Stoichiometric balance of protein copy numbers is measurable and functionally significant in a protein-protein interaction network for yeast endocytosis

Abstract

Stoichiometric balance, or dosage balance, implies that proteins that are subunits of obligate complexes (e.g. the ribosome) should have copy numbers expressed to match their stoichiometry in that complex. Establishing balance (or imbalance) is an important tool for inferring subunit function and assembly bottlenecks. We show here that these correlations in protein copy numbers can extend beyond complex subunits to larger protein-protein interactions networks (PPIN) involving a range of reversible binding interactions. We develop a simple method for quantifying balance in any interface-resolved PPINs based on network structure and experimentally observed protein copy numbers. By analyzing such a network for the clathrin-mediated endocytosis (CME) system in yeast, we found that the real protein copy numbers were significantly more balanced in relation to their binding partners compared to randomly sampled sets of yeast copy numbers. The observed balance is not perfect, highlighting both under and overexpressed proteins. We evaluate the potential cost and benefits of imbalance using two criteria. First, a potential cost to imbalance is that 'leftover' proteins without remaining functional partners are free to misinteract. We systematically quantify how this misinteraction cost is most dangerous for strong-binding protein interactions and for network topologies observed in biological PPINs. Second, a more direct consequence of imbalance is that the formation of specific functional complexes depends on relative copy numbers. We therefore construct simple kinetic models of two sub-networks in the CME network to assess multi-protein assembly of the ARP2/3 complex and a minimal, nine-protein clathrin-coated vesicle forming module. We find that the observed, imperfectly balanced copy numbers are less effective than balanced copy numbers in producing fast and complete multi-protein assemblies. However, we speculate that strategic imbalance in the vesicle forming module allows cells to tune where endocytosis occurs, providing sensitive control over cargo uptake via clathrin-coated vesicles.

Fig 1. Clathrin-mediated endocytosis network in yeast.

(Left) Site graph for the protein-protein interaction network (N = 56, E = 186), displaying interfaces used for binding interactions. Interfaces are color-coded according to domain type, the most common being SH3 domains (orange), Proline-rich regions (pink), phosphosites (yellow), acidic domains (red), and multi-protein complex subunit interfaces (light green). (Right) The ARP2/3 complex, a subset of the larger CME network.

Fig 2. Examples of balanced vs unbalanced copy numbers, and optimal solutions found by our algorithm.

A) A network with balanced copy numbers has just enough proteins (blue numbers) to form the desired number of complexes (black numbers). B) The copy numbers are unbalanced because an excess of “B” proteins is leftover after all possible complexes form. C) Starting from the network of (B) and using its copy numbers as C₀, our algorithm ‘Stoichiometric Balance Optimization of Protein Networks’ (SBOPN) solves for a balanced set of interface copy numbers (green text) that both 1) optimizes distance of the balanced interface copy numbers to C₀ and 2) constrains all interfaces on the same protein to the same copy number. The parameter α controls which of the two constraints is weighted more strongly. A low α (lower solution) forces all interfaces to the same copies on a protein. Higher α (upper solution) allows interfaces to vary to solve for copy numbers closer to C_0, as seen for protein “C”. The protein copy number for “C” is calculated as the average over all its interface copy numbers.

Fig 3. Clathrin-mediated endocytosis proteins are balanced.

(A,B) Histograms for chi-square distance and Jensen-Shannon distance between the real protein copy numbers and their copy numbers after balancing. Compared to 5,000 sets of random sampled copy numbers, the real copy numbers had a statistically significant Jensen-Shannon distance, but not chi-square distance. (C) Graph of CME network, showing which proteins were overexpressed (red) or underexpressed (blue) compared to the balanced copy numbers. Cofilin was highly overexpressed, which led to a high chi-square distance. (D) Histogram for chi-square distance when cofilin was removed from the network. It is now statistically significant, indicating that the other 55 proteins are balanced compared to random copy numbers. (E) The five most underexpressed proteins were two kinases (PRK1 and ARK1), one phosphatase (APP1), and two partners of Actin (AIP1 and YSC84). The former three bind transiently to their partners, so there is no functional need for them to be balanced. The latter two are discussed in the text.

