Anomalous behavior of synchronization in a mutually coupled identical thomas oscillators

Synchronization in a mutually coupled identical Thomas oscillators with non-linear coupling schemes show unusual characteristics than with linear coupling. Linearly coupled systems show expected complete synchronization (CS). Whereas with non-linear coupling there are windows of lag(LS) or anti-lag(ALS) synchronizations after CS in the intermediate rage of coupling followed by CS again, not achieved earlier. More new features in synchronization are observed for a small window of both types of coupling when uncoupled system's dynamics is at the border of chaotic and quasi-periodic regimes. The stability of synchronized states in all the cases for weak and moderate coupling remain slightly below the stable-unstable boundary towards the stable region. Therefore stable synchronized states are not too sensitive to perturbation, means perturbation dies very slowly.Comment: 16 pages, 21 figure

High-Resolution 3D Structure Determination of Kaliotoxin by Solid-State NMR Spectroscopy

High-resolution solid-state NMR spectroscopy can provide structural information of proteins that cannot be studied by X-ray crystallography or solution NMR spectroscopy. Here we demonstrate that it is possible to determine a protein structure by solid-state NMR to a resolution comparable to that by solution NMR. Using an iterative assignment and structure calculation protocol, a large number of distance restraints was extracted from 1H/1H mixing experiments recorded on a single uniformly labeled sample under magic angle spinning conditions. The calculated structure has a coordinate precision of 0.6 Å and 1.3 Å for the backbone and side chain heavy atoms, respectively, and deviates from the structure observed in solution. The approach is expected to be applicable to larger systems enabling the determination of high-resolution structures of amyloid or membrane proteins

Dynamics, Synchronization and Pattern Formation in Coupled Thomas Oscillators

This thesis work is mainly about dynamics, synchronization and pattern formation in coupled Thomas oscillators in the chaotic regime. Two mutually coupled identical oscillators as well as oscillators in a network are considered. The synchronizability of Thomas oscillators on various networks are established via master stability function formalism under linear coupling scheme for identical setting of oscillators. For pattern formation, local, nonlocal, global coupling schemes on a ring are considered. The special nature of Thomas oscillators and its connection to active Brownian particles are established via numerical simulations. The study of dynamics and synchronization of two mutually coupled oscillators are based on the calculations of Lyapunov exponents, Bifurcation diagram, phase portrait, Transverse Lyapunov exponents, Pearson coefficients, Transverse distance and similarity index. Two different values of system parameter are used in the chaotic regime under linear and nonlinear coupling schemes. In both cases the coupled system undergoes a period of transient chaos. Three different types of initial conditions are used to study the transients and synchronization. For low value of coupling strength, the system shows weak forms of synchronization. For linear coupling, the nature of synchronization agrees with the predictions of the general observation found in prototypical Rössler system and Lorenz system. The nature of synchronization is much more complex in the case of nonlinear coupling. The system bifurcates to lag or anti-lag synchronization even after achieving complete synchronization. It also shows space-lag(swarming) and multistability with nonlinear coupling. The emergence of lag or anti-lag is confirmed with similarity index calculation. Our calculation of largest transverse Lyapunov exponent for nonlinear coupling exactly matches with the predictions of Pearson coefficient and Transverse distance which would have been lost on any linearization of the transverse perturbation equation for the coupled system. The variables in our system are components of velocity of a particle moving in a force field and indeed, there are velocity-velocity correlations like in coupled active Brownian particles. Therefore, we claim that the stochastic dynamics of active Brownian particles can be modeled by chaotic dynamics of Thomas system. We found the important results that lag / anti-lag and space lag(swarming) synchronization within the regime of complete synchronization. The synchronization properties of Thomas oscillators in a network is studied for identical oscillators with linear coupling scheme via master stability function formulation. For the set of system parameters in the chaotic regime, they show type-I and type-II behavior of MSF. The synchronizability for various network architectures are also studied. For the study of pattern formation, we considered hundred Thomas oscillators on a ring with nonlocal coupling with nonlinear coupling function. We could achieve chimera states for a certain range of intermediate coupling constants. The Chimera states are quantified by means of strength of incoherence and discontinuity measure calculation. The system shows cluster, chimera, multi-chimera as the coupling is increased. We could also achieve chimera states for nearly local coupling with nonlinear coupling functions. The global coupling shows complete synchronization of oscillators. The obtained result of pattern formation in the network is useful to understand the dynamics of active Brownian particles. For active Brownian particles, the probability distribution of velocities resembles the present observation of the chimera states. The discontinuous jump observed in the case of zero system parameter corresponds to a first order phase transition and matches with the statistical model of self-propelled particles

Strukturuntersuchungen an der periplasmatischen Domäne von CitA und DcuS mit NMR-Spektroskopie

