Connected Component Analysis of Dynamical Perturbation Contact Networks.

Describing protein dynamical networks through amino acid contacts is a powerful way to analyze complex biomolecular systems. However, due to the size of the systems, identifying the relevant features of protein-weighted graphs can be a difficult task. To address this issue, we present the connected component analysis (CCA) approach that allows for fast, robust, and unbiased analysis of dynamical perturbation contact networks (DPCNs). We first illustrate the CCA method as applied to a prototypical allosteric enzyme, the imidazoleglycerol phosphate synthase (IGPS) enzyme from Thermotoga maritima bacteria. This approach was shown to outperform the clustering methods applied to DPCNs, which could not capture the propagation of the allosteric signal within the protein graph. On the other hand, CCA reduced the DPCN size, providing connected components that nicely describe the allosteric propagation of the signal from the effector to the active sites of the protein. By applying the CCA to the IGPS enzyme in different conditions, i.e., at high temperature and from another organism (yeast IGPS), and to a different enzyme, i.e., a protein kinase, we demonstrated how CCA of DPCNs is an effective and transferable tool that facilitates the analysis of protein-weighted networks.

metanetwork: A R package dedicated to handling and representing trophic metanetworks.

Trophic networks describe interactions between species at a given location and time. Due to environmental changes, anthropogenic perturbations or sampling effects, trophic networks may vary in space and time. The collection of network time series or networks in different sites thus constitutes a metanetwork. We present here the R package metanetwork, which will ease the representation, the exploration and analysis of trophic metanetwork data sets that are increasingly available. Our main methodological advance consists in suitable layout algorithm for trophic networks, which is based on trophic levels and dimension reduction in a graph diffusion kernel. In particular, it highlights relevant features of trophic networks (trophic levels, energetic channels). In addition, we developed tools to handle, compare visually and quantitatively and aggregate those networks. Static and dynamic visualisation functions have been developed to represent large networks. We apply our package workflow to several trophic network data sets.

Model biomolecular condensates have heterogeneous structure quantitatively dependent on the interaction profile of their constituent macromolecules.

Biomolecular condensates play numerous roles in cells by selectively concentrating client proteins while excluding others. These functions are likely to be sensitive to the spatial organization of the scaffold proteins forming the condensate. We use coarse-grained molecular simulations to show that model intrinsically-disordered proteins phase separate into a heterogeneous, structured fluid characterized by a well-defined length scale. The proteins are modelled as semi-flexible polymers with punctate, multifunctional binding sites in good solvent conditions. Their dense phase is highly solvated with a spatial structure that is more sensitive to the separation of the binding sites than their affinity. We introduce graph theoretic measures to quantify their heterogeneity, and find that it increases with increasing binding site number, and exhibits multi-timescale dynamics. The model proteins also swell on passing from the dilute solution to the dense phase. The simulations predict that the structure of the dense phase is modulated by the location and affinity of binding sites distant from the termini of the proteins, while sites near the termini more strongly affect its phase behaviour. The relations uncovered between the arrangement of weak interaction sites on disordered proteins and the material properties of their dense phase can be experimentally tested to give insight into the biophysical properties, pathological effects, and rational design of biomolecular condensates.

Singular Interface Dynamics of the SARS-CoV-2 Delta Variant Explained with Contact Perturbation Analysis.

Emerging SARS-CoV-2 variants raise concerns about our ability to withstand the Covid-19 pandemic, and therefore, understanding mechanistic differences of those variants is crucial. In this study, we investigate disparities between the SARS-CoV-2 wild type and five variants that emerged in late 2020, focusing on the structure and dynamics of the spike protein interface with the human angiotensin-converting enzyme 2 (ACE2) receptor, by using crystallographic structures and extended analysis of microsecond molecular dynamics simulations. Dihedral angle principal component analysis (PCA) showed the strong similarities in the spike receptor binding domain (RBD) dynamics of the Alpha, Beta, Gamma, and Delta variants, in contrast with those of WT and Epsilon. Dynamical perturbation networks and contact PCA identified the peculiar interface dynamics of the Delta variant, which cannot be directly imputable to its specific L452R and T478K mutations since those residues are not in direct contact with the human ACE2 receptor. Our outcome shows that in the Delta variant the L452R and T478K mutations act synergistically on neighboring residues to provoke drastic changes in the spike/ACE2 interface; thus a singular mechanism of action eventually explains why it dominated over preceding variants.

Elucidating the Activation Mechanism of AMPK by Direct Pan-Activator PF-739.

