Robust protein protein interactions in crowded cellular environments

Abstract

The capacity of proteins to interact specifically with one another underlies our conceptual understanding of how living systems function. Systems-level study of specificity in protein-protein interactions is complicated by the fact that the cellular environment is crowded and heterogeneous; interaction pairs may exist at low relative concentrations and thus be presented with many more opportunities for promiscuous interactions compared with specific interaction possibilities. Here we address these questions by using a simple computational model that includes specifically designed interacting model proteins immersed in a mixture containing hundreds of different unrelated ones; all of them undergo simulated diffusion and interaction. We find that specific complexes are quite robust to interference from promiscuous interaction partners only in the range of temperatures T(design) > T > T(rand). At T > T(design), specific complexes become unstable, whereas at T < T(rand), formation of specific complexes is suppressed by promiscuous interactions. Specific interactions can form only if T(design) > T(rand). This condition requires an energy gap between binding energy in a specific complex and set of binding energies between randomly associating proteins, providing a general physical constraint on evolutionary selection or design of specific interacting protein interfaces. This work has implications for our understanding of how the protein repertoire functions and evolves within the context of cellular systems.

Fig. 1.

Time and temperature dependence of the A/B ensemble. (A) System energy (defined in Eq. 1) as a function of Monte Carlo step in the MCID algorithm. Each curve corresponds to a different temperature. We find that the system reaches apparent energetic equilibrium within ≈10⁶ steps even at the lowest temperature considered in this work (T = 0.1). At each temperature, the relaxation to equilibrium is approximately exponential. (B) The dependence of system energy on temperature shows an initial decrease in energy (corresponding to the melting of unfavorable complexes) followed by a region of low energy (corresponding to largely AB complexes, although with some AA and BB homodimers) and finally undergoing a sharp transition (corresponding to the melting of the AB complex). (C) The dependence of r (Eq. 2) on temperature mimics that of the energy dependence in B. At low temperatures, many complexes are not specific, whereas at intermediate temperatures, the system exhibits a greater fraction of specific interactions. That r has a maximum ≈0.5 is a consequence of the fact that AA and BB heterodimers are fairly stable at these temperatures, as mentioned above. The melting of the AB complex at high temperatures causes a sharp decrease in r as T increases.

Fig. 2.

Temperature dependence of random protein ensembles. (A) The melting transitions for two different heterogeneous random ensembles of proteins. In this case, the r term is not used to track the behavior of the system because none of the interactions are specific; the number of proteins that are in complexes overall is used as a measure of binding instead. This number decreases sharply with increasing temperature in this case, a behavior similar to that observed in Fig. 1 but with a much lower transition temperature. (B) Similar to A but using systems composed of 100 copies each of two randomly chosen proteins (rather than a fully heterogeneous set). The two curves correspond to different choices of these two random potential interaction partners. The transition temperatures in this case are intermediate between the case in Fig. 1 and that in A.

Fig. 3.

Competition between a heterogeneous random ensemble and designed interactions. (A) These results are taken from simulations run at T = 0.5, a temperature at which some of the random interactions are stable (see Fig. 2) but at which the energy of a pure A/B system is able to reach its minimum value (see Fig. 1B). The black circles correspond to the measure r defined in the text; this is the fraction of A/B proteins in the specific AB complex. The red squares represent the fraction of all proteins in the system that are in a complex of any type, and the blue diamonds represent the fraction of complexes in the system that contain a protein from the heterogeneous random set. Notice the linear decrease in r (i.e., the black curve) as the relative concentration of AB goes from 1 (corresponding 0 on the x axis) to 0 (which corresponds to 1 on the x axis). (B) Similar to A but with simulations run at T = 1, which is after the melting transition in the heterogeneous ensemble but before that of the pure A/B system. Note the robustness of specific interactions in this case compared with the linear decrease in the black curve in A. (C) Similar to A and B but at an even higher temperature of 1.5. The system in this case displays even greater robustness in interaction specificity than that in B.

Fig. 4.

Competition between a single polymer and designed interactions. (A) These results were obtained from simulations at T = 0.5, as in Fig. 3A. The black circles correspond to the measure r defined in the text; this is the fraction of A/B proteins in the specific AB complex. The red squares represent the fraction of all proteins in the system that are in a complex of any type, and the blue diamonds represent the fraction of complexes in the system that contain a protein from the random set. Note that the specific interaction is highly susceptible to competition from the random interaction in this case. (B) Similar to A but at T = 1.0. At this temperature, the specific ensemble shows a linear decrease in prevalence with increasing concentration of the random interacting partner rather than the robustness observed with the heterogeneous ensemble in Fig. 3B. (C) Similar to A but at T = 1.5. In this case, the specific interaction is robust to decreases in relative concentration as in Fig. 3C.