The effect of different cancer treatment strategies on the number of differentiated cancer cells in the presence of resistance.

<p>Panels <b>a</b> and <b>b</b> display the tumor cell population after 500 days of treatment for two different types of treatment. In panel <b>a</b> we consider a treatment that can target all types of cells, and in panel <b>b</b> we consider a treatment that only targets progenitor and differentiated cells. Panels <b>c</b> and <b>d</b> display the tumor cell population after 5000 days of treatment for two different types of treatment. In panel <b>c</b> we consider a treatment that can target all types of cells, and in panel <b>d</b> we consider a treatment that only targets progenitor and differentiated cells. The pre-treatment growth parameters are identical to those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g002" target="_blank">Figure 2</a> and the growth rate of the resistant cells is identical to that in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g004" target="_blank">Figure 4</a>. In all four panels we set <i>u</i> = 5×10⁻⁹ and we set for <i>i</i> = 0,1,2. In panels <b>a</b> and <b>c</b> we set and , and vary (i.e., the drug effect on cancer stem cells) along the horizontal axis. In panels <b>b</b> and <b>d</b>, we set and , and vary (i.e., the drug effect on cancer progenitors) along the horizontal axis. In panels a and b, the vertical axis corresponds to the number of differentiated cancer cells after 500 days of treatment, including resistant and sensitive cancer cells. In panels <b>c</b> and <b>d</b>, the vertical axis corresponds to the number of differentiated cancer cells after 5000 days of treatment, including resistant and sensitive cancer cells.</p

Schematic representation of the mathematical model.

<p>The mathematical model considers three levels of the differentiation hierarchy of cells: stem cells, progenitors and differentiated cells. These cell types are present in the system as healthy cells (left), drug-sensitive cancer cells (middle) and drug-resistant cancer cells (right). Stem cells give rise to progenitors which in turn give rise to differentiated cells. Additionally, cancer progenitors may have the ability to dedifferentiate to stem cells. The rate of dedifferentiation is denoted by <i>γ</i>. Drug-sensitive cancer stem cells produce drug-resistant cancer stem cells at rate <i>u</i> per cell division.</p

The effect of dedifferentiation on the abundance of differentiated cancer cells and the probability of resistance.

<p>In panel <b>a</b>, we show the abundance of differentiated cancer cells over time since the initiation of therapy. In panel <b>b</b>, we plot the probability of resistance versus time. Growth rates during treatment are and , and death rates are for <i>i</i> = 0,1,2. Other parameters are <i>r_x</i> = 0.005, <i>r_y</i> = 0.008, <i>d₀</i> = 0.004, <i>d₁</i> = 0.008, <i>d₂</i> = 0.05, <i>a_x</i> = 100<i>d₁</i>, b<i>_x</i> = 100<i>d₂</i>, <i>a_y</i> = 2<i>a_x</i>, <i>b_y</i> = 2<i>b_x</i>, <i>k_x</i> = 1.2×10⁶, <i>k_y</i> = 6×10⁷, <i>u</i> = 5×10⁻⁹, and ω = 0.1. The initial condition for the panels is found by simulating system (1) using the pretreatment parameter values and the initial condition <i>x</i>₀(0)  = 10⁶, <i>x</i>₁(0)  = 10⁸, <i>x</i>₂(0)  = 10¹⁰, <i>y</i>₀(0)  = 1, and <i>y</i>₁(0)  = <i>y</i>₂(0)  = 0. We simulate this system until detection time <i>T</i>, i.e., when <i>y</i>₂(<i>T</i>) ≥10¹², and then simulate the treatment phase by running system (1) with the initial conditions <i>x</i>₀(<i>T</i>), <i>x</i>₁(<i>T</i>), …, <i>y</i>₂(<i>T</i>) and the treatment parameter values.</p

The effect of different treatment strategies on the abundance of differentiated cancer cells and the probability of resistance.

<p>The figure shows the abundance of differentiated cancer cells, <i>y₂</i>, over time since initiation of therapy in panel <b>a</b> and the probability of resistance, <i>P</i>(<i>t</i>), as a function of time in panel <b>b</b>. We display four different treatment types that affect the cancer cell populations differentially. <i>Treatment 1</i> represents a drug that affects only the production of cancer progenitor and differentiated cells, and . <i>Treatment 2</i> is a drug affecting all cancer cell types while not inhibiting cancer stem cells by a substantial amount, while , and and . <i>Treatment 3</i> represents a drug that affects all cancer cell types and has a substantial effect on stem cells, , and . <i>Treatment 4</i> is a drug that decreases only the growth rate of cancer stem cells, . The pre-treatment parameters are identical to those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g002" target="_blank">Figure 2</a>, and in both panels we set for <i>i</i> = 0,1,2.</p

The effect of different cancer stem cell treatment strategies on the time until disease progression.

