Exploring the dynamics of flagellar dynein within the axoneme with Fluctuating Finite Element Analysis

Flagellar dyneins are the molecular motors responsible for producing the propagating bending motions of cilia and flagella. They are located within a densely packed and highly organised super-macromolecular cytoskeletal structure known as the axoneme. Using the mesoscale simulation technique Fluctuating Finite Element Analysis (FFEA), which represents proteins as viscoelastic continuum objects subject to explicit thermal noise, we have quantified the constraints on the range of molecular conformations that can be explored by dynein-c within the crowded architecture of the axoneme. We subsequently assess the influence of crowding on the 3D exploration of microtubule-binding sites, and specifically on the axial step length. Our calculations combine experimental information on the shape, flexibility and environment of dynein-c from three distinct sources; negative stain electron microscopy, cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET). Our FFEA simulations show that the super-macromolecular organisation of multiple protein complexes into higher-order structures can have a significant influence on the effective flexibility of the individual molecular components, and may, therefore, play an important role in the physical mechanisms underlying their biological function

Tonic Activation of GluN2C/GluN2D-Containing NMDA Receptors by Ambient Glutamate Facilitates Cortical Interneuron Maturation

Developing cortical GABAergic interneurons rely on genetic programs, neuronal activity, and environmental cuesto construct inhibitory circuits during early postnatal development. Disruption of these events can cause long-term changes in cortical inhibition and may be involved in neurological disorders associated with inhibitory circuit dysfunction. We hypothesized that tonic glutamate signaling in the neonatal cortex contributesto, and is necessary for,the maturation of cortical interneurons. Totestthis hypothesis, we used mice of both sexes to quantify extracellular glutamate concentrations in the cortex during development, measure ambient glutamate-mediated activation of developing cortical interneurons, and manipulatetonic glutamate signaling using subtype-specific NMDA receptor antagonists in vitro and in vivo. We report that ambient glutamate levels are high (100 nM) in the neonatal cortex and decrease (to 50 nM) during the first weeks of life, coincident with increases in astrocytic glutamate uptake. Consistent with elevated ambient glutamate, putative parvalbumin-positive interneurons in the cortex (identified using G42:GAD1-eGFP reporter mice) exhibit a transient, tonic NMDA current at the end of the first postnatal week. GluN2C/GluN2D-containing NMDA receptors mediate the majority of this current and contribute to the resting membrane potential and intrinsic properties of developing putative parvalbumin interneurons. Pharmacological blockade of GluN2C/GluN2D-containing NMDA receptors in vivo during the period of tonic interneuron activation, but not later, leads to lasting decreases in interneuron morphological complexity and causes deficits in cortical inhibition later in life. These results demonstrate that dynamic ambient glutamate signaling contributes to cortical interneuron maturation via tonic activation of GluN2C/ GluN2D-containing NMDA receptor

Exponential and moment inequalities for U-statistics

A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized) U-statistics of any order whose kernels are either nonnegative or canonicalComment: 22 page

Hamiltonian dynamics for Einstein's action in G→\rightarrow0 limit

The Hamiltonian analysis for the Einstein's action in $G\to 0$ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $Gto 0$ for Einstein's action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis

Fluctuating Finite Element Analysis (FFEA): A continuum mechanics software tool for mesoscale simulation of biomolecules

Fluctuating Finite Element Analysis (FFEA) is a software package designed to perform continuum mechanics simulations of proteins and other globular macromolecules. It combines conventional finite element methods with stochastic thermal noise, and is appropriate for simulations of large proteins and protein complexes at the mesoscale (length-scales in the range of 5 nm to 1 μm), where there is currently a paucity of modelling tools. It requires 3D volumetric information as input, which can be low resolution structural information such as cryo-electron tomography (cryo-ET) maps or much higher resolution atomistic co-ordinates from which volumetric information can be extracted. In this article we introduce our open source software package for performing FFEA simulations which we have released under a GPLv3 license. The software package includes a C ++ implementation of FFEA, together with tools to assist the user to set up the system from Electron Microscopy Data Bank (EMDB) or Protein Data Bank (PDB) data files. We also provide a PyMOL plugin to perform basic visualisation and additional Python tools for the analysis of FFEA simulation trajectories. This manuscript provides a basic background to the FFEA method, describing the implementation of the core mechanical model and how intermolecular interactions and the solvent environment are included within this framework. We provide prospective FFEA users with a practical overview of how to set up an FFEA simulation with reference to our publicly available online tutorials and manuals that accompany this first release of the package

Continuum Mechanical Parameterisation of Cytoplasmic Dynein from Atomistic Simulation

Cytoplasmic dynein is responsible for intra-cellular transport in eukaryotic cells. Using Fluctuating Finite Element Analysis (FFEA), a novel algorithm that represents proteins as continuum viscoelastic solids subject to thermal noise, we are building computational tools to study the mechanics of these molecular machines. Here we present a methodology for obtaining the material parameters required to represent the flexibility of cytoplasmic dynein within FFEA from atomistic molecular dynamics (MD) simulations, and show this continuum representation is sufficient to capture the principal dynamic properties of the motor

Nano-encapsulated Escherichia coli Divisome Anchor ZipA, and in Complex with FtsZ

The E. coli membrane protein ZipA, binds to the tubulin homologue FtsZ, in the early stage of cell division. We isolated ZipA in a Styrene Maleic Acid lipid particle (SMALP) preserving its position and integrity with native E. coli membrane lipids. Direct binding of ZipA to FtsZ is demonstrated, including FtsZ fibre bundles decorated with ZipA. Using Cryo-Electron Microscopy, small-angle X-ray and neutron scattering, we determine the encapsulated-ZipA structure in isolation, and in complex with FtsZ to a resolution of 1.6 nm. Three regions can be identified from the structure which correspond to, SMALP encapsulated membrane and ZipA transmembrane helix, a separate short compact tether, and ZipA globular head which binds FtsZ. The complex extends 12 nm from the membrane in a compact structure, supported by mesoscale modelling techniques, measuring the movement and stiffness of the regions within ZipA provides molecular scale analysis and visualisation of the early divisome