Lattice Conformation Research Articles

Topology-based optimization of handcuff graphs on 3D lattice

In the field of macromolecular chemistry, handcuff-shaped catenanes and pretzelanes have a conformation consisting of two distinct loops and an edge connecting them. In spatial graph theory, this shape is referred to as a handcuff graph. One topological aspect of interest in these molecular structures involves determining the minimal number of monomers required to create them. In this paper, we focus on a handcuff graph situated in the cubic lattice, which we refer to as a lattice handcuff graph. We explicitly verify that constructing a lattice handcuff graph requires at least 14 lattice sticks, except for the two handcuff graphs: the trivial handcuff graph and the Hopf-linked handcuff graph. Mainly we employ the properly leveled lattice conformation argument, which was developed by the authors to find the lattice stick number of knot-shaped and link-shaped molecules.

Abl2 repairs microtubules and phase separates with tubulin to promote microtubule nucleation

Abl family kinases are evolutionarily conserved regulators of cell migration and morphogenesis. Genetic experiments in Drosophila suggest that Abl family kinases interact functionally with microtubules to regulate axon guidance and neuronal morphogenesis. Vertebrate Abl2 binds to microtubules and promotes their plus-end elongation, both invitro and in cells, but the molecular mechanisms by which Abl2 regulates microtubule (MT) dynamics are unclear. We report here that Abl2 regulates MT assembly via condensation and direct interactions with both the MT lattice and tubulin dimers. We find that Abl2 promotes MT nucleation, which is further facilitated by the ability of the Abl2 C-terminal half to undergo liquid-liquid phase separation (LLPS) and form co-condensates with tubulin. Abl2 binds to regions adjacent to MT damage, facilitates MT repair via fresh tubulin recruitment, and increases MT rescue frequency and lifetime. Cryo-EM analyses strongly support a model in which Abl2 engages tubulin C-terminal tails along an extended MT lattice conformation at damage sites to facilitate repair via fresh tubulin recruitment. Abl2Δ688-790, which closely mimics a naturally occurring splice isoform, retains binding to the MT lattice but does not bind tubulin, promote MT nucleation, or increase rescue frequency. In COS-7 cells, MT reassembly after nocodazole treatment is greatly slowed in Abl2 knockout COS-7 cells compared with wild-type cells, and these defects are rescued by re-expression of Abl2, but not Abl2Δ688-790. We propose that Abl2 locally concentrates tubulin to promote MT nucleation and recruits it to defects in the MT lattice to enable repair and rescue.

Microtubule detyrosination by VASH1/SVBP is regulated by the conformational state of tubulin in the lattice

Tubulin, a heterodimer of α- and β-tubulin, is a GTPase that assembles into microtubule (MT) polymers whose dynamic properties are intimately coupled to nucleotide hydrolysis. In cells, the organization and dynamics of MTs are further tuned by post-translational modifications (PTMs), which control the ability of MT-associated proteins (MAPs) and molecular motors to engage MTs. Detyrosination is a PTM of α-tubulin, wherein its C-terminal tyrosine residue is enzymatically removed by either the vasohibin (VASH) or MT-associated tyrosine carboxypeptidase (MATCAP) peptidases. How these enzymes generate specific patterns of MT detyrosination in cells is not known. Here, we use a novel antibody-based probe to visualize the formation of detyrosinated MTs in real time and employ single-molecule imaging of VASH1 bound to its regulatory partner small-vasohibin binding protein (SVBP) to understand the process of MT detyrosination invitro and in cells. We demonstrate that the activity, but not binding, of VASH1/SVBP is much greater on mimics of guanosine triphosphate (GTP)-MTs than on guanosine diphosphate (GDP)-MTs. Given emerging data showing that tubulin subunits in GTP-MTs are in expanded conformation relative to tubulin subunits in GDP-MTs, we reasoned that the lattice conformation of MTs is a key factor that gates the activity of VASH1/SVBP. We show that Taxol, a drug known to expand the MT lattice, promotes MT detyrosination and that CAMSAP2 and CAMSAP3 are two MAPs that spatially regulate detyrosination in cells. Collectively, our work shows that VASH1/SVBP detyrosination is regulated by the conformational state of tubulin in the MT lattice and that this is spatially determined in cells by the activity of MAPs.

