Symmetry adapted Assur decompositions

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.Comment: 40 pages, 22 figure

Mechanistic insights into allosteric regulation of the A2A adenosine G protein-coupled receptor by physiological cations.

Cations play key roles in regulating G-protein-coupled receptors (GPCRs), although their mechanisms are poorly understood. Here, 19F NMR is used to delineate the effects of cations on functional states of the adenosine A2A GPCR. While Na+ reinforces an inactive ensemble and a partial-agonist stabilized state, Ca2+ and Mg2+ shift the equilibrium toward active states. Positive allosteric effects of divalent cations are more pronounced with agonist and a G-protein-derived peptide. In cell membranes, divalent cations enhance both the affinity and fraction of the high affinity agonist-bound state. Molecular dynamics simulations suggest high concentrations of divalent cations bridge specific extracellular acidic residues, bringing TM5 and TM6 together at the extracellular surface and allosterically driving open the G-protein-binding cleft as shown by rigidity-transmission allostery theory. An understanding of cation allostery should enable the design of allosteric agents and enhance our understanding of GPCR regulation in the cellular milieu

Protein flexibility of dimers: do symmetric motions play a role in allosteric interactions?

How a protein functions depends both on having basic stable forms (tertiary structure) and having some residual flexibility supported within that structure. The modeling of protein flexibility and rigidity in terms imported from physics and engineering has been developed through the theory of generically rigid frameworks and a fast combinatorial algorithm is available in programs such as FIRST. Recent theoretical work on rigidity of frameworks has modified this generic analysis to include the basic symmetry and to predict additional motions. In particular, a framework which would normally count to be combinatorially minimally rigid in generic realizations has been shown to become flexible when realized with 2‐fold rotational symmetry in 3‐space. Protein dimers, formed by two copies of a protein are a good case study for impact of this added flexibility due to 2‐fold rotational symmetry, as dimers generally self‐assemble with a 2‐fold rotational axis, for reasons of minimal energy. We describe an algorithm for predicting possible additional flexibility and consider the question: What is the significance of this for the behavior of dimers, such as tryptophan repressor

Hyperphosphorylation of intrinsically disordered tau protein induces an amyloidogenic shift in its conformational ensemble.

Tau is an intrinsically disordered protein (IDP) whose primary physiological role is to stabilize microtubules in neuronal axons at all stages of development. In Alzheimer's and other tauopathies, tau forms intracellular insoluble amyloid aggregates known as neurofibrillary tangles, a process that appears in many cases to be preceded by hyperphosphorylation of tau monomers. Understanding the shift in conformational bias induced by hyperphosphorylation is key to elucidating the structural factors that drive tau pathology, however, as an IDP, tau is not amenable to conventional structural characterization. In this work, we employ a straightforward technique based on Time-Resolved ElectroSpray Ionization Mass Spectrometry (TRESI-MS) and Hydrogen/Deuterium Exchange (HDX) to provide a detailed picture of residual structure in tau, and the shifts in conformational bias induced by hyperphosphorylation. By comparing the native and hyperphosphorylated ensembles, we are able to define specific conformational biases that can easily be rationalized as enhancing amyloidogenic propensity. Representative structures for the native and hyperphosphorylated tau ensembles were generated by refinement of a broad sample of conformations generated by low-computational complexity modeling, based on agreement with the TRESI-HDX profiles

On the symmetric molecular conjectures

A molecular linkage consists of a set of rigid bodies pairwise connected by revolute hinges where all hinge lines of each body are concurrent. It is an important problem in biochemistry, as well as in robotics, to efficiently analyze the motions of such linkages. The theory of generic rigidity of body-bar frameworks addresses this problem via fast combinatorial algorithms. However, recent work has shown that symmetry (a common feature of many molecular and mechanical structures) can lead to additional motions. These motions typically maintain the original symmetry of the structure throughout the path, and they can often be detected via simple combinatorial counts. In this paper, we outline how these symmetry-based mathematical counts and methods can be used to efficiently predict the motions of symmetric molecular linkages, and we numerically analyze configuration spaces supporting the symmetric Molecular Conjectures formulated herein.Peer Reviewe