<p>The figure shows the time until the disease burden increases despite continuous therapy versus the birth rate (panels <b>a</b> and <b>b</b>) and death rate (panels <b>c</b> and <b>d</b>) of cancer stem cells during therapy. The pre-treatment growth parameters are identical to those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g002" target="_blank">Figure 2</a>, and also and , lastly we set . In panel <b>a,</b> we set for <i>i</i> = 0,1,2, and <i>u</i> = 5×10⁻⁹. The parameter varies along the x-axis and we consider three different values of <i>γ</i>. In panel <b>b</b>, we set for <i>i</i> = 0,1,2, and <i>γ</i> = 10⁻⁴. The parameter varies along the x-axis and we consider three different values of <i>u</i>. In panel <b>c</b>, we set for <i>i</i> = 1,2, <i>u</i> = 10⁻⁷, , vary along the x-axis and consider three different values of <i>γ</i>. In panel <b>d</b>, we set for <i>i</i> = 1,2, <i>γ</i> = 10⁻⁴, , vary along the x-axis and consider three different values of <i>u</i>.</p

The relationship between dedifferentiation rate and pre-existing resistance.

<p>Panel <b>a</b> considers the probability of pre-existing resistance versus the dedifferentiation rate <i>γ</i> for several mutation rates. We use the same pre-treatment growth rates as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g002" target="_blank"><b>Figure 2</b></a> and the same growth rates for the resistant cells as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g004" target="_blank"><b>Figure 4</b></a>, and evolve the system until the tumor population hits size 10¹² and then evaluate the probability of resistance at that time. Panel <b>b</b> plots the response of a tumor population to a drug, assuming that pre-existing resistant population of cells is present at beginning of treatment. The sensitive cells have the same growth rate as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g002" target="_blank"><b>Figure 2</b></a>, and the resistant cell have the same growth rates as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g004" target="_blank"><b>Figure 4</b></a><b>.</b></p

The effect of the dedifferentiation rate on differentiated cancer cells during pulsatile therapy.

<p>The figure shows the dynamics of differentiated cancer cells in response to a treatment strategy in which the drug is administered for 30 days, followed by a treatment holiday of 30 days during each pulse. Panel <b>a</b> shows the effects of a drug which inhibits cancer stem cell proliferation and their differentiation to progenitors, while panel <b>b</b> demonstrates the effects of a drug which additionally inhibits the production of differentiated cancer cells from progenitors. Parameters are for <i>i</i> = 0,1,2, , , and in (<b>a</b>) and in (<b>b</b>). For both panels, the off-treatment parameters are identical to those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014366#pone-0014366-g002" target="_blank">Figure 2</a>.</p

Antigen Presentation Pathway is Active in Tumor-associated Astrocytes.

<p>© 2000–2010 Ingenuity Systems, Inc. All rights reserved.</p><p>Ingenuity Pathway Analysis of genes significantly increased more than four-fold in low-grade glioma- and glioblastoma-associated astrocytes indicates the pathways that are significantly increased in TAAs relative to normal astrocytes. The top ten canonical pathways represented on the array are shown in the table. The Antigen Presentation Pathway is most represented within this gene set.</p

A Small Group of Genes are Expressed Only in GBM-associated Astrocytes.

<p>A list of the genes expressed at higher levels in GBM-associated astrocytes when compared to low-grade-associated astrocytes. Genes are in order of the difference of expression between GBM-associated and low grade-associated-astrocytes. CD44 and TNC are each represented twice on the list. Osteopontin, which is at the top of the list, is a ligand for the CD44 receptor.</p

Temporal sequence of somatic mutations in all samples.

<p>Each arrow indicates the order in which the two alterations arise. <b>A</b>) Map of the temporal order of all CNAs determined using pairwise RESIC analyses. The first number represents the frequency with which the displayed temporal sequence occurs. The second number represents the percent of all bootstrap iterations in which the order determined acts as the dominant temporal sequence. <b>B</b>) Map of all CNAs made using three-mutation RESIC analyses. We tested the effects of including additional mutations in RESIC analyses by first testing the addition of a single mutation independently to each analysis. Investigation of further additions of mutations would require more samples; furthermore, we would expect any epistatic effects on the order of mutations to show some level of effect from each gene independently. Arrows in black are significant orderings, confirmed in at least 80% of the bootstrap iterations. Gold arrows are orderings found significant by three-way interactions, but not by pairwise interactions. Thickness of lines denotes the number of interactions that maintained the ordering. Since multiple three-gene analyses correspond to some arrows, the specific frequencies of orderings and the number of bootstrap iterations are not displayed, although included in the Supplementary Information. The results of using two mutations per RESIC analysis (A) do not differ significantly from the three mutation results (B). In no case is an order determined to be significant in pairwise analyses later found to be reversed in three way analyses. Additionally, we found that most results are stable (confirmed in three-way analyses) as long as the most likely evolutionary path through the mutational network comprises at least 58% of the flow. With the exception of the placement of PTEN of the AKT/PIK3C1 pathway, many of the orderings determined at the pathway level are robust at the gene level.</p