

1. Consider a 1-1-1 quaternionic neural network (called NET 1 here). Let the weight between the input neuron and the hidden neuron be A = a + ib +jc +kd ϵ Q and the weight between a hidden neuron and an output neuron be B = α + iB +jγ +kδ ϵ Q, where Q represents the set of quaternions. The quaternion is a four-dimensional number and was invented by W. R. Hamilton in 1843 ( ElegantPark Women EP11033 Square Toe Low Heel Rhinestones Buckle Satin Wedding Bridal Shoes Silver Zap32
). Let C = p + iq + jr +ks ϵ Q denote the threshold of the hidden neuron and D = µ + iv + jρ +kσ ϵ Q represent the threshold of the output neuron. For a technical reason, we assume that D = 0. The activation functions are defined by the following equations:

(3)
(4)

for the hidden neuron, and:

(5)

for the output neuron. For the sake of simplicity, we omitted the additional assumptions (see ( 16 ) for the details).

2. Create a 2-2-2 complex-valued neural network (called NET 2 here) by decomposing NET 1 described above, where a quaternion is decomposed into two complex numbers. That is, the quaternion A = a + ib + jc + kd ϵ Q representing the quaternionic weight between the input neuron and the hidden neuron is decomposed into the two complex numbers a′ = a +ib ϵ C and c′ = c + id ϵ C, where C is the set of complex numbers. Here, we used the Cayley-Dickson notation: the weight A between the input neuron and the hidden neuron of NET 1 can be written using Cayley-Dickson notation as follows:

(6)

where a’ = a + ib ϵ C and c’ = c + id ϵ C.

Similarly, the quaternion B = α + iβ + jγ +kδ ϵ Q representing the quaternionic weight between the hidden neuron and the output neuron is decomposed into the two complex numbers α′ = α +iβ ϵ C and dγ′ = γ + iδ ϵ C. The quaternion C = p + iq + jr + ks ϵ Q representing the quaternionic threshold of the hidden neuron is decomposed into two complex numbers p′ = p + iq ϵ C and r′ = r + is ϵ C. We use the activation function defined by the following equations for NET 2:

(7)

for the hidden neuron, and

(8)

for the output neuron.

NET 2 has no critical points based on a hierarchical structure (as a complex-valued neural network). See the literature ( 16 ) for the proof.

Political analysis by and beyond

By Dr. Eric Ostermeier February 18, 2013

More than one-third of deceased U.S. presidents died in June or July; none passed away in May

The recognition of George Washington’s birthday by the federal government (and Abraham Lincoln’s birthday by many state governments and the culture generally) highlights the month of February as the month in which the nation’s most famous presidents were born.

Two other presidents were born in February – William Harrison (February 9) and Ronald Reagan (February 6) – though the most common month is October which saw the births of John Adams (October 30), Rutherford Hayes (October 4), Chester Arthur (October 5), Teddy Roosevelt (October 27), Dwight Eisenhower (October 14), and Jimmy Carter (October 1).

Only two presidents have during the month of February: John Quincy Adams (February 23, 1948) and Woodrow Wilson (February 3, 1924).

The most common time of the year in which the 38 deceased presidents in U.S. history have passed away is the summer.

Six presidents died in the month of June:

James Madison (June 28, 1836) Andrew Jackson (June 8, 1845) James Polk (June 15, 1849) James Buchanan (June 1, 1868) Grover Cleveland (June 24, 1908) Ronald Reagan (June 5, 2004)

With seven more dying in July:

Thomas Jefferson (July 4, 1826) John Adams (July 4, 1826) James Monroe (July 4, 1831) Zachary Taylor (July 9, 1850) Martin Van Buren (July 24, 1862) Andrew Johnson (July 31, 1875) Ulysses Grant (July 23, 1885)

Jefferson and Adams died famously just a few hours apart on Independence Day, with Monroe doing so as well just five years later.

Though they are not the only pair of presidents to die on the same day of the year.

Millard Fillmore and William Taft both passed away on March 8th – in 1874 and 1930 respectively.

Meanwhile, Harry Truman and Gerald Ford both died the day after Christmas – on December 26th 1972 and 2006 respectively.

Five died in January: John Tyler, Rutherford Hayes, Teddy Roosevelt, Calvin Coolidge, Lyndon Johnson

Two in February: John Quincy Adams, Woodrow Wilson

Four in March: Millard Fillmore, Benjamin Harrison, William Taft, Dwight Eisenhower

Four in April: William Harrison, Abraham Lincoln, Franklin Roosevelt, Richard Nixon

One in August: Warren Harding

Two in September: James Garfield, William McKinley

Two in October: Franklin Pierce, Herbert Hoover

Two in November: Chester Arthur, John Kennedy

Three in December: George Washington, Harry Truman, Gerald Ford

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.

In fact, more than one-third of deceased presidents have died in the months of June and July – including 12 of the first 22 men to serve in the office.

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DRG is the premier provider of healthcare analytics, data and insight products and services to the worlds leading pharmas, biotech and medical technology companies.

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