Lattice conformation of theta-curves accompanied with Brunnian property

A theta-curve is an embedding of the Greek letter Θ shaped graph in three-dimensional space. This is a useful physical model for polymer chains since theta-curve motifs are often present in many circular proteins with internal bridges. A Brunnian theta-curve is a nontrivial theta-curve with the property that if we remove any one among three edges, then the remaining knot can be laid in the plane without crossings. We focus on the rigidity of polymer chains with the Brunnian theta-curve shape by using the lattice stick number which is the minimal number of sticks glued end-to-end that are necessary to construct the theta-curve in the cubic lattice. The authors have already shown in a previous research that at least 15 lattice sticks are needed to construct Brunnian theta-curves. In this paper, we improve the lower bound of the lattice stick number for Brunnian theta-curves to 16.

Cooperative Dynamics in Bidirectional Transport on Flexible Lattice

Several theoretical models based on totally asymmetric simple exclusion process (TASEP) have been extensively utilized to study various non-equilibrium transport phenomena. Inspired by the the role of microtubule-transported vesicles in intracellular transport, we propose a generalized TASEP model where two distinct particles are directed to hop stochastically in opposite directions on a flexible lattice immersed in a three dimensional pool of diffusing particles. We investigate the interplay between lattice conformation and bidirectional transport by obtaining the stationary phase diagrams and density profiles within the framework of mean field theory. For the case when recycling strength is independent of density of particles, the topology of phase diagram alters quantitatively. However, if the lattice occupancy governs the global conformation of lattice, in addition to the pre-existing phases for bidirectional transport a new asymmetric shock-low density phase originates in the system. We identified that this phase is sensitive to finite size effect and vanishes in the thermodynamic limit.

Microtubule instability driven by longitudinal and lateral strain propagation.

Tubulin dimers associate longitudinally and laterally to form metastable microtubules (MTs). MT disassembly is preceded by subtle structural changes in tubulin fueled by GTP hydrolysis. These changes render the MT lattice unstable, but it is unclear exactly how they affect lattice energetics and strain. We performed long-time atomistic simulations to interrogate the impacts of GTP hydrolysis on tubulin lattice conformation, lateral inter-dimer interactions, and (non-)local lateral coordination of dimer motions. The simulations suggest that most of the hydrolysis energy is stored in the lattice in the form of longitudinal strain. While not significantly affecting lateral bond stability, the stored elastic energy results in more strongly confined and correlated dynamics of GDP-tubulins, thereby entropically destabilizing the MT lattice.

Taxanes convert regions of perturbed microtubule growth into rescue sites.

Microtubules are polymers of tubulin dimers, and conformational transitions in the microtubule lattice drive microtubule dynamic instability and affect various aspects of microtubule function. The exact nature of these transitions and their modulation by anticancer drugs such as Taxol and epothilone, which can stabilize microtubules but also perturb their growth, are poorly understood. Here, we directly visualize the action of fluorescent Taxol and epothilone derivatives and show that microtubules can transition to a state that triggers cooperative drug binding to form regions with altered lattice conformation. Such regions emerge at growing microtubule ends that are in a pre-catastrophe state, and inhibit microtubule growth and shortening. Electron microscopy and in vitro dynamics data indicate that taxane accumulation zones represent incomplete tubes that can persist, incorporate tubulin dimers and repeatedly induce microtubule rescues. Thus, taxanes modulate the material properties of microtubules by converting destabilized growing microtubule ends into regions resistant to depolymerization.

