Statistical physics of interacting proteins: impact of dataset size and quality assessed in synthetic sequences

Abstract

Identifying protein-protein interactions is crucial for a systems-level understanding of the cell. Recently, algorithms based on inverse statistical physics, e.g. Direct Coupling Analysis (DCA), have allowed to use evolutionarily related sequences to address two conceptually related inference tasks: finding pairs of interacting proteins, and identifying pairs of residues which form contacts between interacting proteins. Here we address two underlying questions: How are the performances of both inference tasks related? How does performance depend on dataset size and the quality? To this end, we formalize both tasks using Ising models defined over stochastic block models, with individual blocks representing single proteins, and inter-block couplings protein-protein interactions; controlled synthetic sequence data are generated by Monte-Carlo simulations. We show that DCA is able to address both inference tasks accurately when sufficiently large training sets of known interaction partners are available, and that an iterative pairing algorithm (IPA) allows to make predictions even without a training set. Noise in the training data deteriorates performance. In both tasks we find a quadratic scaling relating dataset quality and size that is consistent with noise adding in square-root fashion and signal adding linearly when increasing the dataset. This implies that it is generally good to incorporate more data even if its quality is imperfect, thereby shedding light on the empirically observed performance of DCA applied to natural protein sequences.

Impact of phylogeny on structural contact inference from protein sequence data

“…Figure 3 shows the performance of contact prediction versus T for equilibrium sequences (no phylogeny), and for sequences generated with μ = 15 and μ = 5. At equilibrium, our model possesses a ferromagnetic–paramagnetic phase transition, whose approximate temperature T C = 4.2 was found by inspecting magnetization histograms [38]. For equilibrium sequences at low T , inference performance without APC is poor (figure 3, left panel), and DCA methods perform substantially better than local methods (which are overlapping).…”

Impact of phylogeny on structural contact inference from protein sequence data

“…Figure 3 shows the performance of contact prediction versus T for equilibrium sequences (no phylogeny), and for sequences generated with µ = 15 and µ = 5. At equilibrium, our model possesses a ferromagnetic-paramagnetic phase transition, whose approximate temperature T C = 4.2 was found by inspecting magnetisation histograms [31]. For equilibrium sequences at low T , inference performance without APC is poor (Figure 3, left panel), and DCA methods perform substantially better than local methods (which are overlapping).…”

“…These trends are consistent with those previously described in Refs. [1, 31]. Inference is difficult either if sequences are all frozen and redundant (very small T ) or if sequences are too noisy (very large T ), yielding better performance for intermediate values of T .…”

“…These trends are consistent with those previously described in Refs. [1, 38], which analysed synthetic data generated independently at equilibrium, i.e. without phylogeny.…”

Inter-protein residue covariation information unravels physically interacting protein dimers

“…In literature, the problem of hybrid PPI inference approaches has thus far been presented in two different concepts [21,22]. Some of those approaches explore the interaction between specific protein partners inside a paired MSA [23][24][25][26][27][28][29][30] whereas a handful of others assess the possibility of interaction between protein families [31][32][33].…”