Topological Relaxation Research Articles

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends.

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ_{d,R} for rings of length N_{R} blended with linear chains of length N_{l} to scale as τ_{d,R}∼N_{R}^{2}N_{L}^{3.4}.

Assembly of dysprosium(III) cubanes in a metal-organic framework with an ecu topology and slow magnetic relaxation.

A dysprosium(III) metal-organic framework constructed using dysprosium(III) cubanes as secondary building units has been reported to exhibit field-induced slow magnetic relaxation behavior and an unprecedented ecu topology, which is the first example of an 8-connected Ln-cubane-based framework material and a rare Dy4-MOF showing slow magnetic relaxation.

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation.

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

Nucleosome destabilization by polyamines

The roles and molecular interactions of polyamines (PAs) in the nucleus are not fully understood. Here their effect on nucleosome stability, a key regulatory factor in eukaryotic gene control, is reported, as measured in agarose embedded nuclei of H2B-GFP expressor HeLa cells. Nucleosome stability was assessed by quantitative microscopy [1,2] in situ, in close to native state of chromatin, preserving the nucleosome constrained topology of the genomic DNA. A robust destabilizing effect was observed in the millimolar concentration range in the case of spermine, spermidine as well as putrescine, which was strongly pH and salt concentration-dependent, and remained significant also at neutral pH. The integrity of genomic DNA was not affected by PA treatment, excluding DNA break-elicited topological relaxation as a factor in destabilization. The binding of PAs to DNA was demonstrated by the displacement of ethidium bromide, both from deproteinized nuclear halos and from plasmid DNA. The possibility that DNA methylation patterns may be influenced by PA levels is contemplated in the context of gene expression and DNA methylation correlations identified in the NCI-60 panel-based CellMiner database: methylated loci in subsets of high-ODC1 cell lines and the dependence of PER3 DNA methylation on PA metabolism.

Topological Friction and Relaxation Dynamics of Spatially Confined Catenated Polymers.

We study catenated ring polymers confined inside channels and slits with Langevin dynamics simulations and address how the contour position and size of the interlocked or physically linked region evolve with time. We show that the catenation constraints generate a drag, or topological friction, that couples the contour motion of the interlocked regions. Notably, the coupling strength decreases as the interlocking is made tighter, but also shorter, by confinement. Though the coupling strength differs for channel and slit confinement, the data outline a single universal curve when plotted against the size of the linked region. Finally, we study how the relaxation kinetics changes after one of the rings is cut open and conclude that considering interlocked circular polymers is key for isolating the manifestations of topological friction. The results ought to be relevant for linked biomolecules in experimental or biological confining conditions.

Relaxing topological surfaces in four dimensions

In this paper, we show the use of visualization and topological relaxation methods to analyze and understand the underlying structure of mathematical surfaces embedded in 4D. When projected from 4D to 3D space, mathematical surfaces often twist, turn, and fold back on themselves, leaving their underlying structures behind their 3D figures. Our approach combines computer graphics, relaxation algorithm, and simulation to facilitate the modeling and depiction of 4D surfaces, and their deformation toward the simplified representations. For our principal test case of surfaces in 4D, this for the first time permits us to visualize a set of well-known topological phenomena beyond 3D that otherwise could only exist in the mathematician’s mind. Understanding a fairly long mathematical deformation sequence can be aided by visual analysis and comparison over the identified “key moments” where only critical changes occur in the sequence. Our interface is designed to summarize the deformation sequence with a significantly reduced number of visual frames. All these combine to allow a much cleaner exploratory interface for us to analyze and study mathematical surfaces and their deformation in topological space.

Crystal Growth in Polyethylene by Molecular Dynamics: The Crystal Edge and Lamellar Thickness.

We carried out large-scale atomistic molecular dynamics simulations to study the growth of twin lamellar crystals of polyethylene initiated by small crystal seeds. By examining the size distribution of the stems—straight crystalline polymer segments—we show that the crystal edge has a parabolic profile. At the growth front, there is a layer of stems too short to be stable, and new stable stems are formed within this layer, leading to crystal growth. Away from the edge, the lengthening of the stems is limited by a lack of available slack length in the chains. This frustration can be relieved by mobile crystal defects that allow topological relaxation by traversing through the crystal. The results shed light on the process of polymer crystal growth and help explain initial thickness selection and lamellar thickening.

