AmplificationTimeR: an R package for timing sequential amplification events

Abstract

Motivation: Few methods exist for timing individual amplification events in regions of focal amplification. Current methods are also limited in the copy number states that they are able to time. Here we introduce AmplificationTimeR, a method for timing higher level copy number gains and inferring the most parsimonious order of events for regions that have undergone both single gains and whole genome duplication. Our method is an extension of established approaches for timing genomic gains.

Results: We can time more copy number states, and in states covered by other methods our results are comparable to previously published methods.

Availability and implementation: AmplificationTimer is freely available as an R package hosted at https://github.com/Wedge-lab/AmplificationTimeR.

Figure 1.

Principle behind timing amplifications. (A) A schematic representation of a single copy gain. Symbols represent point mutations occurring both before and after the depicted chromosomal gain. $t_0$ represents tumour initiation, $t_1$ or $t_{G1}$ represents the time of the first gain, and $t_S$ represents the time of tumour sampling. Mutations occurring before $t_1$ are duplicated, and thus present on two chromosome copies. Mutations occurring after $t_1$, or on the unaffected chromosome, are present on one chromosome copy. (B) A schematic representations of three scenarios ($S_1$, $S_2$, and $S_3$) leading to a copy number state of $4+2$ in a whole genome duplicated sample. W and G are used to refer to whole genome duplication (WGD) and gain, respectively. In $S_1$ a WGD event is followed by two sequential gains of the same chromosome, in which case mutations are expected to occur in all multiplicity states in the set $\{1,2,3,4\}$. However, if no mutations of multiplicity three are observed, this suggests that the order of events may be a single gain followed by a whole genome duplication ($S_3$), which can be timed, or a whole genome duplication followed by gains of two separate chromosomes ($S_2$), which cannot be timed. Red lines indicate gain or WGD events. Image created with BioRender.com.

Figure 2.

Comparison of first and second MYC gain ($t_1$ and $t_2$) in BRCA and OV cancers using available timing methods and mutation types. Point shapes indicate whether the timed gain was clonal or subclonal, and colour indicates the number of mutations used. Vertical bars represent the 95% confidence intervals provided by cancerTiming and MutationTimeR, whereas horizontal bars represent the 95% confidence intervals provided by AmplificationTimeR. “All mutations” represents timing estimates derived using all unfiltered mutations, “C > T at CpG” represents timing estimates calculated using only C > T mutations at CpG sites, and “SBS1 and SBS5” represents timing estimates generated using only mutations identified as belonging to mutational signatures SBS1 and SBS5. (A) First MYC gain in BRCA samples. (B) Second MYC gain in BRCA samples. (C) First MYC gain in OV samples. (D) Second MYC gain in OV samples.

Figure 3.

Average error rate of time points calculated from simulated data, expressed as a percentage. n = 100 randomly simulated sets of time points for each order, copy number state, and condition. Colour scales are capped at 100% error rate to allow better visualization of lower percentages. (A) Average error rate of calculated time points when varying the number of simulated mutations. (B) Average error rate of calculated time points when varying the proportion of clock-like mutations simulated.

Figure 4.

Spearman correlation between the simulated and calculated time for each time point when timed using all possible equations and event orders for timeable copy number states from 4 + 0 to 9 + 2 (A–F). Results for 10 + 0, 10 + 1, and 10 + 2 are shown in Supplementary Fig. S3. The trailing diagonal represents the correlation between time points calculated using the same order of events from which the data were simulated. n = 100 randomly simulated sets of time points for each order from which a set of 100 mutations was simulated for timing. Cell colours and numbers indicate the Spearman $\rho$. Cell borders indicate Benjamini–Hochberg adjusted P-values relative to an $\alpha$ of 0.05. Grey cells and cell borders indicate comparisons for which correlation could not be calculated due to differences in the number of time points available.

Figure 5.

Timing estimates for MYC gains in BRCA samples. Mutations attributed to mutational signatures SBS1 and SBS5 were used to time the gain of each segment. Each row represents one sample, indicated by the patient identifier starting with “DO,” followed by the order of events inferred by AmplificationTimeR. G represents gains, and W represents whole genome duplications.

Figure 6.

Comparison of timing estimates obtained using different mutation types for initial MYC gains or WGDs in BRCA (A–C) and OV (D–F) samples. The colour scheme indicates the ratio of the number of mutations used for each timing estimate (y/x). The mean difference in timing estimates and the results of paired Wilcoxon Rank Sum tests are listed in Supplementary Table S5 for each comparison.