Fig 4. Misinteractions in network motifs from biological IINs.

(A) Five network motifs that have been shown to impact specificity of binding in biological IINs were tested for the effects of imbalance on misinteractions. (B) Surface plot obtained for the triangle network. The z-axis is the frequency of misinteractions at steady-state (Eq 1) averaged across 1000 runs. The x and y axes are the number of B and C proteins; the number of A proteins is fixed at 50. As one protein becomes overexpressed, misinteractions increase exponentially.

Fig 5. Misinteractions are motif dependent only when concentrations are imbalanced.

(A) At balanced concentrations, misinteraction frequency increased linearly with the ratio of K_D,specific to K_{D, nonspecific}. It was also roughly equal for all five network motifs. (B) At unbalanced concentrations, misinteractions can occur even at a large energy gap (low K_D ratio), unless the overall binding is weak (i.e. red curve). (C) Surface plot for the square network, measuring the ratio of (#nonspecific complexes: #specific complexes + free proteins) when A1 and A2 are fixed while B1 and B2 are varied. The principal component (black line) is shown across the region of lowest misinteraction frequency. (D) Cost sensitivity to concentration imbalance varies significantly between motifs. The “distance” is measured along the principal component of the surface plots as you move away from the optimal region. Two different pairs of fixed proteins were analyzed for the chain and flag networks. The hub and square networks were the most sensitive to imbalance, while the flag and triangle were the least.

Fig 6. Biological IIN topologies have more misinteractions under imbalance.

Shown are trends in misinteraction frequency under balanced concentrations (blue arrows) and sensitivity to imbalance (red arrows). Several features that make networks perform better under balanced concentrations make them perform worse under unbalanced concentrations: sparseness, a topology that matches with real interface networks, and a power-law degree distribution. Strong average binding caused both increased misinteractions and increased sensitivity.

Fig 7. Clathrin membrane recruitment model.

(A) In clathrin-mediated endocytosis, adaptor proteins bind to the lipid membrane and recruit clathrin triskelia to the surface. These triskelia assemble a hexagonal cage around the plasma membrane vesicle. (B) Binding model of the clathrin module. Included are seven adaptor or accessory proteins (SYP1, EDE1, YAP1801/2, ENT1/2, and SLA2), clathrin heavy chains already assumed to be in trimer form, and clathrin light chains. Five of the adaptor/accessory proteins can bind directly to the lipid membrane. Picture generated with Rulebender.

Fig 8. Vesicle formation is tunable with adaptor proteins.

(A) Vesicles were formed faster with balanced copy numbers, indicating that the biological copy numbers are not optimized for maximum vesicle formation. (B) Adaptor proteins in the network were underexpressed. Vesicle frequency could be increased by doubling their concentrations. (C,D) The system is sensitive to adaptor protein knockouts. Knocking out either SYP1 or ENT1/2 nearly halts vesicle formation. SYP1 and EDE1 appear to have an aggregating effect, allowing vesicles to form with less triskelia on the membrane.

Fig 9. Misinteractions interfere with clathrin recruitment.

(A) Adding misinteractions to the network decreased vesicle formation and (B) interferes with recruitment of triskelia to the membrane. This was caused by aggregates containing too many adaptor proteins, draining them from the cytoplasmic pool. (C) Average adaptor proteins in each vesicle. With strong misinteractions, vesicle aggregates contained many adaptors and incomplete triskelia.

Fig 10. Example network for constructing inputs to the SBOPN algorithm.

(A) This example PPIN with interfaces resolved has no nontrivial balanced solution when all constraints are applied. (B) The “A” and “H” matrices that are used as inputs for the SPOBN method are shown for the left network.