Structural determinants of microtubule minus end preference in CAMSAP CKK domains

CAMSAP/Patronins regulate microtubule minus-end dynamics. Their end specificity is mediated by their CKK domains, which we proposed recognise specific tubulin conformations found at minus ends. To critically test this idea, we compared the human CAMSAP1 CKK domain (HsCKK) with a CKK domain from Naegleria gruberi (NgCKK), which lacks minus-end specificity. Here we report near-atomic cryo-electron microscopy structures of HsCKK- and NgCKK-microtubule complexes, which show that these CKK domains share the same protein fold, bind at the intradimer interprotofilament tubulin junction, but exhibit different footprints on microtubules. NMR experiments show that both HsCKK and NgCKK are remarkably rigid. However, whereas NgCKK binding does not alter the microtubule architecture, HsCKK remodels its microtubule interaction site and changes the underlying polymer structure because the tubulin lattice conformation is not optimal for its binding. Thus, in contrast to many MAPs, the HsCKK domain can differentiate subtly specific tubulin conformations to enable microtubule minus-end recognition.

Spin crossover-induced colossal positive and negative thermal expansion in a nanoporous coordination framework material

External control over the mechanical function of materials is paramount in the development of nanoscale machines. Yet, exploiting changes in atomic behaviour to produce controlled scalable motion is a formidable challenge. Here, we present an ultra-flexible coordination framework material in which a cooperative electronic transition induces an extreme abrupt change in the crystal lattice conformation. This arises due to a change in the preferred coordination character of Fe(II) sites at different spin states, generating scissor-type flexing of the crystal lattice. Diluting the framework with transition-inactive Ni(II) sites disrupts long-range communication of spin state through the lattice, producing a more gradual transition and continuous lattice movement, thus generating colossal positive and negative linear thermal expansion behaviour, with coefficients of thermal expansion an order of magnitude greater than previously reported. This study has wider implications in the development of advanced responsive structures, demonstrating electronic control over mechanical motion.

Synthetic Modularity of Protein–Metal–Organic Frameworks

Previously, we adopted the construction principles of metal-organic frameworks (MOFs) to design a 3D crystalline protein lattice in which pseudospherical ferritin nodes decorated on their C3 symmetric vertices with Zn coordination sites were connected via a ditopic benzene-dihydroxamate linker. In this work, we have systematically varied both the metal ions presented at the vertices of the ferritin nodes (Zn(II), Ni(II), and Co(II)) and the synthetic dihydroxamate linkers, which yielded an expanded library of 15 ferritin-MOFs with the expected body-centered (cubic or tetragonal) lattice arrangements. Crystallographic and small-angle X-ray scattering (SAXS) analyses indicate that lattice symmetries and dimensions of ferritin-MOFs can be dictated by both the metal and linker components. SAXS measurements on bulk crystalline samples reveal that some ferritin-MOFs can adopt multiple lattice conformations, suggesting dynamic behavior. This work establishes that the self-assembly of ferritin-MOFs is highly robust and that the synthetic modularity that underlies the structural diversity of conventional MOFs can also be applied to the self-assembly of protein-based crystalline materials.

On the anisotropy of lattice polymers

We quantified the anisotropy of various lattice models used in polymer simulations based on two quantities: the Fourier transform of the normalized Boltzmann factor of allowable bonds on a lattice (which is the central quantity for describing lattice chain conformations) and the bulk lamellar period at the mean-field order-disorder transition (ODT) of symmetric diblock copolymers on a lattice (which is pertinent to the study of microphase separation). This allowed us to compare the anisotropy of different lattices and to design new lattice models that minimize the quantified anisotropy. A lattice field theory based on the same Hamiltonian used in the newly proposed fast lattice Monte Carlo simulations [Q. Wang, Soft Matter 5, 4564 (2009)] is also presented, along with some mean-field results on the ODT of symmetric diblock copolymers on these lattices obtained under the random-phase approximation.

