Flip Dynamics Research Articles

Quenches in the Sherrington–Kirkpatrick model

The Sherrington–Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that locally aim to decrease energy. We analyse the energy at convergence for two distinct algorithmic classes, single-spin flip and synchronous dynamics, focusing on greedy and reluctant strategies. We provide precise numerical analysis of the finite size effects and conclude that, perhaps counter-intuitively, the reluctant algorithm is compatible with converging to the ground state energy density, while the greedy strategy is not. Inspired by the single-spin reluctant and greedy algorithms, we investigate two synchronous time algorithms, the sync-greedy and sync-reluctant algorithms. These synchronous processes can be analysed using dynamical mean field theory (DMFT), and a new backtracking version of DMFT. Notably, this is the first time the backtracking DMFT is applied to study dynamical convergence properties in fully connected disordered models. The analysis suggests that the sync-greedy algorithm can also achieve energies compatible with the ground state, and that it undergoes a dynamical phase transition.

Direct flipping dynamics and quantized enrichment of chirality at single-molecule resolution.

Chirality is an important aspect of nature, and numerous macroscopic methods have been developed to understand and control chirality. For the chiral tertiary amines, their flexible flipping process makes it possible to achieve high chiral controllability without bond formation and breaking. Here, we present a type of stable chiral single-molecule devices formed by tertiary amines, using graphene-molecule-graphene single-molecule junctions. These single-molecule devices allow real-time, in situ, and long-time measurements of the flipping process of an individual chiral nitrogen center with high temporal resolution. Temperature- and bias voltage-dependent experiments, along with theoretical investigations, revealed diverse chiral intermediates, indicating the regulation of the flipping dynamics by energy-related factors. Angle-dependent measurements further demonstrated efficient enrichment of chiral states using linearly polarized light by a symmetry-related factor. This approach offers a reliable means for understanding the chirality's origin, elucidating microscopic chirality regulation mechanisms, and aiding in the design of effective drugs.

Key influence factors in magneto-controlled motion of micro-nano graphite flakes

Magneto-controlling micro-nano materials’ motion is a promising way that enable the noncontact, remote, and nondestructive controlling of their macrostructure as well as functionalities. Here, an optical microscope with an electromagnet was constructed to in-situ monitor the magneto-controlled motion process microscopically. Taking micro-nano graphite flake (MGF) as a model system, we experimentally demonstrate the key factors that influence the magneto-controlling of materials’ motion. First, the product of intensity and gradient of the magnetic field (B∇B) has been confirmed as the dominant driving force and the flipping direction of the MGFs is accordingly determined by the vector direction of B×∇B. Second, quantitatively comparative experiments further revealed that the threshold driving force has an exponential relationship with the structural aspect ratio (b/a) of MGFs. Third, the critical magneto-driving force is found as proportional to the viscosity of the solvent. Accordingly, a dynamic model is developed that describes the flip of the diamagnetic flake under external magnetic field excitation considering the shape factor. It is shown experimentally that the model accurately predicts the flip dynamics of the flake under different magnetic field conditions. In addition, we also discovered the delay effect, multiple cycle acceleration effect, and the fatigue effects due to gas adsorption in magneto-controlled MGFs flipping. These findings can be used to achieve magneto-controlling materials’ macrostructure as well as their functionalities.

Investigation of the Flipping Dynamics of 1, N6-Ethenoadenine in Alkyladenine DNA Glycosylase.

Alkyladenine DNA glycosylase (AAG) is an essential enzyme responsible for maintaining genome integrity by repairing several DNA lesions damaged by alkylation or deamination. Understanding how it can recognize and excise the lesions thus lays the foundation for therapeutic treatment against lesion-associated diseases or cancers. However, the molecular details of how the lesion can be distinguished from the matched base by AAG and how it enters the cleavage site, ready for excision, are not fully elucidated. In this study, we have revealed the molecular details of the flipping dynamics of 1, N6-ethenoadenine (εA) not only in the form of free double-stranded DNA (dsDNA) but also in the form of the AAG-dsDNA complex. Our MD simulations and PMF calculations have shown that the flipping of εA and dA is thermodynamically disfavored in the free dsDNA, even though εA has a lower flipping energy barrier than dA. By sharp contrast, the flipping of εA is thermodynamically favored in AAG with an obvious free energy drop, while dA is equally stabilized before and after the flipping. Moreover, a comparison of the PMFs in the forms of free dsDNA and the AAG-dsDNA complex has pinpointed the role of AAG in discriminating εA against dA and facilitating the flipping of εA. Besides, the flipping process is simulated along the major and minor grooves, and our results have additionally demonstrated that the flipping is not directional in the free dsDNA while flipping along the major groove is kinetically more favorable than the minor groove in the AAG-dsDNA complex. Overall, our study has offered molecular insights into the flipping dynamics of εA and revealed its discrimination mechanism by AAG, which is expected to guide further enzyme engineering for therapeutic applications.

Free-Energy Landscape and Rate Estimation of the Aromatic Ring Flips in Basic Pancreatic Trypsin Inhibitors Using Metadynamics.