Nucleosome stability measured in situ by automated quantitative imaging

Current approaches have limitations in providing insight into the functional properties of particular nucleosomes in their native molecular environment. Here we describe a simple and powerful method involving elution of histones using intercalators or salt, to assess stability features dependent on DNA superhelicity and relying mainly on electrostatic interactions, respectively, and measurement of the fraction of histones remaining chromatin-bound in the individual nuclei using histone type- or posttranslational modification- (PTM-) specific antibodies and automated, quantitative imaging. The method has been validated in H3K4me3 ChIP-seq experiments, by the quantitative assessment of chromatin loop relaxation required for nucleosomal destabilization, and by comparative analyses of the intercalator and salt induced release from the nucleosomes of different histones. The accuracy of the assay allowed us to observe examples of strict association between nucleosome stability and PTMs across cell types, differentiation state and throughout the cell-cycle in close to native chromatin context, and resolve ambiguities regarding the destabilizing effect of H2A.X phosphorylation. The advantages of the in situ measuring scenario are demonstrated via the marked effect of DNA nicking on histone eviction that underscores the powerful potential of topological relaxation in the epigenetic regulation of DNA accessibility.

Topological Control on the Structural Relaxation of Atomic Networks under Stress.

Upon loading, atomic networks can feature delayed irreversible relaxation. However, the effect of composition and structure on relaxation remains poorly understood. Herein, relying on accelerated molecular dynamics simulations and topological constraint theory, we investigate the relationship between atomic topology and stress-induced structural relaxation, by taking the example of creep deformations in calcium silicate hydrates (C─S─H), the binding phase of concrete. Under constant shear stress, C─S─H is found to feature delayed logarithmic shear deformations. We demonstrate that the propensity for relaxation is minimum for isostatic atomic networks, which are characterized by the simultaneous absence of floppy internal modes of relaxation and eigenstress. This suggests that topological nanoengineering could lead to the discovery of nonaging materials.

Geometry and topology optimization of sheet metal profiles by using a branch‐and‐bound framework

In this paper well established procedures from partial differential equation (PDE)‐constrained and discrete optimization are combined in a new way to find an optimal design of a multi‐chambered profile. Given a starting profile design, a load case and corresponding design constraints (e.g. sheet thickness, chamber sizes), the aim is to find an optimal subdivision into a predefined number of chambers with optimal shape subject to structural stiffness. In the presented optimization scheme a branch‐and‐bound tree is generated with one additional chamber in each level. Before adding the next chamber, the geometry of the profile is optimized. Then a relaxation of a topology optimization problem is solved. Based on this relaxation, a best fitting feasible topology subject to manufacturability conditions is determined using a new mixed integer method employing shortest paths. To improve the running time, the finite element simulations for the geometry optimization and topology relaxation are performed with different levels of accuracy. Finally, numerical experiments are presented including different starting geometries, load scenarios and mesh sizes.

Point-pattern matching based on point pair local topology and probabilistic relaxation labeling

This paper presents a robust point-pattern matching (PPM) algorithm, in which the invariant feature and probabilistic relaxation labeling are combined to improve the assignment accuracy and efficiency. A local feature descriptor, namely, point pair local topology (PPLT), is proposed first. The feature descriptor is defined by histogram which is constructed using the weighting of distance measures and angle measures based on local point pair. We use the matching scores of point pair local topology descriptor’s statistic test to define new compatibility coefficients. Then, the robust support functions are constructed based on the obtained compatibility coefficients. Finally, according to the relaxed iterations of matching probability matrix and the mapping constraints required by the bijective correspondence, the correct matching results are obtained. A number of comparison and evaluation experiments on both synthetic point sets and real-world data demonstrate that the proposed algorithm performs better in the presence of outliers and positional jitter. In addition, it achieves the superior performance under similarity and even nonrigid transformation among point sets in the meantime compared with state-of-the-art approaches.

