Topology of protein interaction network shapes protein abundances and strengths of their functional and nonspecific interactions

Abstract

How do living cells achieve sufficient abundances of functional protein complexes while minimizing promiscuous nonfunctional interactions? Here we study this problem using a first-principle model of the cell whose phenotypic traits are directly determined from its genome through biophysical properties of protein structures and binding interactions in a crowded cellular environment. The model cell includes three independent prototypical pathways, whose topologies of protein-protein interaction (PPI) subnetworks are different, but whose contributions to the cell fitness are equal. Model cells evolve through genotypic mutations and phenotypic protein copy number variations. We found a strong relationship between evolved physical-chemical properties of protein interactions and their abundances due to a "frustration" effect: Strengthening of functional interactions brings about hydrophobic interfaces, which make proteins prone to promiscuous binding. The balancing act is achieved by lowering concentrations of hub proteins while raising solubilities and abundances of functional monomers. On the basis of these principles we generated and analyzed a possible realization of the proteome-wide PPI network in yeast. In this simulation we found that high-throughput affinity capture-mass spectroscopy experiments can detect functional interactions with high fidelity only for high-abundance proteins while missing most interactions for low-abundance proteins.

Fig. 1.

A schematic diagram of the model cell. (A) A model cell consists of six cell division controlling genes (CDCG) that are expressed into multiple copies of proteins. The CDCGs constitute three independent pathways with different PPI network topologies. The first protein functions in a free state (monomer, green cubes). The second and third proteins exclusively form a functional heterodimer (stable pair) (red), but the fourth, fifth, and sixth proteins circularly establish three functional heterodimers. (date triangle, blue). (B) Within a cell, proteins can stay as monomers or form dimers, whose concentrations are determined by interaction energies among them through the law of mass action equations (Eqs. S4 and S5). The cubes colored as in A represent CDC proteins in their functional states that contribute to an organism's fitness (growth rate) according to Eq. 3. Gray cubes represent proteins in their nonfunctional states.

Fig. 2.

Evolution of protein abundances and PPIs after several rounds of preequilibration (Fig. S1). Green curves correspond to a functional monomer, the red curve is the average over two proteins forming a stable pair heterodimer (k = 1), and the blue curve corresponds to the average over three date triangle proteins (k = 2). (A) Mean concentration of each protein, C_i. (B) The fraction of protein material that is sequestered in nonfunctional interactions, ns_i. (C) The strength of PPI in the functional complex, P_int, except the first protein that does not form any functional complex. All curves are ensemble averaged over 200 independent simulation runs.

Fig. 3.

Scatter plot between amino acid propensities on functional interfaces of model and real proteins. We calculated the propensities for all model proteins from protein orthologs from 152 representative strains as described in Eq. S6. The propensities for real proteins are obtained from table 2 of ref. . The color scheme is as follows: black, hydrophobic; red, positively charged; blue, negatively charged; cyan, uncharged polar; and green, remaining amino acids.

Fig. 4.

The node degree in the functional PPI network and the strength of PNF-PPI negatively correlate with protein abundance. Both the average degree in the functional PPI network (A) and the dissociation constants of PNF-PPI complexes, , which are inversely proportional to the strength of PNF-PPI (B), are plotted as a function of protein abundance,C_i.

Fig. 5.

System-wide proteomics simulation of PPI detection and comparison with AC-MS high-throughput experiments. (A) Simulated AC-MS type of experiment in our model. We “designed” a set of 6,228 functional interactions among 3,868 proteins and assigned dissociation constants to all PPIs as described in Eqs. 5 and 6. The blue dashed line represents the average node degree of designed true PPIs and black and red solid lines correspond to the node degrees of captured PPI networks in our proteomics model at different values of the detection threshold. (B) The fractions of functional PPIs of all captured PPIs in our simulation at low (black) and high (red) thresholds are plotted as a function of protein abundance. (C) The fraction of detected PNF-PPIs of all captured PPIs. (D) The average degree of a protein in the S. cerevisiae PPI network vs. protein abundance. Black symbols correspond to all ∼28,800 AC-MS–labeled interactions in the BioGRID database, whereas red symbols correspond to ∼2,600 highly reproducible interactions confirmed in three or more independent experiments.