From evidence to inference: probing the evolution of protein interaction networks

Abstract

The evolutionary mechanisms by which protein interaction networks grow and change are beginning to be appreciated as a major factor shaping their present-day structures and properties. Starting with a consideration of the biases and errors inherent in our current views of these networks, we discuss the dangers of constructing evolutionary arguments from naïve analyses of network topology. We argue that progress in understanding the processes of network evolution is only possible when hypotheses are formulated as plausible evolutionary models and compared against the observed data within the framework of probabilistic modeling. The value of such models is expected to be greatly enhanced as they incorporate more of the details of the biophysical properties of interacting proteins, gene phylogeny, and measurement error and as more advanced methodologies emerge for model comparison and the inference of ancestral network states.

Figure 1. Evolutionary fates of a duplicated gene pair within a protein interaction network.

After a single gene duplication event, the two duplicate genes are thought to assume one of several fates (Conant and Wolfe, 2008): (a) The most likely outcome is that one gene will be silenced by pseudogenization; alternatively, if both genes are preserved, this may be (b) owing to selection for increased dosage (c) because they acquire complementary deleterious mutations in independent subfunctions such that both are required to produce the full set of ancestral function (subfunctionalization), or (d) because one gene may acquire a new function (neofunctionalization).

Figure 2. Three generative models of network evolution.

(a) In a preferential attachment step, a new node (green) is attached to one of the existing nodes with probability proportional to their degree. (b) In a single step of the duplication-divergence model, a parent node is randomly chosen and its edges are duplicated (blue). For each parental edge, the parental and duplicated ones are then lost with respective probabilities p and q, though at least one link is retained to all neighboring nodes. The parent node may be attached to its child with probability r (orange edge). (c) In the related model known as duplication-attachment, either of the duplicates may be attached to another existing node in the simulated network with probability s (purple edge).

Figure 3. Repeated simulations under qualitative models of network growth can provide a starting point to explore plausible genome-wide modes of network evolution.

Networks are grown to the number of known proteins of a given organism, and binary interaction data sets are subsequently obtained under explicit assumptions of measurement error (Wiuf and Ratmann, 2009). These simulations are compared to the observed data in terms of summary statistics, such as those in Box 2: for methods that help in choosing summaries, we refer to (Ratmann et al., 2007; Joyce and Marjoram, 2008). ABC under model uncertainty (Ratmann et al., 2009) provides a Bayesian framework for these comparisons, and enables the inference of posterior distributions of the model parameters and summary errors. Crucially, the latter may provide information on model adequacy and the interpretability of the model parameters.

Figure 4. Gene-species tree reconciliation (Durand et al., 2006) forms the basis for a more detailed approach to modeling network evolution of gene families, focusing on the reconstruction of ancestral network states (Dutkowski and Tiuryn, 2007; Pinney et al., 2007; Gibson and Goldberg, 2009b).

Using probabilistic models for both the evolution and measurement of the true unknown network, observed interaction data (boxes with dashed coloured borders) may be integrated across different species in a statistically coherent way, allowing the true states of both ancestral (boxes with solid black borders) and present-day networks (boxes with solid coloured borders) to be inferred.