Self-Healing Biomaterials: Entangled DNA Networks

The material that the cell uses to store genetic information actually becomes self-healing material when it must be segregated, transported across the length of the cell even in the face of its entanglements with itself, or condensed to prepare for this large scale transport. This is a naturally-occuring soft material that is capable of self-repair. Moreover, there is evidence that the material first senses the possibility of a stress-inducing, potentially fatal (to genome stability) topological entanglement, and quickly fortifies itself to limit or prevent the damage. The issue of how topology is conserved (controlled) by this type of biomaterial is itself an interesting mystery. I will present our experimental results using a bottom-up design approach, borrowing the naturally-occurring materials from the cell to study the design principles of this behavior. We incorporated micron-sized particles in lambda-DNA entangled networks in the presence of the topoisomerase II motor that performs the strand passage, at controllable ratio of enzyme units per average DNA entanglement and ATP concentration. We used bright-field microscopy to directly track the movement of the particles, which couple to the DNA fluctuating movement. Our observed scaling behavior suggests entangled dynamics in the bare DNA system, and nonentangled Rouse dynamics, with enzyme performing topological constraint relaxation, in the DNA+topo II + ATP system. These very time-dependent scaling behaviors are all predicted theoretically for entangled polymers with inclusion of a constrained release process in the case of presence of active topo II. The material self-heals to such a degree that, at saturating topoisomerase II motor and ATP concentrations, the long DNA polymer molecules do not even “feel” one another despite being entangled. We compare our experimental results to predictions of the constraint release model, measuring the “healing rate” at different dynamical length scales.

Control of Directionality in Streptomyces Phage φBT1 Integrase-Mediated Site-Specific Recombination

Streptomyces phage φBT1 integrates its genome into the attB site of the host chromosome with the attP site to generate attL and attR. The φBT1 integrase belongs to the large serine recombinase subfamily which directly binds to target sites to initiate double strand breakage and exchange. A recombination directionality factor (RDF) is commonly required for switching integration to excision. Here we report the characterization of the RDF protein for φBT1 recombination. The RDF, is a phage-encoded gp3 gene product (28 KDa), which allows efficient active excision between attL and attR, and inhibits integration between attB and attP; Gp3 can also catalyze topological relaxation with the integrase of supercoiled plasmids containing a single excision site. Further study showed that Gp3 could form a dimer and interact with the integrase whether it bound to the substrate or not. The synapse formation of attL or attR alone with integrase and Gp3 showed that synapsis did not discriminate between the two sites, indicating that complementarity of central dinucleotides is the sole determinant of outcome in correct excision synapses. Furthermore, both in vitro and in vivo evidence support that the RDFs of φBT1 and φC31 were fully exchangeable, despite the low amino acid sequence identity of the two integrases.

Micromechanics of dilatancy and critical state in granular matter

To understand the microscale mechanisms that govern dilatancy and critical state, the changes in topology of a granular assembly during numerical simulations of quasi-static deformation are analysed. In this article we show that explanations for these unique features of granular matter lie in the interplay of evolving frequency of microscopic topological events (flips) and elastic relaxation of particles, both of which are consequences of the history-dependent organisation of interparticle forces in force chains. Specifically, dilatancy has two components – one is the result of increasing frequency of flips and the other arises from the elementary volume increases that accompany the flips as elastic relaxation. The critical state arises as the balance between the dilation rate and the compaction rate under shear-induced disturbances.

Double-stranded DNA homology produces a physical signature

DNA is found in the cell largely as a negatively supercoiled molecule. This high-energy form of the genetic material can engender sequence-dependent structures, such as cruciforms, Z-DNA, or H-DNA, even though they are not favored by conventional conditions in relaxed DNA. A key feature of DNA in living systems is the presence of homology. We have sought homology-dependent structural phenomena based on topological relaxation. Using two-dimensional electrophoresis, we demonstrate a structural transition in supercoiled plasmid molecules containing homologous segments. Atomic force microscopy (AFM) reveals a dumbbell structure in molecules whose linking difference is beyond the transition point. The position of the dumbbell shaft is a function of the site of homology, and its extent is proportional to the linking difference. Second-site-reversion electrophoresis data support the notion that the shaft contains PX-DNA. Predicted cross-linking patterns generated in vivo suggest that homology-dependent structures can occur within the cell.