Zwei-Komponenten regulatorische Systeme sind die häufigsten Systeme für transmembrane Signaltransduktion in Bakterien und spielen eine Hauptrolle bei der zellulären Adaptation an die Bedingungen der Umwelt und Stress. Sie bestehen aus zwei verschiedenen Proteinen, einer sensorischen Histidinkinase, die normalerweise in der Membran lokalisiert ist, und einem verwandten Antwortregulator im Cytoplasma. Für diese Systeme gibt es eine Fülle von molekularbiologischen Studien. Trotzdem sind keine Strukturinformationen über die transmembrane Signaltransduktion vorhanden. Das Ziel dieser Untersuchung war es, Informationen über die Struktur und Dynamik der Signalerkennung und -transduktion von der periplasmatischen sensorischen Domäne über den membranständigen zwei-Komponenten Sensor in die cytoplasmatische Domäne zu erhalten. In dieser Arbeit werden Strukturuntersuchungen mittels NMR an der periplasmatischen Domäne von zwei Histidinkinasen präsentiert. DcuS und CitA sind bakterielle Sensorhistidinkinasen, die eine transmembrane Domäne besitzen. Sie sind Teil eines zwei-Komponenten Signaltransduktionssystems, das den Transport und Metabolismus von Di- und Tri-Carboxylaten in Abhängigkeit ihrer Konzentration in der Umgebung regulieren. Ihre periplasmitischen Domänen (DcuS-PD und CitAP) sind homolog, haben eine PAS-Domäne und eine Bindungsstelle für die Carboxylate. CitA fungiert als ein hochspezifischer Citratrezeptor während DcuS von einer Reihe von C4-Dicarboxylaten wie Fumarat und Succinat stimuliert wird. Als ein erster Schritt in Hinblick auf die Aufklärung des Signaltransduktionsprozesses wurde die Lösungs-NMR-Struktur der periplasmatischen Domäne von DcuS gelöst. Die Struktur wurde mit residualen dipolaren Kopplungen (RDCs), die über eine neuartige Strategie zur simultanen Messung von RDCs mit minimalem Resonanzüberlap gemessen wurden, verfeinert. Die Bindungstasche von DcuS-PD für einige C4 Di-Carboxylate wurde mittels 15N-1H HSQC basierter Titrationen definiert. Der Einfluss der Ligandenbindung an DcuS-PD war schwach.Weder Veränderungen der chemischen Verschiebungen noch Anstieg der Signalintensitäten für Reste außerhalb der Bindungstasche wurden beobachtet. Deshalb blieb der Mechanismus der Signalransduktion ungewiss. Lösungs-NMR-Strukturen von CitAP konnten aufgrund starker Linienverbreiterung, die in den NMR-Spektren beobachtet wurde, nicht gelöst werden. Konformationeller Austausch war der Hauptgrund der Linienverbreiterung. Die Kristallstrukturen der citrat-freien und gebundenen Form von CitAP konnten aufgeklärt werden. Hauptunterschiede wurden in der Citratbindungsregion und in der C-terminalen Region des Proteins beobachtet. Zusätzlich veränderten sich die chemischen Verschiebungen und die HetNOE-Werte in diesen Teilen des Proteins stark. In der citrat-gebundenen Struktur wurde ein Na+-Ion zwischen die Nterminale Helix und die beta-Faltblätter gesetzt. Das wurde auch durch NMR-Titrationen bestätigt. Damit könnte CitAP in Lösung sowohl an der Erkennung von Citrat als auch von Na+ beteiligt sein. Überraschenderweise passen die für cirtatfreies CitAP gemessenen RDCs besser zu der citratgebundenen Struktur von CitAP. Das deutet darauf hin, dass in Lösung eine vorgeformte Bindungstasche von CitAP vorliegt. Nichtsdestotrotz ermöglichten die spezifische strukturellen Unterschiede zwischen der citratfreien und den -gebundenen Strukturen den Vorschlag eines Modells für den Mechanismus der Signaltransduktion. Dieses Modell passt zu den verfügbaren NMR-Daten und ist auch ähnlich zu dem für Aspartatsensoren beschriebenen Mechanismus der Signaltransduktion

Dynamics of a Charged Thomas Oscillator in an External Magnetic Field

In this letter, we provide a detailed numerical examination of the dynamics of a charged Thomas oscillator in an external magnetic field. We do so by adopting and then modifying the cyclically symmetric Thomas oscillator to study the dynamics of a charged particle in an external magnetic field. These dynamical behaviours for weak and strong field strength parameters fall under two categories; conservative and dissipative. The system shows a complex quasi-periodic attractor whose topology depends on initial conditions for high field strengths in the conservative regime. There is a transition from adiabatic motion to chaos on decreasing the field strength parameter. In the dissipative regime, the system is chaotic for weak field strength and weak damping but shows a limit cycle for high field strengths. Such behaviour is due to an additional negative feedback loop that comes into action at high field strengths and forces the system dynamics to be stable in periodic oscillations. For weak damping and weak field strength, the system dynamics mimic Brownian motion via chaotic walks.Comment: 9 pages, 48 figure

