16 research outputs found

### Variability of population is influenced by both the magnitude and auto-correlation properties of noise.

<p>Time evolution of <i>P</i>(<i>C</i><sub><i>l</i></sub>, <i>t</i>) shown at <i>t</i> = 0.001 + 0.4<i>n</i> (<i>n</i> = 0, 1, 2, â€¦10) for <i>C</i><sub>0</sub> = 1. <i>Ï„</i><sub><i>c</i></sub> = 0.01 and <i>D</i> = 100 in panel (A); <i>Ï„</i><sub><i>c</i></sub> = 1 and <i>D</i> = 1 in panel (B); <i>Ï„</i><sub><i>c</i></sub> = 0.01 and <i>D</i> = 1 in panel (C). Time increases from narrower to wider distributions in each panel.</p

### <i>P</i>(<i>C</i><sub><i>n</i></sub>, <i>t</i>) converges on a stationary distribution.

<p><i>P</i>(<i>C</i><sub><i>n</i></sub>, <i>t</i>) for <i>C</i><sub>0</sub> = 1 and <i>t</i> = 0.001 + 0.4<i>n</i> where <i>n</i> = 0, 1, 2, 3, â€¦10 for the parameter values of <i>Î³</i> = 1, <i>Ïµ</i> = 0.5, <i>Î²</i> = 500 [panel (A)]; <i>Î³</i> = 1, <i>Ïµ</i> = 0.5, <i>Î²</i> = 50 [panel (B)]; <i>Î³</i> = 0.5, <i>Ïµ</i> = 0.5, <i>Î²</i> = 5 [panel (C)]. The initial PDF <i>P</i>(<i>C</i><sub>0</sub>, 0) = <i>Î´</i>(<i>C</i><sub>0</sub> âˆ’ 1) is shown in a vertical dotted line; the stationary PDF at <i>t</i> = 4 is shown in a thick solid line in panels (A)-(C). Stationary PDFs in panels (A)-(C) are superimposed in panel (D).</p

### Evolution under noisy selection regimes.

<p>Initial distributions (solid line) and fitness functions (dotted line) are plotted for various selection regimes. Panel (A) is representative of a directed (positive) selection regime, panel (B) is representative of a stabilizing selection regime, while panel (C) is representative of a selection regime representative of therapeutic treatment.</p

### High- and low-<i>Î²</i> limits for âŸ¨<i>C</i><sub><i>n</i></sub>âŸ©.

<p>Various trajectories for âŸ¨<i>C</i><sub><i>n</i></sub>âŸ© for increasing <i>Ïµ</i>/<i>Î·</i> plotted for various <i>Î²</i> at <i>Î³</i> = 0.5. Shown are <i>Î²</i> values where <i>Î²</i> = 10<sup><i>n</i></sup> (<i>n</i> = âˆ’0.5, 0, 0.5, â€¦, 2.0). Trajectories of âŸ¨<i>C</i><sub><i>n</i></sub>âŸ© approach a limit as <i>Î²</i> increases from small <i>Î²</i> = 10<sup>âˆ’0.5</sup> (long dashes) to large <i>Î²</i> = 10<sup>2</sup> (right-most solid).</p

### Growth rate variability of <i>C</i><sub><i>n</i></sub>.

<p>Local growth rates of <i>Ï‡</i>(<i>C</i><sub><i>n</i></sub>, <i>t</i>) corresponding to the three cases in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132397#pone.0132397.g002" target="_blank">Fig 2(A), 2(B) and 2(C)</a> shown in solid, dotted and dashed lines, respectively. Negative growth rates are not shown in panel (A)-(C). <i>Ï‡</i>(<i>C</i><sub><i>n</i></sub>, <i>t</i>) at <i>t</i> = 0.8 in panel (A), (B), and (C) are plotted together in panel (D).</p

### The time evolution of âŒ©<i>C</i><sub><i>n</i></sub>âŒª.

<p>Time evolution of âŒ©<i>C</i><sub><i>n</i></sub>âŒª corresponding to the three cases in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132397#pone.0132397.g002" target="_blank">Fig 2(A), 2(B) and 2(C)</a> shown in solid, dotted and dashed lines, respectively.</p

### The BPMS is prognostic for metastasis-free survival of breast cancer patients with tumors of the basal subtype.

<p>PAM50 was used to categorize breast tumors into (<b>A</b>) Basal (16 BPMS+ patients out of 120 Basal patients, Ï‡<sup>2</sup>â€Š=â€Š13.7), (<b>B</b>) luminal A (0 BPMS+ patients out of 110 luminal A patients), (<b>C</b>) luminal B (1 BPMS+ patient out of 97 luminal B patients, Ï‡<sup>2</sup>â€Š=â€Š0.5), (<b>D</b>) HER2 (4 BPMS+ patients out of 67 HER2 patients, Ï‡<sup>2</sup>â€Š=â€Š0) and (<b>E</b>) normal (3 BPMS+ patients out of 48 Normal patients, Ï‡<sup>2</sup>â€Š=â€Š0.8) subtypes as indicated. BrCa443 patients were stratified for MFS using the BPMS. Red indicates patient tumors that express the BPMS signature while black indicates patient tumors that do not. Survival curves were generated by Kaplanâ€“Meier analysis, and the indicated P-values were calculated by the log-rank test.</p

### The BPMS is prognostic for metastasis-free survival of TNBC patients.

<p>The proliferation signature was used to categorize breast tumors into (<b>A</b>) ER-HER2- (15 BPMS+ patients out of 121 ER-HER- patients, Ï‡<sup>2</sup>â€Š=â€Š10.5), (<b>B</b>) TNBC (18 BPMS+ patients out of 118 TNBC patients, Ï‡<sup>2</sup>â€Š=â€Š9.4), (<b>C</b>) ER+HER2- (nâ€Š=â€Š1), and (<b>D</b>) HER2+ (8 BPMS+ patients out of 117 HER2 patients, Ï‡<sup>2</sup>â€Š=â€Š0). BrCa443 patients were stratified for MFS using the BPMS. Red indicates patient tumors that express the BPMS signature while black indicates patient tumors that do not. Survival curves were generated by Kaplanâ€“Meier analysis, and the indicated P-values were calculated by the log-rank test.</p

### Gene targets comprising the <i>let</i>-7 meta-gene (left) and BACH1 meta-gene (right).

<p>Gene targets comprising the <i>let</i>-7 meta-gene (left) and BACH1 meta-gene (right).</p

### The BPMS is a single patient predictor.

<p>Using frozen RMA pre-processed data, the BPMS was trained to be applied on a patient-to-patient basis. The BrCa871 set was processed using fRMA, divided into the BrCa436-Train and BrCa435-CV sets and 7,500 potential solutions were optimized. Using a cross-validation strategy, a final set of BPMS parameters were trained for fRMA processed data. Shown is the application of these parameters to the fRMA processed BrCa341 data set.</p