RNA folding on the 3D triangular lattice

BackgroundDifficult problems in structural bioinformatics are often studied in simple exact models to gain insights and to derive general principles. Protein folding, for example, has long been studied in the lattice model. Recently, researchers have also begun to apply the lattice model to the study of RNA folding.ResultsWe present a novel method for predicting RNA secondary structures with pseudoknots: first simulate the folding dynamics of the RNA sequence on the 3D triangular lattice, next extract and select a set of disjoint base pairs from the best lattice conformation found by the folding simulation. Experiments on sequences from PseudoBase show that our prediction method outperforms the HotKnot algorithm of Ren, Rastegari, Condon and Hoos, a leading method for RNA pseudoknot prediction. Our method for RNA secondary structure prediction can be adapted into an efficient reconstruction method that, given an RNA sequence and an associated secondary structure, finds a conformation of the sequence on the 3D triangular lattice that realizes the base pairs in the secondary structure. We implemented a suite of computer programs for the simulation and visualization of RNA folding on the 3D triangular lattice. These programs come with detailed documentation and are accessible from the companion website of this paper at http://www.cs.usu.edu/~mjiang/rna/DeltaIS/.ConclusionFolding simulation on the 3D triangular lattice is effective method for RNA secondary structure prediction and lattice conformation reconstruction. The visualization software for the lattice conformations of RNA structures is a valuable tool for the study of RNA folding and is a great pedagogic device.

Metalated Nitriles: Internal 1,3‐Asymmetric Induction

AbstractStereoselective alkylations of acyclic, metalated nitriles are intimately controlled by a remote stereocenter. Probing the optimal steric demand through alkylations with a series of substituted pentanenitriles reveal the fundamental requirements for 1,3‐asymmetric induction. Relaying these requirements into a predictive model suggests that the stereoselectivity arises from a preferential electrophilic attack on the more stable diamond lattice conformation of the metalated nitrile. Using this strategy a series of metalated alkanenitriles selectively intercept a diverse range of electrophiles in alkylations that efficiently install new quaternary centers. The metalated nitrile alkylations provide fundamental insight for remote stereoinduction and a solid foundation for further advances in stereoselective alkylations of flexible nucleophiles having a defined shape.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009)

Use of machine learning algorithms to classify binary protein sequences as highly-designable or poorly-designable.

BackgroundBy using a standard Support Vector Machine (SVM) with a Sequential Minimal Optimization (SMO) method of training, Naïve Bayes and other machine learning algorithms we are able to distinguish between two classes of protein sequences: those folding to highly-designable conformations, or those folding to poorly- or non-designable conformations.ResultsFirst, we generate all possible compact lattice conformations for the specified shape (a hexagon or a triangle) on the 2D triangular lattice. Then we generate all possible binary hydrophobic/polar (H/P) sequences and by using a specified energy function, thread them through all of these compact conformations. If for a given sequence the lowest energy is obtained for a particular lattice conformation we assume that this sequence folds to that conformation. Highly-designable conformations have many H/P sequences folding to them, while poorly-designable conformations have few or no H/P sequences. We classify sequences as folding to either highly – or poorly-designable conformations. We have randomly selected subsets of the sequences belonging to highly-designable and poorly-designable conformations and used them to train several different standard machine learning algorithms.ConclusionBy using these machine learning algorithms with ten-fold cross-validation we are able to classify the two classes of sequences with high accuracy – in some cases exceeding 95%.

