Intrinsic Localized Modes in Proteins

Einstein Model of a Graph to Characterize Protein Folded/Unfolded States

The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, we focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, we show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randić resistance, in terms of effective force constants of a linear chain. We derive an exact relation between the Kirchhoff index and the average shortest path length for a linear graph and define the free energies of a graph using an Einstein model. Second, we represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, we compute the topological descriptors and the graph free energies for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The present work shows that the local, nonlocal, and global force constants and free energies of a graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states.

Intrinsically disordered proteins: Ensembles at the limits of Anfinsen's dogma

Intrinsically disordered proteins (IDPs) are proteins that lack rigid 3D structure. Hence, they are often misconceived to present a challenge to Anfinsen's dogma. However, IDPs exist as ensembles that sample a quasi-continuum of rapidly interconverting conformations and, as such, may represent proteins at the extreme limit of the Anfinsen postulate. IDPs play important biological roles and are key components of the cellular protein interaction network (PIN). Many IDPs can interconvert between disordered and ordered states as they bind to appropriate partners. Conformational dynamics of IDPs contribute to conformational noise in the cell. Thus, the dysregulation of IDPs contributes to increased noise and "promiscuous" interactions. This leads to PIN rewiring to output an appropriate response underscoring the critical role of IDPs in cellular decision making. Nonetheless, IDPs are not easily tractable experimentally. Furthermore, in the absence of a reference conformation, discerning the energy landscape representation of the weakly funneled IDPs in terms of reaction coordinates is challenging. To understand conformational dynamics in real time and decipher how IDPs recognize multiple binding partners with high specificity, several sophisticated knowledge-based and physics-based in silico sampling techniques have been developed. Here, using specific examples, we highlight recent advances in energy landscape visualization and molecular dynamics simulations to discern conformational dynamics and discuss how the conformational preferences of IDPs modulate their function, especially in phenotypic switching. Finally, we discuss recent progress in identifying small molecules targeting IDPs underscoring the potential therapeutic value of IDPs. Understanding structure and function of IDPs can not only provide new insight on cellular decision making but may also help to refine and extend Anfinsen's structure/function paradigm.

New Insights into Folding, Misfolding, and Nonfolding Dynamics of a WW Domain

Intermediate states in protein folding are associated with formation of amyloid fibrils, which are responsible for a number of neurodegenerative diseases. Therefore, prevention of the aggregation of folding intermediates is one of the most important problems to overcome. Recently, we studied the origins and prevention of formation of intermediate states with the example of the Formin binding protein 28 (FBP28) WW domain. We demonstrated that the replacement of Leu26 by Asp26 or Trp26 (in ∼15% of the folding trajectories) can alter the folding scenario from three-state folding, a major folding scenario for the FBP28 WW domain (WT) and its mutants, toward two-state or downhill folding at temperatures below the melting point. Here, for a better understanding of the physics of the formation/elimination of intermediates, (i) the dynamics and energetics of formation of β-strands in folding, misfolding, and nonfolding trajectories of these mutants (L26D and L26W) is investigated; (ii) the experimental structures of WT, L26D, and L26W are analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. We show that the formation of each β-strand in folding trajectories is accompanied by the emergence of kinks in internal coordinate space as well as a decrease in local free energy. In particular, the decrease in downhill folding trajectory is ∼7 kcal/mol, while it varies between 31 and 48 kcal/mol for the three-state folding trajectory. The kink analyses of the experimental structures give new insights into formation of intermediates, which may become a useful tool for preventing aggregation.

From Anodic Oxidation of Aliphatic α-Amino Acids to Polypeptides by Quantum Electrochemistry Approach: Beyond Miller-Urey Experiments

For years, polypeptide formation has fascinated the scientific world because its understanding could lead to one of the possible explanations for the origin of life. Anodic oxidation of aliphatic α-amino acids in aqueous electrolytes can result either in their decomposition or in their polymerization into polypeptide. This behavior depends experimentally on both amino acid concentration and pH. The elucidation of the involved mechanisms remains a challenge because of the multitude of products which can be obtained. In this context, the electrochemical behavior of glycine and alanine on a biased platinum surface was examined at the nanoscale by quantum electrochemistry via the effective screening medium method. Several electrochemical systems with different concentrations and pH values have been explored. Simulations of the anodic oxidation of the amino acids have not only confirmed their electropolymerization and decomposition at high and low concentrations, respectively, but also have revealed unsuspected mechanisms at the origin of polypeptide formation. This sheds new light on electrochemistry of α-amino acids, on occurrence of polypeptides, and more generally on organic electrochemistry.

Phonon–phonon scattering selection rules and control: an application to nanofriction and thermal transport

Phonon–phonon scattering processes are the crucial phenomena which account for phonon decay, thermal expansion, heat transfer, protein dynamics, spin relaxation and related quantities. In this work, we show how the symmetries of the system determine which scattering processes are allowed at any order of anharmonic approximation, irrespective of the chemical composition. We also discuss how to control the system symmetries to switch on and off any single scattering process. We apply the presented results to the study and control of nanoscale intrinsic friction and thermal transport in lamellar van der Waals transition metal dichalcogenides. Thanks to its general formulation, the presented framework expands the materials science tool set for the design of nanoengineered thermally-active materials, irrespective of the specific chemical composition and atomic topology.

Symmetry-based selection rules are a guide on how to switch on or off multi-phonon scattering processes.

Allostery Wiring Map for Kinesin Energy Transduction and Its Evolution

How signals between the kinesin active and cytoskeletal binding sites are transmitted is an open question and an allosteric question. By extracting correlated evolutionary changes within 700+ sequences, we built a model of residues that are energetically coupled and that define molecular routes for signal transmission. Typically, these coupled residues are located at multiple distal sites and thus are predicted to form a complex, non-linear network that wires together different functional sites in the protein. Of note, our model connected the site for ATP hydrolysis with sites that ultimately utilize its free energy, such as the microtubule-binding site, drug-binding loop 5, and necklinker. To confirm the calculated energetic connectivity between non-adjacent residues, double-mutant cycle analysis was conducted with 22 kinesin mutants. There was a direct correlation between thermodynamic coupling in experiment and evolutionarily derived energetic coupling. We conclude that energy transduction is coordinated by multiple distal sites in the protein rather than only being relayed through adjacent residues. Moreover, this allosteric map forecasts how energetic orchestration gives rise to different nanomotor behaviors within the superfamily.