A statistically rigorous method for determining antigenic switching networks

Abstract

Many vector-borne pathogens rely on antigenic variation to prolong infections and increase their likelihood of onward transmission. This immune evasion strategy often involves mutually exclusive switching between members of gene families that encode functionally similar but antigenically different variants during the course of a single infection. Studies of different pathogens have suggested that switching between variant genes is non-random and that genes have intrinsic probabilities of being activated or silenced. These factors could create a hierarchy of gene expression with important implications for both infection dynamics and the acquisition of protective immunity. Inferring complete switching networks from gene transcription data is problematic, however, because of the high dimensionality of the system and uncertainty in the data. Here we present a statistically rigorous method for analysing temporal gene transcription data to reconstruct an underlying switching network. Using artificially generated transcription profiles together with in vitro var gene transcript data from two Plasmodium falciparum laboratory strains, we show that instead of relying on data from long-term parasite cultures, accuracy can be greatly improved by using transcription time courses of several parasite populations from the same isolate, each starting with different variant distributions. The method further provides explicit indications about the reliability of the resulting networks and can thus be used to test competing hypotheses with regards to the underlying switching pathways. Our results demonstrate that antigenic switch pathways can be determined reliably from short gene transcription profiles assessing multiple time points, even when subject to moderate levels of experimental error. This should yield important new information about switching patterns in antigenically variable organisms and might help to shed light on the molecular basis of antigenic variation.

Figure 1. Target network and transcript data for initial testing.

Four switch networks of different complexities were considered for the initial testing and method calibration: (A) one-to-one (1∶1), (B) single-many-single (SMS), (C) lattice, and (D) uniform. The sizes of the discs in the switch matrices correspond to the transition biases from variant to variant , , and the sizes of the discs in the off-rate vectors are proportional to the per-generation de-activation rates, . The major switch pathways described by these matrices are highlighted in the middle column and the right column shows the proportional transcription levels of all 10 variants from point of cloning until 60 generations post cloning, taken at 20 generation intervals; the insets depict the proportional transcript levels of the 10 variants on a log scale at generations 20, 40 and 60, with each colour representing a different variant.

Figure 2. Resolved networks from a single time series.

Using simulated annealing the (A) 1∶1, (B) SMS and (D) uniform networks are resolved to up to four consecutive switches, although the complex lattice network (C) is less well described. The starter genes, which were assumed to be clonally transcribed at generation 0, are highlighted in red. The simulated time courses (right column) show a very good agreement between the target data and the transcription data resulting from the determined network.

Figure 3. Resolved networks from noisy data.

The accuracy in determining switch networks from single transcription time courses is significantly affected by the level of noise in the data (here ) and can lead to poorly resolved networks, as shown for both the (A) 1∶1 and (B) SMS pathways. (C) The error shows a linear correlation with the level of noise.

Figure 4. Resolved networks from multiple time series.

Transcription histories from eight different clones, each defined by a different starting gene (highlighted in red), were used to resolve four different switch pathways describing 1∶1, SMS, lattice and uniform networks (A–D, respectively). Without any noise, all matrices and off-rate vectors can be resolved to a high degree of accuracy, even for the non-starter genes (middle column). The use of multiple data sets also yields better estimates when significant levels of noise are added to the data (, right column).

Figure 5. Resolved transcription time courses from noisy data.

When the model is fitted to multiple data sets with different starting genes, the transcript levels of the predicted network (right column) are more similar to the noiseless data of the underlying network (left column) than to the noisy data used as input (middle column). Results are shown for two different clones of a 1∶1 switch network with transcript levels measured at generation 20 (blue), 30 (purple), 40 (green), 60 (light blue) and 80 (orange). The insets depict the proportional transcript levels of the 16 variants on a log scale at generations 20, 30, 40, 60 and 80, with each colour representing a different variant.

Figure 6. Using MCMC on noisy transcription data.

In the MCMC output for the four different switch pathways: 1∶1, SMS, lattice and uniform, (A–D, respectively), the parameter range for each switch bias and off-rate was divided into bins, represented by rings. If a large proportion of recorded solutions contained similar values for a parameter then the corresponding ring is coloured dark, indicating a high likelihood that the true parameter value lies within that range. The proportions were measured relative to a null distribution , which assumed that all solutions were equally likely to be accepted. The darkest colour corresponds to proportions that differed from the mean by at least 25 standard deviations.

Figure 7. Results following dimension reduction.

Left column: target parameters for the (A) 1∶1 and (B) SMS networks reduced from 60 to 16 genes. Right column: MCMC output after adding noise with . To perform the reduction, genes were ranked by their average transcription levels across all time points and all cultures in the data generated by the 60-dimensional matrix (after adding noise). The 16 most highly ranked genes were then selected and their data renormalised. The starter gene parameters are shown in red.

Figure 8. Results from experimental data.

Best-fit parameter estimates derived by simulated annealing (top row) and MCMC parameter distributions (bottom row) are shown for three sets of P. falciparum var gene transcription data previously analysed by Recker et al. . Each data set comprises a single time series of measurements from an initially clonal culture. The results are consistent with an SMS network structure although the MCMC output (right column) also indicates the likelihood of alternative pathways.