Adenosine monophosphate-activated protein kinase (AMPK) is a key energy sensor regulating the cell metabolism in response to energy supply and demand. The evolutionary adaptation of AMPK to different tissues is accomplished through the expression of distinct isoforms that can form up to 12 heterotrimeric complexes, which exhibit notable differences in the sensitivity to direct activators. To comprehend the molecular factors of the activation mechanism of AMPK, we have assessed the changes in the structural and dynamical properties of ß1- and ß2-containing AMPK complexes formed upon binding to the pan-activator PF-739. The analysis revealed the molecular basis of the PF-739-mediated activation of AMPK and enabled us to identify distinctive features that may justify the slightly higher affinity towards the ß1-isoform, such as the ß1-Asn111 to ß2-Asp111 substitution, which seems to be critical for modulating the dynamical sensitivity of ß1- and ß2 isoforms. The results are valuable in the design of selective activators to improve the tissue specificity of therapeutic treatment.

Mapping Function from Dynamics: Future Challenges for Network-Based Models of Protein Structures.

Proteins fulfill complex and diverse biological functions through the controlled atomic motions of their structures (functional dynamics). The protein composition is given by its amino-acid sequence, which was assumed to encode the function. However, the discovery of functional sequence variants proved that the functional encoding does not come down to the sequence, otherwise a change in the sequence would mean a change of function. Likewise, the discovery that function is fulfilled by a set of structures and not by a unique structure showed that the functional encoding does not come down to the structure either. That leaves us with the possibility that a set of atomic motions, achievable by different sequences and different structures, encodes a specific function. Thanks to the exponential growth in annual depositions in the Protein Data Bank of protein tridimensional structures at atomic resolutions, network models using the Cartesian coordinates of atoms of a protein structure as input have been used over 20 years to investigate protein features. Combining networks with experimental measures or with Molecular Dynamics (MD) simulations and using typical or ad-hoc network measures is well suited to decipher the link between protein dynamics and function. One perspective is to consider static structures alone as alternatives to address the question and find network measures relevant to dynamics that can be subsequently used for mining and classification of dynamic sequence changes functionally robust, adaptable or faulty. This way the set of dynamics that fulfill a function over a diversity of sequences and structures will be determined.

Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins.

In this chapter, we focus on topology measurements of the adjacent amino acid networks for a data set of oligomeric proteins and some of its subnetworks. The aim is to present many mathematical tools in order to understand the structures of proteins implicitly coded in such networks and subnetworks. We mainly investigate four important networks by computing the number of connected components, the degree distribution, and assortativity measures. We compare each result in order to prove that the four networks have quite independent topologies.

Exploring Allosteric Pathways of a V-Type Enzyme with Dynamical Perturbation Networks.

Elucidation of the allosteric pathways in proteins is a computational challenge that strongly benefits from combination of atomistic molecular dynamics (MD) simulations and coarse-grained analysis of the complex dynamical network of chemical interactions based on graph theory. Here, we introduce and assess the performances of the dynamical perturbation network analysis of allosteric pathways in a prototypical V-type allosteric enzyme. Dynamical atomic contacts obtained from MD simulations are used to weight the allosteric protein graph, which involves an extended network of contacts perturbed by the effector binding in the allosteric site. The outcome showed good agreement with previously reported theoretical and experimental extended studies and it provided recognition of new potential allosteric spots that can be exploited in future mutagenesis experiments. Overall, the dynamical perturbation network analysis proved to be a powerful computational tool, complementary to other network-based approaches that can assist the full exploitation of allosteric phenomena for advances in protein engineering and rational drug design.

In proteins, the structural responses of a position to mutation rely on the Goldilocks principle: not too many links, not too few.

A disease has distinct genetic and molecular hallmarks such as sequence variants that are likely to produce the alternative protein structures accountable for individual responses to drugs and disease development. Thus, to set up customized therapies, the structural influences of amino acids on one another need to be tracked down. Using network-based models and classical analysis of amino acid and atomic packing in protein structures, the influence of first shell neighbors on the structural fate of a position upon mutation, is revisited. Regardless of the type and position in a structure, amino acids satisfy on average over their neighbors, a low and similar number of atomic interactions, the average called the neighborhood watch (Nw). The structural tolerance of a position to mutation depends on the modulation of the composition and/or proximity of neighbors to maintain the same Nw, before and after mutation, at every position. Changes, upon mutation of the number of atomic interactions at the level of individual pairs (wij) are structurally tolerated but influence structural dynamics. Robust, fragile and rescue interactions can be identified with Nw and wij, offering a framework to classify sequence variants according to position-dependent structural changes.

Protein structural robustness to mutations: an in silico investigation.

