Convergence of an Approximation Scheme for Curvature-Dependent Motions of Sets SIAM Journal on Numerical Analysis

Because an extended 15 residue linker could span up to 40 Å, each N domain dimer should be somewhat flexible in the ClpX hexamer. Although explicit linkers were not modeled, 15–25 Å separates the C terminus of each N domain and the N terminus of the large AAA+ domain to which it connects. Pore loops of the AAA+ ClpX machine grip substrates to drive translocation and unfolding. Role of the processing pore of the ClpX AAA+ Dependent Motions ATPase in the recognition and engagement of specific protein substrates. Functional domains of the ClpA and ClpX molecular chaperones identified by limited proteolysis and deletion analysis. Unfolding and internalization of proteins by the ATP-dependent proteases ClpXP and ClpAP. Namy O, Moran S, Stuart D, Gilbert R, Brierley I. A mechanical explanation of rna pseudoknot function in programmed ribosomal frameshifting.

Structural dynamics of single SARS-CoV-2 pseudoknot molecules reveal topologically distinct conformers. Jones C, Ferre-D’amare A. Crystal structure of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) frameshifting pseudoknot.

Comparisons to experimental structures

Presentation of peptides by class I MHC (MHC-I) proteins to T cell receptors is a key component of cellular immunity. The first structures of peptide/MHC-I structures illustrated how peptides were presented by MHC-I proteins, lying in an extended form embedded within a binding groove formed by two flanking α helices and a β sheet floor .

Thus, motions induced by nucleotide binding progress from lighter to darker shades. Asymmetry of the nucleotide-free and nucleotide-bound hexamers is evident in the top and bottom views and in the side views. The views in and were generated from that in by 180° and 90° rotations, respectively, around the x axis. The views shown in and represent rotations around the y axis in 50° and 75° increments, respectively, from the view in https://turbo-tax.org/ . The third approach is to target the 3_6 pseudoknot structural switch between the L and linear shapes. In the mRNA-ribosome Cryo-EM structure captured during translation20, the L shape 3_6 wedges at the mRNA entry channel and resists unwinding by the helicase, which generates tension on the upstream mRNA20. This structural switch might then enhance fluctuations of this tension and send frameshifting signals to the ribosome.

Particle representations of superprocesses with dependent motions

Comparing the mutant with longest Stem 2 to its corresponding wildtype model, we observe a dramatic transformation from L shape to linear shape (Fig.7). Indeed, all 3_6 mutant systems adopt this linear shape (Supplementary Table6, Supplementary Fig.14), and the structural switch between the two shapes has been suppressed in most systems (Supplementary Fig.19).

We propose that one or both of these hinge interfaces open in an elastic fashion to allow passage of substrates that are too large to transit the undistorted pore . Opening might occur by unraveling the type 2 linker (or part of the adjacent 320–327 helix) as a consequence of attempts by ClpX to force translocation of larger substrates. This model is analogous to the elastically hinged jaws of a snake, which allow it to consume prey larger than its normal mouth size. The inability of type 2 subunits to bind nucleotide is an important aspect of our pore expansion model because ligand binding at the “hinge” interface would hinder opening. Structural biology of peptides presented by MHC proteins has transformed our understanding of immunology, with impacts ranging from our understanding of fundamental immune mechanisms to the design and optimization of vaccines. However, considering peptide/MHC complexes not as static structures but as molecules that move and breathe has opened new avenues of investigation and shed new light on factors that impact immunogenicity. The mobility of peptides within MHC protein binding grooves can impact antigen immunogenicity, regardless of whether mobility or conformational variability is apparent from crystallographic structures.

Functional Consequences of Pore-Loop Staggering

Now that we have done a careful derivation, we should be able to more quickly derive constraint equations, e.g. Crystal structure of T7 gene 4 ring helicase indicates a mechanism for sequential hydrolysis of nucleotides. The structure of ClpP at 2.3 Å resolution suggests a model for ATP-dependent proteolysis. Evolutionary relationships and structural mechanisms of AAA+ proteins. Visualization of substrate binding and translocation by the ATP-dependent protease, ClpXP.

Before sharing sensitive information, make sure you’re on a federal government site. In these equations, it is important to remember that the values represent the changes in length, rather than direct measures of velocities. Though both vehicles would have positive velocities in the example above , one \(\dot\) value will be positive and one will be negative. This is because the truck is getting closer to the tree while the car is getting further away. A similar situation will occur for the accelerations, where both vehicles would have positive accelerations even if the \(\ddot\) values are a mix of positive and negative values.

Structures of Asymmetric ClpX Hexamers Reveal Nucleotide-Dependent Motions in a AAA+ Protein-Unfolding Machine

The general architecture of peptide/MHC-I complexes is widely recognized, with representations found within thousands of reviews, research publications, and textbooks ranging from general biology to advanced immunology. The solution of peptide/MHC-I structures answered fundamental questions in immunology, including how a single receptor can simultaneously recognize both self and non-self in antigen recognition . The subsequent solution of structures of complexes between TCRs and peptide/MHC-I complexes illustrated at an atomic level how simultaneous recognition of self/non-self occurs . Axial staggering places the GYVG loops of some subunits next to the pore 2 loops of other subunits, and it is plausible that a binding site for the ssrA tag is formed by an interaction between both loops. The importance of the GYVG and pore 2 loops in protein unfolding could be explained by roles in translocation and/or in preventing substrate slipping following translocation. Mutations in the GYVG loops but not the pore 2 loops slow translocation, and thus the pore 2 loops may function largely to grip substrates after a translocation step.

