Constraints imposed by non-functional protein–protein interactions on gene expression and proteome size

Jingshan Zhang¹, Sergei Maslov² & Eugene I Shakhnovich¹

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Synopsis

Most proteins need to bind their specific protein partners to properly perform their biological function. When proteins diffuse in crowded intracellular environments searching for these functional partners, they randomly encounter functionally unrelated proteins and form transient non-functional complexes. If too many protein types coexist in a cellular compartment, the waste of resource to such non-functional interactions would significantly impair the functions of proteins. We hypothesize that the need to reduce such inefficiency down to an acceptable level sets an upper limit to the proteome diversity.

Among the 4500 types of baker's yeast proteins simultaneously expressed under the log-growth conditions (Ghaemmaghami et al, 2003; Huh et al, 2003), about 1800 types are known to be co-localized in the cytoplasm (Huh et al, 2003). How much do non-functional interactions affect normal protein functioning in the cytoplasm and other compartments of yeast cells? To check our hypothesis, we sketch the phase diagram in Figure 3 and find that the cytoplasm, nucleus and mitochondria are all located near a special corner of the phase diagram. The shadowed region is a biologically problematic one in which the ability of proteins to form a sufficient number of functional specific complexes is significantly impaired. Namely, if the number m of protein types co-expressed and co-localized in a compartment was to increase considerably, the system would enter the shadowed undesirable region where a typical protein spends more time tied up inside non-functional complexes than in the functionally important ones. On the other hand, if the average concentration of individual proteins was to decrease, the system would once again enter the undesirable region where proteins spend most of their time in a monomeric, unbound state.

Figure 3

The phase diagram for baker's yeast. The area in shade is the 'dead zone'. Its boundaries, defined by Equations (13) and (15), are blurred to indicate they are crossover rather than sharp transitions. The colours indicate the average fraction of proteins tied up inside non-functional complexes in the yeast cytoplasm as defined in Equation (12). The white circle shows the and m for a group of proteins coexpressed and colocalized in the yeast cytoplasm, whereas the white star and cross represents these parameters for the cell nucleus and mitochondria.

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Although it is advantageous for compartments of a real cell to avoid the dangerous 'shadowed' region, why are they positioned close to the upper limit of m and the lower limit of ? First, we conjecture that, in general, the biological evolution pushes an organism towards higher protein diversity, as this allows the organism to perform a broader spectrum of functionally important tasks. This explains our observation that m is close to the upper limit. Secondly, given the value of m, the organism decreases all the way down to its lower bound to reduce the fraction of time proteins waste inside non-functional complexes. Our analysis shown in colour in Figure 3 indicates that a typical protein localized in yeast cytoplasm wastes 20% of the searching time tied up in non-functional complexes. Owing to the variation of concentrations and other parameters of individual proteins, for some proteins the fraction of time wasted searching for their specific partners is considerably larger. Thus, a substantial increase in could impair the temporal efficiency of biochemical processes.

The major quantities required to produce Figure 3 are the concentrations and subcellular localizations of individual proteins, as well as the typical binding (free) energy of their functional (specific) and non-functional (non-specific) interactions. For protein concentrations, we use the large-scale experimental data on expression levels and localizations of nearly all yeast proteins (Ghaemmaghami et al, 2003; Huh et al, 2003; Belle et al, 2006), and average compartment volumes reported by Visser et al (1995) and Jorgensen et al (2007). The median binding energy of specific interactions is taken from the PINT (Protein Interaction Thermodynamic) Database (Kumar and Gromiha, 2006). Binding energies of non-functional interactions are not readily available from the literature. To obtain a rough estimate, we adopt a simple model (Deeds et al, 2006), which assumes that the free energy of binding between two functionally unrelated proteins is given by a linear function of the Gaussian-distributed hydrophobic coverage of their surfaces. As large-scale yeast two-hybrid experiments check for interactions between all possible pairs of highly overexpressed bait-and-prey proteins, we expect relatively strong non-functional interactions to be amply represented among the results of such assays. Hence, the fraction of interacting pairs in large-scale yeast two-hybrid core data sets (Ito et al, 2001; Uetz et al, 2000), which report all PPIs with affinities of the order of K_d*1 M (Estojak et al, 1995) and stronger, allows us to estimate the typical strength of non-functional interactions and its distribution across the whole proteome.

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