Determining the three-dimensional structure of myoglobin, the first solved structure of a protein, fundamentally changed the way protein function was understood. Even more revolutionary was the information that came afterward: protein dynamics play a critical role in biological functions. Therefore, understanding conformational dynamics is crucial to obtaining a more complete picture of protein evolution. We recently analyzed the evolution of different protein families including green fluorescent proteins (GFPs), β-lactamase inhibitors, and nuclear receptors, and we observed that the alteration of conformational dynamics through allosteric regulation leads to functional changes. Moreover, proteome-wide conformational dynamics analysis of more than 100 human proteins showed that mutations occurring at rigid residue positions are more susceptible to disease than flexible residue positions. These studies suggest that disease-associated mutations may impair dynamic allosteric regulations, leading to loss of function. Thus, in this study, we analyzed the conformational dynamics of the wild-type light chain subunit of human ferritin protein along with the neutral and disease forms. We first performed replica exchange molecular dynamics simulations of wild-type and mutants to obtain equilibrated dynamics and then used perturbation response scanning (PRS), where we introduced a random Brownian kick to a position and computed the fluctuation response of the chain using linear response theory. Using this approach, we computed the dynamic flexibility index (DFI) for each position in the chain for the wild-type and the mutants. DFI quantifies the resilience of a position to a perturbation and provides a flexibility/rigidity measurement for a given position in the chain. The DFI analysis reveals that neutral variants and the wild-type exhibit similar flexibility profiles in which experimentally determined functionally critical sites act as hinges in controlling the overall motion. However, disease mutations alter the conformational dynamic profile, making hinges more loose (i.e., softening the hinges), thus impairing the allosterically regulated dynamics.

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings. DOI: 10.1103/PhysRevLett.114.135501 PACS numbers: 62.20.D-, 63.50.Lm, 64.60.ah Disordered elastic networks and sphere packings represent a large class of amorphous athermal materials, ranging from (bio)polymer networks to granular media and foams [1][2][3]. Random networks of springs lose their rigidity when enough springs are cut; this random bond dilution process is known as rigidity percolation (RP) [4][5][6][7][8]. Packings of soft spheres do the same when their confining pressure is lowered towards zero: This is called (un)jamming [9][10][11][12][13]. These rigidity loss scenarios have been studied extensively, in particular, for the simplest cases of networks of harmonic springs [7,8] or soft frictionless harmonic spheres [10][11][12][13]. In that case, the linear elastic properties of packings can be mapped to those of a spring network, where each contact is replaced by the appropriate spring [14][15][16]. Lowering the pressure, the number of bonds in the equivalent network decreases.Given this close correspondence, it is surprising that the nature of the RP and unjamming transitions, and of their respective marginally rigid states, are significantly different. For packings of a large number (N) of soft spheres, extensive studies have shown that (i) the connectivity, i.e., the average number of contacts z per particle, goes to z c ¼ 2D þ Oð1=NÞ at the marginal point, where D is the space dimension [3,[9][10][11][12][13][17][18][19][20], (ii) the system remains homogeneously jammed up to the point of unjamming (with the exception of individual loose particles called rattlers or very rare small particle clusters) [10], and (iii) the shear modulus G vanishes as Δz ≔ z − z c whereas the bulk modulus K remains finite when Δz → 0 [9-14]. In contrast, in the rigidity percolation of generic networks, extensive studies have revealed that for large systems (i) the connectivity z, which gives the average number of springs per node, approaches z c ¼ 3.9612… < 2D for the bond diluted triangular network [7,8], (ii) the largest rigid cluster takes on a heterogeneous, fractal shape, and (iii) both the shear modulus G and bulk modulus K smoothly vanish at the critical point in a way typ...

Amorphous graphene is a realization of a two-dimensional Zachariasen glass as first proposed 80 years ago. Planar continuous random networks of this archetypal two-dimensional network are generated by two complementary simulation methods. In the first, a Monte Carlo bond switching algorithm is employed to systematically amorphize a crystalline graphene sheet. In the second, molecular dynamics simulations are utilized to quench from the high temperature liquid state. The two approaches lead to similar results as detailed here, through the pair distribution function and the associated diffraction pattern. Details of the structure, including ring statistics and angular distortions, are shown to be sensitive to preparation conditions, and await experimental confirmation.

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Theoretical modeling is presented for a free-standing vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. While such two-dimensional continuous random covalent networks should likely occur on energetic grounds, no synthetic pathway had been discovered previously. Here the bilayer is modelled using a computer assembly procedure initiated from a single layer of a model of amorphous graphene, generated using a bond switching algorithm from an initially crystalline graphene structure. Each bond is decorated with an oxygen atom and the carbon atoms are relabeled as silicon, generating a two dimensional network of corner sharing triangles. Each triangle is transformed into a tetrahedron, by raising the silicon atom above each triangular base and adding an additional singly coordinated oxygen atom at the apex. The final step in this construction is to mirror-reflect this layer to form a second layer and attach the two layers to form the bilayer. We show that this vitreous silica bilayer has the additional macroscopic degrees of freedom to form easily a network of identical corner sharing tetrahedra if there is a symmetry plane through the center of the bilayer going through the layer of oxygen ions that join the upper and lower monolayers. This has the consequence that the upper rings lie exactly above the lower rings, which are tilted in general. The assumption of a network of perfect corner sharing tetrahedra leads to a range of possible densities that we characterize as a flexibility window; with some similarity to flexibility windows in three dimensional zeolites. Finally, using a realistic potential, we have relaxed the bilayer to determine the density and other structural characteristics such as the Si-Si pair distribution functions and the Si-O-Si bond angle distribution, which are compared with experimental results obtained by direct imaging.