Proteins possess qualities of robustness and adaptability to perturbations such as mutations, but occasionally fail to withstand them, resulting in loss of function. Herein, the structural impact of mutations is investigated independently of the functional impact. Primarily, we aim at understanding the mechanisms of structural robustness pre-requisite for functional integrity. The structural changes due to mutations propagate from the site of mutation to residues much more distant than typical scales of chemical interactions, following a cascade mechanism. This can trigger dramatic changes or subtle ones, consistent with a loss of function and disease or the emergence of new functions. Robustness is enhanced by changes producing alternative structures, in good agreement with the view that proteins are dynamic objects fulfilling their functions from a set of conformations. This result, robust alternative structures, is also coherent with epistasis or rescue mutations, or more generally, with non-additive mutational effects and compensatory mutations. To achieve this study, we developed the first algorithm, referred to as Amino Acid Rank (AAR), which follows the structural changes associated with mutations from the site of the mutation to the entire protein structure and quantifies the changes so that mutations can be ranked accordingly. Assessing the paths of changes opens the possibility of assuming secondary mutations for compensatory mechanisms.

From local to global changes in proteins: a network view.

To fulfill the biological activities in living organisms, proteins are endowed with dynamics, robustness and adaptability. The three properties co-exist because they allow global changes in structure to arise from local perturbations (dynamics). Robustness refers to the ability of the protein to incur such changes without suffering loss of function; adaptability is the emergence of a new biological activity. Since loss of function may jeopardize the survival of the organism and lead to disease, adaptability may occur through the combination of two local perturbations that together rescue the initial function. The review highlights the relevancy of computational network analysis to understand how a local change produces global changes.

Intermolecular ß-strand networks avoid hub residues and favor low interconnectedness: a potential protection mechanism against chain dissociation upon mutation.

Altogether few protein oligomers undergo a conformational transition to a state that impairs their function and leads to diseases. But when it happens, the consequences are not harmless and the so-called conformational diseases pose serious public health problems. Notorious examples are the Alzheimer's disease and some cancers associated with a conformational change of the amyloid precursor protein (APP) and of the p53 tumor suppressor, respectively. The transition is linked with the propensity of ß-strands to aggregate into amyloid fibers. Nevertheless, a huge number of protein oligomers associate chains via ß-strand interactions (intermolecular ß-strand interface) without ever evolving into fibers. We analyzed the layout of 1048 intermolecular ß-strand interfaces looking for features that could provide the ß-strands resistance to conformational transitions. The interfaces were reconstructed as networks with the residues as the nodes and the interactions between residues as the links. The networks followed an exponential decay degree distribution, implying an absence of hubs and nodes with few links. Such layout provides robustness to changes. Few links per nodes do not restrict the choices of amino acids capable of making an interface and maintain high sequence plasticity. Few links reduce the "bonding" cost of making an interface. Finally, few links moderate the vulnerability to amino acid mutation because it entails limited communication between the nodes. This confines the effects of a mutation to few residues instead of propagating them to many residues via hubs. We propose that intermolecular ß-strand interfaces are organized in networks that tolerate amino acid mutation to avoid chain dissociation, the first step towards fiber formation. This is tested by looking at the intermolecular ß-strand network of the p53 tetramer.

Beta-strand interfaces of non-dimeric protein oligomers are characterized by scattered charged residue patterns.

Protein oligomers are formed either permanently, transiently or even by default. The protein chains are associated through intermolecular interactions constituting the protein interface. The protein interfaces of 40 soluble protein oligomers of stœchiometries above two are investigated using a quantitative and qualitative methodology, which analyzes the x-ray structures of the protein oligomers and considers their interfaces as interaction networks. The protein oligomers of the dataset share the same geometry of interface, made by the association of two individual ß-strands (ß-interfaces), but are otherwise unrelated. The results show that the ß-interfaces are made of two interdigitated interaction networks. One of them involves interactions between main chain atoms (backbone network) while the other involves interactions between side chain and backbone atoms or between only side chain atoms (side chain network). Each one has its own characteristics which can be associated to a distinct role. The secondary structure of the ß-interfaces is implemented through the backbone networks which are enriched with the hydrophobic amino acids favored in intramolecular ß-sheets (MCWIV). The intermolecular specificity is provided by the side chain networks via positioning different types of charged residues at the extremities (arginine) and in the middle (glutamic acid and histidine) of the interface. Such charge distribution helps discriminating between sequences of intermolecular ß-strands, of intramolecular ß-strands and of ß-strands forming ß-amyloid fibers. This might open new venues for drug designs and predictive tool developments. Moreover, the ß-strands of the cholera toxin B subunit interface, when produced individually as synthetic peptides, are capable of inhibiting the assembly of the toxin into pentamers. Thus, their sequences contain the features necessary for a ß-interface formation. Such ß-strands could be considered as 'assemblons', independent associating units, by homology to the foldons (independent folding unit). Such property would be extremely valuable in term of assembly inhibitory drug development.