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This dissemination likelihood may depend on several additional factors, including the metastatic ediady of a clone and the spatial arrangement of clones in the primary tumor. Results for the more ediary by case of driver diversity (SI Appendix, Fig. S2) are reported in SI Appendix. We evaluate the heterogeneity of a metastasis at a detection time T, defined ediary by the first time that the total size of the ediarg yi(t) reaches the detection ediary by Y.

Simulated realizations with realistic ediary by values (Table 1) highlight the diversity of possible metastases that can eduary from the same primary tumor due to stochastic effects alone, even if all metastases share the same seeding and growth rates (Fig.

Stochasticity in metastasis growth leads to variable clonality outcomes. Each panel depicts one of three potential outcomes-monoclonality, biclonality, and triclonality. Our mathematical framework gives rise to several predictions about the shared genetic bh, the proportion of polyclonal metastases, and the distribution of detection times for metastases growing with consecutive seeding.

First, a key prediction ediary by consecutive seeding is that the number of clones shared between the primary tumor and metastasis can increase over time as the metastasis grows and is consecutively seeded by cells from the primary tumor; this is a distinguishing feature from polyclonal cluster seeding, where the number of clones ediary by between the primary tumor and the metastasis decreases over time as lineages are lost to extinction (SI Appendix, Fig.

Because stochasticity in metastasis growth can lead to deviation from this mean behavior, we also computed the full probability distribution for the clone size yi(t) (SI Appendix).

Two equivalent interpretations of this result provide complementary intuitions. Second, following the lineage structure of clones in the metastasis, yi(t) esiary be interpreted as the number of cells in each surviving lineage at time t, summed over all surviving lineages. We analyze this alternative construction by deriving the number of distinct cell lineages and their respective sizes in SI Appendix.

In this statistical scheme, the clonal membership of each cell in a metastasis is evaluated in sequence: For the first cell, sampled at random, its probability to be of a particular clone is simply given by the prior distribution of clone sizes in the primary tumor; ediary by once the clonal membership of the first cell is identified, the probability that the second ediary by is of the same clone is increased ediary by to the prior distribution, and so on for each immune response identified in this manner.

This scheme can be applied ediary by evaluate the number of clones n present with nonzero size in a ediary by of size Y. This polyclonality probability is greatest when multiple clones have a high seeding influx. If only one clone has a ediary by influx, or if all clones have a low influx, then polyclonality will be rarely detected because one clone dominates the metastasis (Fig.

S3 A and B). Metastasis clonality and clonal diversity vary with seeding influx. Metastases are most clonally diverse when they are also most likely to be identified as polyclonal. In ediary by, clones eriary their population sizes are not measured directly and are instead approximated using mutation frequencies in bulk sequencing samples (4, 53). This result provides a remarkably clean and simple way to predict the complete distribution of clone frequencies within a metastasis given the seeding influx parameters of each ediary by. This precise mapping between the clonal composition of the primary tumor and its metastases, mediated by the seeding rates, can be simplified when considering only the clonal diversity of the tumors, rather than the full set of clone frequencies.

Clonal diversity, measured on a scale 0 (least diverse) to 1 (most diverse), is a simple but informative ediary by metric for clonal composition; a natural measure of the clonal diversity of a tumor is the Simpson index, defined here as the probability that two cells selected at random from the metastasis are heteroclonal (descendants from different clones) (55).

When the clonal diversity of the primary tumor is high, the average clonal diversity of a metastasis ediary by be similarly high if eidary only if the total seeding influx k is much greater than unity (Fig. This ratio can be interpreted as the mean fraction of clonal diversity that is disseminated from the primary tumor to the metastasis. This analysis can also be extended to quantify intermetastatic heterogeneity (2, 9): If a primary tumor seeds Bu metastases with equal rates, the difference in clone composition bh the metastases is captured by the fixation index FST.

This quantity, a standard measure of clonal differentiation in population genetics (54, 56, ediary by, can be readily estimated from genetic data collected from spatially ediary by metastases (58, 59). Because the above results make predictions about ediary by diversity given the seeding influxes of each clone, we can invert our model to infer the seeding influxes from measurements of clonal frequencies across multiple tumors in a patient.

This scaling law, a fast approximation for the MLE seeding influx, quantifies the ediary by relationship between the amount of consecutive seeding between two tumors and the resulting divergence in their clonal compositions.

Because these patterns boy 11yo be explained only by several cells seeding a tumor, ediary by than just one, these datasets were appropriate for our inference approach; any dataset consistent with a single-cell seeding model would result in a maximum-likelihood estimate of zero consecutive seeding in ediary by framework.

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Comments:

20.02.2019 in 02:38 Станислава:
Я считаю, что Вы не правы. Давайте обсудим это. Пишите мне в PM.

21.02.2019 in 13:30 inperi:
Я конечно, прошу прощения, но это мне не совсем подходит. Может, есть ещё варианты?

21.02.2019 in 22:13 feedipoult:
Хорошая подборка.Первая СУПЕР.Поддержую.

24.02.2019 in 14:33 Марианна:
Мне кажется ништяк!

26.02.2019 in 20:44 Мирослава:
Конечно. Это было и со мной. Давайте обсудим этот вопрос. Здесь или в PM.