Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

What are the molecular determinants of protein–protein binding affinity and whether they are similar to those regulating fold stability are two major questions of molecular biology, whose answers bring important implications both from a theoretical and applicative point of view. Here, we analyze chemical and physical features on a large dataset of protein–protein complexes with reliable experimental binding affinity data and compare them with a set of monomeric proteins for which melting temperature data was available. In particular, we probed the spatial organization of protein (1) intramolecular and intermolecular interaction energies among residues, (2) amino acidic composition, and (3) their hydropathy features. Analyzing the interaction energies, we found that strong Coulombic interactions are preferentially associated with a high protein thermal stability, while strong intermolecular van der Waals energies correlate with stronger protein–protein binding affinity. Statistical analysis of amino acids abundances, exposed to the molecular surface and/or in interaction with the molecular partner, confirmed that hydrophobic residues present on the protein surfaces are preferentially located in the binding regions, while charged residues behave oppositely. Leveraging on the important role of van der Waals interface interactions in binding affinity, we focused on the molecular surfaces in the binding regions and evaluated their shape complementarity, decomposing the molecular patches in the 2D Zernike basis. For the first time, we quantified the correlation between local shape complementarity and binding affinity via the Zernike formalism. In addition, considering the solvent interactions via the residue hydropathy, we found that the hydrophobicity of the binding regions dictates their shape complementary as much as the correlation between van der Waals energy and binding affinity. In turn, these relationships pave the way to the fast and accurate prediction and design of optimal binding regions as the 2D Zernike formalism allows a rapid and superposition-free comparison between possible binding surfaces.

Understanding the molecular mechanisms of thermal stability is a challenge in protein biology. Indeed, knowing the temperature at which proteins are stable has important theoretical implications, which are intimately linked with properties of the native fold, and a wide range of potential applications from drug design to the optimization of enzyme activity. Here, we present a novel graph-theoretical framework to assess thermal stability based on the structure without any a priori information. In this approach we describe proteins as energy-weighted graphs and compare them using ensembles of interaction networks. Investigating the position of specific interactions within the 3D native structure, we developed a parameter-free network descriptor that permits to distinguish thermostable and mesostable proteins with an accuracy of 76% and area under the receiver operating characteristic curve of 78%. Code is available upon request to edoardo.milanetti@uniroma1.it Supplementary data are available at Bioinformatics online.

Understanding the mechanisms driving bio-molecules binding and determining the resulting complexes’ stability is fundamental for the prediction of binding regions, which is the starting point for drug-ability and design. Characteristics like the preferentially hydrophobic composition of the binding interfaces, the role of van der Waals interactions, and the consequent shape complementarity between the interacting molecular surfaces are well established. However, no consensus has yet been reached on the role of electrostatic. Here, we perform extensive analyses on a large dataset of protein complexes for which both experimental binding affinity and pH data were available. Probing the amino acid composition, the disposition of the charges, and the electrostatic potential they generated on the protein molecular surfaces, we found that (i) although different classes of dimers do not present marked differences in the amino acid composition and charges disposition in the binding region, (ii) homodimers with identical binding region show higher electrostatic compatibility with respect to both homodimers with non-identical binding region and heterodimers. Interestingly, (iii) shape and electrostatic complementarity, for patches defined on short-range interactions, behave oppositely when one stratifies the complexes by their binding affinity: complexes with higher binding affinity present high values of shape complementarity (the role of the Lennard-Jones potential predominates) while electrostatic tends to be randomly distributed. Conversely, complexes with low values of binding affinity exploit Coulombic complementarity to acquire specificity, suggesting that electrostatic complementarity may play a greater role in transient (or less stable) complexes. In light of these results, (iv) we provide a novel, fast, and efficient method, based on the 2D Zernike polynomial formalism, to measure electrostatic complementarity without the need of knowing the complex structure. Expanding the electrostatic potential on a basis of 2D orthogonal polynomials, we can discriminate between transient and permanent protein complexes with an AUC of the ROC of $$\sim$$∼ 0.8. Ultimately, our work helps shedding light on the non-trivial relationship between the hydrophobic and electrostatic contributions in the binding interfaces, thus favoring the development of new predictive methods for binding affinity characterization.

Despite the huge effort to contain the infection, the novel SARS-CoV-2 coronavirus has rapidly become pandemic, mainly due to its extremely high human-to-human transmission capability, and a surprisingly high viral charge of symptom-less people. While the seek for a vaccine is still ongoing, promising results have been obtained with antiviral compounds. In particular, lactoferrin is regarded to have beneficial effects both in preventing and soothing the infection. Here, we explore the possible molecular mechanisms with which lactoferrin interferes with SARS-CoV-2 cell invasion, preventing attachment and/or entry of the virus. To this aim, we search for possible interactions lactoferrin may have with virus structural proteins and host receptors. Representing the molecular iso-electron surface of proteins in terms of 2D-Zernike descriptors, we 1) identified putative regions on the lactoferrin surface able to bind sialic acid present on the host cell membrane, sheltering the cell from the virus attachment; 2) showed that no significant shape complementarity is present between lactoferrin and the ACE2 receptor, while 3) two high complementarity regions are found on the N- and C-terminal domains of the SARS-CoV-2 spike protein, hinting at a possible competition between lactoferrin and ACE2 for the binding to the spike protein.

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2Din-vitromodel of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.