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The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation,…
Focusing on a small set of proteins that i) fold in a concerted, all-or-none fashion and ii) do not contain knots or slipknots, we show that the Gauss linking integral, the torsion and the number of sequence-distant contacts provide…
A simple lattice model, recently introduced as a generalization of the Wako--Sait\^o model of protein folding, is used to investigate the properties of widely studied molecules under external forces. The equilibrium properties of the model…
Accurate protein structure prediction from amino-acid sequences is critical to better understanding the protein function. Recent advances in this area largely benefit from more precise inter-residue distance and orientation predictions,…
The protein folding problem has been fundamentally transformed by artificial intelligence, evolving from static structure prediction toward the modeling of dynamic conformational ensembles and complex biomolecular interactions. This review…
A quantitative understanding of how cells interact with their extracellular matrix via molecular bonds is fundamental for many important processes in cell biology and engineering. In these interactions, the deformability of cells and matrix…
The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…
How proteins fold remains a central unsolved problem in biology. While the idea of a folding code embedded in the amino acid sequence was introduced more than 6 decades ago, this code remains undefined. While we now have powerful predictive…
Many biologically important ligands of proteins are large, flexible, and often charged molecules that bind to extended regions on the protein surface. It is infeasible or expensive to locate such ligands on proteins with standard methods…
A novel energy landscape model, ELM, for proteins recently explained a collection of incoherent, elastic neutron scattering data from proteins. The ELM of proteins considers the elastic response of the proton and its environment to the…
Musculoskeletal models have been widely used for detailed biomechanical analysis to characterise various functional impairments given their ability to estimate movement variables (i.e., muscle forces and joint moment) which cannot be…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
We show how to evaluate mobility profiles, characterizing the transport of confined fluids under a perturbation, from equilibrium molecular simulations. The correlation functions derived with the Green-Kubo formalism are difficult to sample…
Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to…
We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which…
Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the…
Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in…
While recent advances in AI have transformed protein structure prediction, protein function is also strongly influenced by the thermodynamic and kinetic features encoded in its underlying free-energy surface. Here, we propose a…
We study the dynamics of hydration water/protein association in folded proteins, using lysozyme and myoglobin as examples. Extensive molecular dynamics simulations are performed to identify underlying mechanisms of the dynamical transition…