Evolutionary pressure on the topology of protein interface interaction networks

Thermodynamics and Free Energy Landscape of BAR-Domain Dimerization from Molecular Simulations

Proteins with BAR domains function to bind to and remodel biological membranes, where the dimerization of BAR domains is a key step in this function. These domains can dimerize in solution or after localizing to the membrane surface. Here, we characterize the binding thermodynamics of homodimerization between the LSP1 BAR domain proteins in solution, using molecular dynamics (MD) simulations. By combining the MARTINI coarse-grained protein models with enhanced sampling through metadynamics, we construct a two-dimensional free energy surface quantifying the bound versus unbound ensembles as a function of two distance variables. With this methodology, our simulations can simultaneously characterize the structures and relative stabilities of a range of sampled dimers, portraying a heterogeneous and extraordinarily stable bound ensemble, where the proper crystal structure dimer is the most stable in a 100 mM NaCl solution. Nonspecific dimers that are sampled involve contacts that are consistent with experimental structures of higher-order oligomers formed by the LSP1 BAR domain. Because the BAR dimers and oligomers can assemble on membranes, we characterize the relative alignment of the known membrane binding patches, finding that only the specific dimer is aligned to form strong interactions with the membrane. Hence, we would predict a strong selection of the specific dimer in binding to or assembling when on the membrane. Establishing the pairwise stabilities of homodimer contacts is difficult experimentally when the proteins form stable oligomers, but through the method used here, we can isolate these contacts, providing a foundation to study the same interactions on the membrane.

Quantifying Protein-Protein Interactions in Molecular Simulations

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B₂. As a measure of nonspecific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid–liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B₂ from insertion and removal energies by applying Bennett’s acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K_d and B₂ allow us to separate out the contributions of nonbinding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K_d and B₂ calculations make them well suited for high-throughput studies of large interactomes.

Hidden long evolutionary memory in a model biochemical network

We introduce a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. Starting with a functional core module, random evolutionary drift increases network complexity even in the absence of specific selective pressures. Surprisingly, we uncover a hidden order in sequence space that gives rise to long-term evolutionary memory, implying strong constraints on network evolution due to the topology of accessible sequence space.

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

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.

Protein copy numbers are often found to be stoichiometrically balanced for subunits of multi-protein complexes. Imbalance is believed to be deleterious because it lowers complex yield (the dosage balance hypothesis) and increases the risk of misinteractions, but imbalance may also provide unexplored functional benefits. We show here that the benefits of stoichiometric balance can extend to larger networks of interacting proteins. We develop a method to quantify to what degree protein networks are balanced, and apply it to two networks. We find that the clathrin-mediated endocytosis system in yeast is statistically balanced, but not perfectly so, and explore the consequences of imbalance in the form of misinteractions and endocytic function. We also show that biological networks are more robust to misinteractions than random networks when balanced, but are more sensitive to misinteractions under imbalance. This suggests evolutionary pressure for proteins to be balanced and that any conserved imbalance should occur for functional reasons. We explore one such reason in the form of bottlenecking the endocytosis process. Our method can be generalized to other networks and used to identify out-of-balance proteins. Our results provide insight into how network design, expression level regulation, and cell fitness are intertwined.

Protein-protein binding selectivity and network topology constrain global and local properties of interface binding networks

Protein-protein interactions networks (PPINs) are known to share a highly conserved structure across all organisms. What is poorly understood, however, is the structure of the child interface interaction networks (IINs), which map the binding sites proteins use for each interaction. In this study we analyze four independently constructed IINs from yeast and humans and find a conserved structure of these networks with a unique topology distinct from the parent PPIN. Using an IIN sampling algorithm and a fitness function trained on the manually curated PPINs, we show that IIN topology can be mostly explained as a balance between limits on interface diversity and a need for physico-chemical binding complementarity. This complementarity must be optimized both for functional interactions and against mis-interactions, and this selectivity is encoded in the IIN motifs. To test whether the parent PPIN shapes IINs, we compared optimal IINs in biological PPINs versus random PPINs. We found that the hubs in biological networks allow for selective binding with minimal interfaces, suggesting that binding specificity is an additional pressure for a scale-free-like PPIN. We confirm through phylogenetic analysis that hub interfaces are strongly conserved and rewiring of interactions between proteins involved in endocytosis preserves interface binding selectivity.