Prediction of protein loop conformations using multiscale modeling methods with physical energy scoring functions

This article examines ab initio methods for the prediction of protein loops by a computational strategy of multiscale conformational sampling and physical energy scoring functions. Our approach consists of initial sampling of loop conformations from lattice-based low-resolution models followed by refinement using all-atom simulations. To allow enhanced conformational sampling, the replica exchange method was implemented. Physical energy functions based on CHARMM19 and CHARMM22 parameterizations with generalized Born (GB) solvent models were applied in scoring loop conformations extracted from the lattice simulations and, in the case of all-atom simulations, the ensemble of conformations were generated and scored with these models. Predictions are reported for 25 loop segments, each eight residues long and taken from a diverse set of 22 protein structures. We find that the simulations generally sampled conformations with low global root-mean-square-deviation (RMSD) for loop backbone coordinates from the known structures, whereas clustering conformations in RMSD space and scoring detected less favorable loop structures. Specifically, the lattice simulations sampled basins that exhibited an average global RMSD of 2.21 +/- 1.42 A, whereas clustering and scoring the loop conformations determined an RMSD of 3.72 +/- 1.91 A. Using CHARMM19/GB to refine the lattice conformations improved the sampling RMSD to 1.57 +/- 0.98 A and detection to 2.58 +/- 1.48 A. We found that further improvement could be gained from extending the upper temperature in the all-atom refinement from 400 to 800 K, where the results typically yield a reduction of approximately 1 A or greater in the RMSD of the detected loop. Overall, CHARMM19 with a simple pairwise GB solvent model is more efficient at sampling low-RMSD loop basins than CHARMM22 with a higher-resolution modified analytical GB model; however, the latter simulation method provides a more accurate description of the all-atom energy surface, yet demands a much greater computational cost.

Torsional random-walk statistics on lattices using convolution on crystallographic motion groups

This paper presents a new algorithm for generating the conformational statistics of lattice polymer models. The inputs to the algorithm are the distributions of poses (positions and orientations) of reference frames attached to sequentially proximal bonds in the chain as it undergoes all possible torsional motions in the lattice. If z denotes the number of discrete torsional motions allowable around each of the n bonds, our method generates the probability distribution in end-to-end pose corresponding to all of the zn independent lattice conformations in O(nD+1) arithmetic operations for lattices in D-dimensional space. This is achieved by dividing the chain into short segments and performing multiple generalized convolutions of the pose distribution functions for each segment. The convolution is performed with respect to the crystallographic space group for the lattice on which the chain is defined. The formulation is modified to include the effects of obstacles (excluded volumes) and to calculate the frequency of the occurrence of each conformation when the effects of pairwise conformational energy are included. In the latter case (which is for three dimensional lattices only) the computational cost is O(z4n4). This polynomial complexity is a vast improvement over the O(zn) exponential complexity associated with the brute-force enumeration of all conformations. The distribution of end-to-end distances and average radius of gyration are calculated easily once the pose distribution for the full chain is found. The method is demonstrated with square, hexagonal, cubic and tetrahedral lattices.

Dynamics of Bacteriophage T4 Presynaptic Filament Assembly from Extrinsic Fluorescence Measurements of Gp32-Single-stranded DNA Interactions

In the bacteriophage T4 homologous recombination system, presynaptic filament assembly on single-stranded (ssDNA) DNA requires UvsX recombinase, UvsY mediator, and Gp32 ssDNA-binding proteins. Gp32 exerts both positive and negative effects on filament assembly: positive by denaturing ssDNA secondary structure, and negative by competing with UvsX for ssDNA binding sites. UvsY is believed to help UvsX displace Gp32 from the ssDNA. To test this model we developed a real-time fluorescence assay for Gp32-ssDNA interactions during presynapsis, based on changes in the fluorescence of a 6-iodoacetamidofluorescein-Gp32 conjugate. Results demonstrate that the formation of UvsX presynaptic filaments progressively disrupts Gp32-ssDNA interactions. Under stringent salt conditions the disruption of Gp32-ssDNA by UvsX is both ATP- and UvsY-dependent. The displacement of Gp32 from ssDNA during presynapsis requires ATP binding, but not ATP hydrolysis, by UvsX protein. Likewise, UvsY-mediated presynapsis strongly requires UvsY-ssDNA interactions, and is optimal at a 1:1 stoichiometry of UvsY to UvsX and/or ssDNA binding sites. Presynaptic filaments formed in the presence of UvsY undergo assembly/collapse that is tightly coupled to the ATP hydrolytic cycle and to stringent competition for ssDNA binding sites between Gp32 and various nucleotide-liganded forms of UvsX. The data directly support the Gp32 displacement model of UvsY-mediated presynaptic filament assembly, and demonstrate that the transient induction of high affinity UvsX-ssDNA interactions by ATP are essential, although not sufficient, for Gp32 displacement. The underlying dynamics of protein-ssDNA interactions within presynaptic filaments suggests that rearrangements of UvsX, UvsY, and Gp32 proteins on ssDNA may be coupled to central processes in T4 recombination metabolism.