Recovery of Bulk Proton Magnetization and Sensitivity Enhancement in Ultrafast Magic-Angle Spinning Solid-State NMR

The sensitivity of solid-state NMR experiments is limited by the proton magnetization recovery delay and by the duty cycle of the instrument. Ultrafast magic-angle spinning (MAS) can improve the duty cycle by employing experiments with low-power radio frequency (RF) irradiation which reduce RF heating. On the other hand, schemes to reduce the magnetization recovery delay have been proposed for low MAS rates, but the enhancements rely on selective transfers where the bulk of the ¹H magnetization pool does not contribute to the transfer. We demonstrate here that significant sensitivity enhancements for selective and broadband experiments are obtained at ultrafast MAS by preservation and recovery of bulk ¹H magnetization. We used [¹³C, ¹⁵N]-labeled glutamine as a model compound, spinning in a 1.3 mm rotor at a MAS frequency of 65 kHz. Using low-power ¹H RF (13.4 kHz), we obtain efficient ¹H spin locking and ¹H–¹³C decoupling at ultrafast MAS. As a result, large amounts of ¹H magnetization, from 35% to 42% of the initial polarization, are preserved after cross-polarization and decoupling. Restoring this magnetization to the longitudinal axis using a flip-back pulse leads to an enhancement of the sensitivity, an increase ranging from 14% to 21% in the maximal achievable sensitivity regime and from 24% to 50% in the fast pulsing regime, and to a shortening of the optimal recycling delay to 68% of its original duration. The analysis of the recovery and sensitivity curves reveals that the sensitivity gains do not rely on a selective transfer where few protons contribute but rather on careful conservation of bulk ¹H magnetization. This makes our method compatible with broadband experiments and uniformly labeled materials, in contrast to the enhancement schemes proposed for low MAS. We tested seven different cross-polarization schemes and determined that recovery of bulk ¹H magnetization is a general method for sensitivity enhancement. The physical insight gained about the behavior of proton magnetization sharing under spin lock will be helpful to break further sensitivity boundaries, when even higher external magnetic fields and faster spinning rates are employed

Role of G326 in Determining the Aggregation Propensity of R3 Tau Repeat: Insights from Studies on R1R3 Tau Construct

The Microtubule-binding repeat region (MTBR) of Tau has been studied extensively due to its pathological implications in neurodegenerative diseases like Alzheimer’s disease. The pathological property of MTBR is mainly due to the R3 repeat’s high propensity for self-aggregation, highlighting the critical molecular grammar of the repeat. Utilizing the R1R3 construct (WT) and its G326E mutant (EE), we determine the distinct characteristics of various peptide segments that modulate the aggregation propensity of the R3 repeat using NMR spectroscopy. Through time-dependent experiments, we have identified 317KVTSKCGS324 in R3 repeat as the aggregation initiating motif (AIM) due to its role at the initial stages of aggregation. The G326E mutation induces changes in conformation and dynamics at the AIM, thereby effectively abrogating the aggregation propensity of the R1R3 construct. We further corroborate our findings through MD simulations and propose that AIM is a robust site of interest for tauopathy drug design

NMR Relaxation Experiments Probe Monomer–Fibril Interaction and Identify Critical Interacting Residues Responsible for Distinct Tau Fibril Morphologies

Tau aggregation is governed by secondary processes, a major pathological pathway for tau protein fibril propagation, yet its molecular mechanism remains unknown. This work uses saturation transfer and lifetime line-broadening experiments to identify the critical residues involved in these secondary processes. Distinct residue-specific NMR relaxation parameters were obtained for the truncated three repeat tau construct (K19) in equilibrium with structurally different, self-aggregated (saK19) or heparin-induced (hK19) fibrils. The interacting residues are restricted to R3 repeat for hK19 and to R3, R4, and R′ repeats for saK19 fibrils. Furthermore, the relaxation profiles of tau monomers in equilibrium with the structurally comparable, in vitro pathological fibrils (tauAD and tauCTE) were similar but distinct from hK19 or saK19 fibrils. Thus, residue-specific relaxation identifies the important residues involved in the binding of monomers to the fibrils. The relaxation profile of the monomers in equilibrium with the NMR invisible fibril seeds potentially distinguishes the distinct structures of tau fibrils