The resultant spatial waves in cylindrical air-columns exhibit very similar time-dependent behavior to those observed by experiments for the clarinet. Actually, a progressive and a regressive rounded-off-step shaped wave are observed. We also discuss difference in wave shapes and their time-dependent behavior between different shapes of air-columns, cylindrical bores like the clarinet, conical bores like the saxophone and a horn-shaped bore like brass instruments.

A Dominant motions of the threaded L shape 77-nt 3_6 pseudoknot, 77-nt 3_3 pseudoknot, and 77-nt compact 3_5 junction extracted by principal component analysis . B Flexibility of the three conformations as reflected by root mean square fluctuations . For the 3_6 and 3_3 pseudoknots, the RMSF is shown for the common 77-nt region at various lengths; for 3_5 junction, RMSF at 77-nt. In some crystal structures of peptide/MHC-I complexes, peptides are poorly refined in the binding groove, with side chains and even backbones lacking electron density (Figure ​ . Many subsequent structures demonstrated that peptide conformational changes frequently occur upon TCR binding (Figure ​ . 1B). Peptides can also be “pulled” away from the binding groove in response to TCR binding, an occurrence which could be related to the identity of the primary anchor residues . Cartoon of the pore 2 loops (structured parts yellow; modeled parts purple) from subunits A , B , and C of the nucleotide-bound ClpX hexamer.

Determine the speed of A in the figure if B has an upward speed of 6ft/s.1. Your library or institution may also provide you access to related full text documents in ProQuest. Copyright © 2022 Elsevier Inc. except certain content provided by third parties. The content on this site is intended for healthcare professionals. The protein was concentrated to a final concentration of 40 μM in 50 mM Tris-HCl (pH 7.5), 300 mM KCl, 10% glycerol, 0.1 mM EDTA, and 1 mM DTT. Structural insights into RNA-dependent ring closure and ATPase activation by the Rho termination factor. Mechanism of DNA translocation in a replicative hexameric helicase.

Associated Data

However, moving from structural indications of motion to more detailed, actual assessments of motion requires additional experiments. There can be multiple reasons for weak or missing electron density in protein structures, such as poor crystal morphology or even the existence of multiple peptides in one crystal, as was the case in the very first structure of HLA-A2 . Another reason for poor electron density is structural heterogeneity, stemming from the existence of multiple peptide conformations or the interconversion between different conformations on the timescale of the X-ray diffraction experiment. Such heterogeneity was demonstrated in an early experiment with the GP2 HER-2/neu epitope, which had missing density in the peptide center when bound to HLA-A2 . In other cases, electron density is clear enough to identify peptides in multiple conformations (Figure ​ . Additional conformations, for example those stabilized by ATP and substrate binding, will certainly be used during ClpX function.

• Atomic coordinates are along the x axis and free energy is along the y axis.
• Together, our observations provide new insights into frameshifting mechanisms and anti-viral strategies.
• The covalent tethers between subunits were not observed in electron density maps.
• Mutations in the GYVG loops but not the pore 2 loops slow translocation, and thus the pore 2 loops may function largely to grip substrates after a translocation step.
• The root mean square deviation for contiguous peptide backbone atoms between TCR-free and TCR-bound is 1.3 Å.

The 19 convergent and validated wildtype MD trajectories and the 11 mutant trajectories are numbered as indicated by the superscript. Representative trajectories for the Results section are marked with asterisks. This is an open-access article distributed under the terms of the Creative Commons Attribution License . The use, distribution or reproduction in other forums is permitted, provided the original author or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Finally, you can find the acceleration of the two particles by taking the derivative of equation 3 or the double derivative of equation 2 in respect to time. @Danfoa One next important step for MTC is to provide a drop-in-replacement for MoveIt’s pick-and-place capability .

Cartoon of the nucleotide-bound ClpX hexamer showing the positions of the four nucleotide-binding sites relative to type 1 and type 2 subunits. Model for protein unfolding and degradation by the ClpXP protease. Cutaway view showing how the degradation tag of a protein substrate could initially bind in the pore of ClpX. ATP-dependent translocation could then lead to unfolding and degradation of the polypeptide by ClpP.

• Thus, a mixture of type 1 and type 2 subunits appears to be required to form a closed ClpX ring.
• No use, distribution or reproduction is permitted which does not comply with these terms.
• With our continuously evolving computational and experimental toolkit for investigating RNA systems at increasing complexity, biophysical approaches will continue to contribute to disease diagnostics and treatment.
• End threading that may impact ribosomal pausing to the L shape model (Fig.3).
• Additional conformations, for example those stabilized by ATP and substrate binding, will certainly be used during ClpX function.