Homology modeling of tubulin: influence predictions for microtubule’s biophysical properties

Using comparative modeling, we have generated structural models of 475 alpha and beta tubulins. Using these models, we observed a global, structural similarity between the tubulin isotypes. However, a number of subtle differences in the isotypes physical properties, including net electric charges, solvent accessible surface areas, and electric dipole moments were also apparent. In order to examine the roles that these properties may play in microtubule (MT) assembly and stability, we have created a model to evaluate the dipole-dipole interaction energies of varying MT lattice conformations, using human tubulin isotypes as particularly important examples. We conclude that the dipole moments of each tubulin isotype may influence their functional characteristics within the cell, resulting in differences for MT assembly kinetics and stability.

Three-Helix Bundle DNA Tiles Self-Assemble into 2D Lattice or 1D Templates for Silver Nanowires

We present a DNA nanostructure, the three-helix bundle (3HB), which consists of three double helical DNA domains connected by six immobile crossover junctions such that the helix axes are not coplanar. The 3HB motif presents a triangular cross-section with one helix lying in the groove formed by the other two. By differential programming of sticky-ends, 3HB tiles can be arrayed in two distinct lattice conformations: one-dimensional filaments and two-dimensional lattices. Filaments and lattices have been visualized by high-resolution, tapping mode atomic force microscopy (AFM) under buffer. Their dimensions are shown to be in excellent agreement with designed structures. We also demonstrate an electroless chemical deposition for fabricating metallic nanowires templated on self-assembled filaments. The metallized nanowires have diameters down to 20 nm and display Ohmic current-voltage characteristic.

Comparing Folding Codes in Simple Heteropolymer Models of Protein Evolutionary Landscape: Robustness of the Superfunnel Paradigm

Understanding the evolution of biopolymers is a key element in rationalizing their structures and functions. Simple exact models (SEMs) are well-positioned to address general principles of evolution as they permit the exhaustive enumeration of both sequence and structure (conformational) spaces. The physics-based models of the complete mapping between genotypes and phenotypes afforded by SEMs have proven valuable for gaining insight into how adaptation and selection operate among large collections of sequences and structures. This study compares the properties of evolutionary landscapes of a variety of SEMs to delineate robust predictions and possible model-specific artifacts. Among the models studied, the ruggedness of evolutionary landscape is significantly model-dependent; those derived from more proteinlike models appear to be smoother. We found that a common practice of restricting protein structure space to maximally compact lattice conformations results in (i.e., “designs in”) many encodable (designable) structures that are not otherwise encodable in the corresponding unrestrained structure space. This discrepancy is especially severe for model potentials that seek to mimic the major role of hydrophobic interactions in protein folding. In general, restricting conformations to be maximally compact leads to larger changes in the model genotype-phenotype mapping than a moderate shifting of reference state energy of the model potential function to allow for more specific encoding via the “designing out” effects of repulsive interactions. Despite these variations, the superfunnel paradigm applies to all SEMs we have tested: For a majority of neutral nets across different models, there exists a funnel-like organization of native stabilities for the sequences in a neutral net encoding for the same structure, and the thermodynamically most stable sequence is also the most robust against mutation.