Ensemble spaghetti plot view

Spaghetti plots have been traditionally used to visualize ensemble data; each single plot represents an individual ensemble member. Color-coding may also be used to differentiate members. In this work, we extend the spaghetti concept to specific simulations over time: by extension, each “ensemble” member represents the probability behavior at a particular time point. The horizontal axis represents the copy numbers of molecules, while the vertical axis represents the probability value. Thus, an individual plot describes the probability distribution over the states with the copy number from zero to the maximum copy number for that protein.

We use color to encode different species of proteins, and the intensity of the color to encode the probability distribution of the corresponding protein at different time steps. The plot intensity from lighter to darker represents the time from the beginning of the simulation to the end.

In our early prototyping stage a third dimension was used to encode time, in the style of space-time cube representations [28]. In practice, however, the encoding suffered from occlusions which made difficult the tracking of temporal peak changes, and was later discarded. The domain experts specifically stated that the 2D ensemble spaghetti plots yielded better performance than the cube representations.

In Fig. ​Fig.22 (top), the Protein A of spaghetti plots represents the temporal probability distribution of protein A. In this representation, the peak changes can be easily tracked in terms of both peak location and value. We notice that protein A has only one peak, whose location shifts to the left in time towards the state with a lower copy number, and whose probability value increases over time. Protein B also has one peak, which stays at the same location without too much change in the probability value. Protein C has three peaks. The locations of these three peaks do not change over time. However, the probability value of one peak in the middle increases as the other one on the right decreases over time.

Spaghetti Plots (top) show the probability distribution of each gene and the changes in distributions over time. The Spaghetti Plots view on the bottom displays the probability distribution of each gene at a user selected time step

In most cases, the peaks either increase or decrease over time, and thus do not cause overlaying or crossing issues. Rare plot overlays and crossings bear in fact meaning, by encoding frequent peak location changes (see Protein A in Fig. ​Fig.2)2) or peak changes in both directions (increasing and decreasing).

However, it is not easy to detect the probability distribution at a particular time step from the spaghetti plots. To this end, a checkbox filter allows the users to draw the plots at an interactively-selected time step. Figure ​Figure22 (bottom) displays the probability distributions of these three proteins at the 10th time step.