A new activity of anti-HIV and anti-tumor protein GAP31: DNA adenosine glycosidase – Structural and modeling insight into its functions

We report here the high-resolution atomic structures of GAP31 crystallized in the presence of HIV-LTR DNA oligonucleotides systematically designed to examine the adenosine glycosidase activity of this anti-HIV and anti-tumor plant protein. Structural analysis and molecular modeling lead to several novel findings. First, adenine is bound at the active site in the crystal structures of GAP31 to HIV-LTR duplex DNA with 5′ overhanging adenosine ends, such as the 3′-processed HIV-LTR DNA but not to DNA duplex with blunt ends. Second, the active site pocket of GAP31 is ideally suited to accommodate the 5′ overhanging adenosine of the 3′-processed HIV-LTR DNA and the active site residues are positioned to perform the adenosine glycosidase activity. Third, GAP31 also removes the 5′-end adenine from single-stranded HIV-LTR DNA oligonucleotide as well as any exposed adenosine, including that of single nucleotide dAMP but not from AMP. Fourth, GAP31 does not de-purinate guanosine from di-nucleotide GT. These results suggest that GAP31 has DNA adenosine glycosidase activity against accessible adenosine. This activity is distinct from the generally known RNA N-glycosidase activity toward the 28S rRNA. It may be an alternative function that contributes to the antiviral and anti-tumor activities of GAP31. These results provide molecular insights consistent with the anti-HIV mechanisms of GAP31 in its inhibition on the integration of viral DNA into the host genome by HIV-integrase as well as irreversible topological relaxation of the supercoiled viral DNA.

Current sheets during spontaneous reconnection in a current-carrying fusion plasma

An analysis of plasma dynamics during impulsive magnetic reconnection events in the RFX-mod reversed field pinch (RFP) is performed by means of a large set of magnetic in-vessel coils and of an insertable edge probe, equipped with a matrix of electrostatic (Langmuir) and magnetic probes. It is observed that reconnection of field lines, which leads to a global reconfiguration of the magnetic topology (relaxation), is associated with the rapid formation of a strongly localized magnetic perturbation characterized by a main m = 0 periodicity, due to enhanced dynamo modes activity. Soon after its formation, the m = 0 perturbation is observed to move in the toroidal direction and is shown to correspond to a poloidal current sheet, whose existence was predicted by three-dimensional MHD numerical simulations on RFP sustainment through magnetic reconnection processes. A reconstruction of the current density structure associated with the rotating magnetic perturbation is performed by means of the insertable probe, along with an investigation of the large induced modification of electron temperature, density and plasma velocity shear at the edge.

A systematic enumeration of local topological relaxation mechanisms in amorphous networks and their efficiency in network relaxation

We consider the infinite hierarchy of local collective rearrangements on bond networks that preserves the valency of each atom and explicitly enumerate those involving 4, 5, and 6 particles. The only 4-particle rearrangement is identical to the Wooten-Winer-Weaire (WWW) mechanism. Each rearrangement mechanism is applied in a Monte Carlo (MC) algorithm in order to determine the rate at which it equilibrate a network and relax the structure at equilibrium. At low temperature the 4-particle mechanism provides the fastest relaxation rate but we find that there is a crossover with increasing temperature to 5-particle mechanisms.

Topological Structure and Relaxation Properties of Branched Polymers

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Dynamic strain in magnetic films on piezoelectric crystals

Reversible biaxial strain has been induced in ferromagnetic films of several lanthanum manganites which have been epitaxially grown on the (0 0 1) face of high-strain piezoelectric crystals of Pb(Mg 1/3Nb 2/3) 0.72Ti 0.28O 3 (PMN-PT). The strain-induced changes of the Curie temperature and the remanent magnetization have been observed. PMN-PT(0 0 1) crystals used as substrates are characterized with respect to their lattice parameters, domain-related surface topology and electric relaxation behavior. A sample consisting of a magnetic film on a piezo-crystal forms a simple and well-defined model system for strain-mediated magnetoelectric coupling.