Dynamics of Co-translational Membrane Protein Integration and Translocation via the Sec Translocon

An important aspect of cellular function is the correct targeting and delivery of newly synthesized proteins. Central to this task is the machinery of the Sec translocon, a transmembrane channel that is involved in both the translocation of nascent proteins across cell membranes and the integration of proteins into the membrane. Considerable experimental and computational effort has focused on the Sec translocon and its role in nascent protein biosynthesis, including the correct folding and expression of integral membrane proteins. However, the use of molecular simulation methods to explore Sec-facilitated protein biosynthesis is hindered by the large system sizes and long (i.e., minute) timescales involved. In this work, we describe the development and application of a coarse-grained simulation approach that addresses these challenges and allows for direct comparison with both in vivo and in vitro experiments. The method reproduces a wide range of experimental observations, providing new insights into the underlying molecular mechanisms, predictions for new experiments, and a strategy for the rational enhancement of membrane protein expression levels

Substitution effects on the temperature vs. magnetic-field phase diagrams of the quasi-1D effective Ising spin-1/2 chain system BaCo2_2V2_2O8_8

BaCo$_2$V$_2$O$_8$ is a one-dimensional antiferromagnetic spin-1/2 chain system with pronounced Ising anisotropy of the magnetic exchange. Due to finite interchain interactions long-range antiferromagnetic order develops below $T_{\rm N} \simeq 5.5$ K, which is accompanied by a structural distortion in order to lift magnetic frustration effects. The corresponding temperature $vs.$ magnetic-field phase diagram is highly anisotropic with respect to the magnetic-field direction and various details are still under vivid discussion. Here, we report the influence of several substitutions on the magnetic properties and the phase diagrams of BaCo$_2$V$_2$O$_8$. We investigate the substitution series Ba$_{\text{1-x}}$Sr$_{\text{x}}$Co$_{\text{2}}$V$_{\text{2}}$O$_{\text{8}}$ over the full range $0\le x \le 1$ as well as the influence of a partial substitution of the magnetic Co$^{2+}$ by small amounts of other magnetic transition metals or by non-magnetic magnesium. In all cases, the phase diagrams were obtained on single crystals from magnetization data and/or high-resolution studies of the thermal expansion and magnetostriction.Comment: 10 pages, 10 figure

Three-dimensional solutions for the geostrophic flow in the Earth's core

In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically-averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically-averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalisation of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any 3D Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully 3D case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular.Comment: 29 Pages, 8 figure

Reconstruction of the thermal properties in a wave-type model of bio-heat transfer

Purpose: This study aims to at numerically retrieve five constant dimensional thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements. Design/methodology/approach: The thermal-wave model of bio-heat transfer is used as an appropriate model because of its realism in situations in which the heat flux is extremely high or low and imposed over a short duration of time. For the numerical discretization, an unconditionally stable finite difference scheme used as a direct solver is developed. The sensitivity coefficients of the dimensionless boundary temperature measurements with respect to five constant dimensionless parameters appearing in a non-dimensionalised version of the governing hyperbolic model are computed. The retrieval of those dimensionless parameters, from both exact and noisy measurements, is successfully achieved by using a minimization procedure based on the MATLAB optimization toolbox routine lsqnonlin. The values of the five-dimensional parameters are recovered by inverting a nonlinear system of algebraic equations connecting those parameters to the dimensionless parameters whose values have already been recovered. Findings: Accurate and stable numerical solutions for the unknown thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements are obtained using the proposed numerical procedure. Research limitations/implications: The current investigation is limited to the retrieval of constant physical properties, but future work will investigate the reconstruction of the space-dependent blood perfusion coefficient. Practical implications: As noise inherently present in practical measurements is inverted, the paper is of practical significance and models a real-world situation. Social implications: The findings of the present paper are of considerable significance and interest to practitioners in the biomedical engineering and medical physics sectors. Originality/value: In comparison to Alkhwaji et al. (2012), the novelty and contribution of this work are as follows: considering the more general and realistic thermal-wave model of bio-heat transfer, accounting for a relaxation time; allowing for the tissue to have a finite size; and reconstructing five thermally significant dimensional parameters

Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators

We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector representing the initial condition. The matrix function is a linear combination of the matrix exponential and other functions related to the exponential (the so-called phi-functions). Such computations are the major computational burden in the implementation of exponential integrators, which can solve general ODEs. Our approach is to compute the action of the matrix function by constructing a Krylov subspace using Arnoldi or Lanczos iteration and projecting the function on this subspace. This is combined with time-stepping to prevent the Krylov subspace from growing too large. The algorithm is fully adaptive: it varies both the size of the time steps and the dimension of the Krylov subspace to reach the required accuracy. We implement this algorithm in the Matlab function phipm and we give instructions on how to obtain and use this function. Various numerical experiments show that the phipm function is often significantly more efficient than the state-of-the-art.Comment: 20 pages, 3 colour figures, code available from http://www.maths.leeds.ac.uk/~jitse/software.html . v2: Various changes to improve presentation as suggested by the refere

Force transduction creates long-ranged coupling in ribosomes stalled by arrest peptides

Force-sensitive arrest peptides regulate protein biosynthesis by stalling the ribosome as they are translated. Synthesis can be resumed when the nascent arrest peptide experiences a pulling force of sufficient magnitude to break the stall. Efficient stalling is dependent on the specific identity of a large number of amino acids, including amino acids which are tens of angstroms away from the peptidyl transferase center (PTC). The mechanism of force-induced restart and the role of these essential amino acids far from the PTC is currently unknown. We use hundreds of independent molecular dynamics trajectories spanning over 120 μs in combination with kinetic analysis to characterize the barriers along the force-induced restarting pathway for the arrest peptide SecM. We find that the essential amino acids far from the PTC play a major role in controlling the transduction of applied force. In successive states along the stall-breaking pathway, the applied force propagates up the nascent chain until it reaches the C-terminus of SecM and the PTC, inducing conformational changes that allow for restart of translation. A similar mechanism of force propagation through multiple states is observed in the VemP stall-breaking pathway, but secondary structure in VemP allows for heterogeneity in the order of transitions through intermediate states. Results from both arrest peptides explain how residues that are tens of angstroms away from the catalytic center of the ribosome impact stalling efficiency by mediating the response to an applied force and shielding the amino acids responsible for maintaining the stalled state of the PTC

Improving membrane protein expression by optimizing integration efficiency

The heterologous overexpression of integral membrane proteins in Escherichia coli often yields insufficient quantities of purifiable protein for applications of interest. The current study leverages a recently demonstrated link between co-translational membrane integration efficiency and protein expression levels to predict protein sequence modifications that improve expression. Membrane integration efficiencies, obtained using a coarse-grained simulation approach, robustly predicted effects on expression of the integral membrane protein TatC for a set of 140 sequence modifications, including loop-swap chimeras and single-residue mutations distributed throughout the protein sequence. Mutations that improve simulated integration efficiency were 4-fold enriched with respect to improved experimentally observed expression levels. Furthermore, the effects of double mutations on both simulated integration efficiency and experimentally observed expression levels were cumulative and largely independent, suggesting that multiple mutations can be introduced to yield higher levels of purifiable protein. This work provides a foundation for a general method for the rational overexpression of integral membrane proteins based on computationally simulated membrane integration efficiencies

Structurally detailed coarse-grained model for Sec-facilitated co-translational protein translocation and membrane integration

We present a coarse-grained simulation model that is capable of simulating the minute-timescale dynamics of protein translocation and membrane integration via the Sec translocon, while retaining sufficient chemical and structural detail to capture many of the sequence-specific interactions that drive these processes. The model includes accurate geometric representations of the ribosome and Sec translocon, obtained directly from experimental structures, and interactions parameterized from nearly 200 μs of residue-based coarse-grained molecular dynamics simulations. A protocol for mapping amino-acid sequences to coarse-grained beads enables the direct simulation of trajectories for the co-translational insertion of arbitrary polypeptide sequences into the Sec translocon. The model reproduces experimentally observed features of membrane protein integration, including the efficiency with which polypeptide domains integrate into the membrane, the variation in integration efficiency upon single amino-acid mutations, and the orientation of transmembrane domains. The central advantage of the model is that it connects sequence-level protein features to biological observables and timescales, enabling direct simulation for the mechanistic analysis of co-translational integration and for the engineering of membrane proteins with enhanced membrane integration efficiency