Aromatic side chains (phenylalanine and tyrosine) of a protein flip by 180° around the Cβ-Cγ axis (χ2 dihedral of the side chain), producing two symmetry-equivalent states. The study of ring flip dynamics with nuclear magnetic resonance (NMR) experiments helps to understand local conformational fluctuations. Ring flips are categorized as slow (milliseconds and onward) or fast (nanoseconds to near milliseconds) based on timescales accessible to NMR experiments. In this study, we investigated the ability of the infrequent metadynamics approach to estimate the flip rate and discriminate between slow and fast ring flips for eight individual aromatic side chains (F4, Y10, Y21, F22, Y23, F33, Y35, and F45) of the basic pancreatic trypsin inhibitor. Well-tempered metadynamics simulations were performed to estimate the ring-flipping free-energy surfaces for all eight aromatic residues. The results indicate that χ2 as a standalone collective variable (CV) is not sufficient to obtain computationally consistent results. Inclusion of a complementary CV, such as χ1(Cα-Cβ), solved the problem for most residues and enabled us to classify fast and slow ring flips. This indicates the importance of librational motions in ring flips. Multiple pathways and mechanisms were observed for residues F4, Y10, and F22. Recrossing events were observed for residues F22 and F33, indicating a possible role of friction effects in ring flipping. The results demonstrate the successful application of infrequent metadynamics to estimate ring flip rates and identify certain limitations of the approach.

Multi species asymmetric simple exclusion process with impurity activated flips

We obtain an exact matrix product steady state for a class of multi species asymmetric simple exclusion process with impurities, under periodic boundary condition. Alongside the usual hopping dynamics, an additional flip dynamics is activated only in the presence of impurities. Although the microscopic dynamics renders the system to be non-ergodic, exact analytical results for observables are obtained in steady states for a specific class of initial configurations. Interesting physical features including negative differential mobility and transition of correlations from negative to positive with changing vacancy density, have been observed. We discuss plausible connections of this exactly solvable model with multi lane asymmetric simple exclusion processes as well as enzymatic chemical reactions.

Lipid distributions and transleaflet cholesterol migration near heterogeneous surfaces in asymmetric bilayers

Specific and nonspecific protein-lipid interactions in cell membranes have important roles in an abundance of biological functions. We have used coarse-grained (CG) molecular dynamics (MD) simulations to assess lipid distributions and cholesterol flipping dynamics around surfaces in a model asymmetric plasma membrane containing one of six structurally distinct entities: aquaporin-1 (AQP1), the bacterial β-barrel outer membrane proteins OmpF and OmpX, the KcsA potassium channel, the WALP23 peptide and a carbon nanotube (CNT). Our findings revealed varied lipid partitioning and cholesterol flipping times around the different solutes and putative cholesterol binding sites in AQP1 and KcsA. The results suggest that protein-lipid interactions can be highly variable, and that surface-dependent lipid profiles are effectively manifested in CG simulations with the Martini force field.

Quantum Persistent Tennis Racket Dynamics of Nanorotors.

Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate moment of inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect, quickly averages to zero in classical ensembles since the flipping period varies significantly upon approaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermal asymmetric nanorotors and show that classically forbidden tunneling gives rise to persistent tennis racket dynamics, in stark contrast to the classical expectation. We characterize this effect, demonstrating that quantum coherent flipping dynamics can persist even in the regime where millions of angular momentum states are occupied. This persistent flipping offers a promising route for observing and exploiting quantum effects in rotational degrees of freedom for molecules and nanoparticles.

Ineffective OH Pinning of the Flipping Dynamics of a Spherical Guest within a Tight‐Fitting Tube

AbstractA supramolecular/synthetic method has been devised to affix a sterically hindered substituent onto a fullerene guest encapsulated in a tubular host. A two‐wheeled complex of (C59N)‐(C59N) with a tubular host was oxidatively bisected to afford a C59N+ cation captured in the tube. The C59N+ cation in the tube was then trapped by ethanol or water, which led to an oxy substituent pinned on the guest. The guest motions within the tube were modulated by the pinned substituent, and up‐and‐down flipping motions were halted by an ethoxy substituent. A hydroxy substituent, however, was ineffective in halting the flipping motions, despite the tight‐fitting relationship between the tubular host and the spherical guest. Theoretical calculations of the dynamics revealed that the flipping motions were assisted by OH‐π hydrogen bonds between the guest and the carbon‐rich wall and that sliding motions of the OH group were also facilitated by deformations of the tube.

Ineffective OH Pinning of the Flipping Dynamics of a Spherical Guest within a Tight-Fitting Tube.

A supramolecular/synthetic method has been devised to affix a sterically hindered substituent onto a fullerene guest encapsulated in a tubular host. A two-wheeled complex of (C59 N)-(C59 N) with a tubular host was oxidatively bisected to afford a C59 N+ cation captured in the tube. The C59 N+ cation in the tube was then trapped by ethanol or water, which led to an oxy substituent pinned on the guest. The guest motions within the tube were modulated by the pinned substituent, and up-and-down flipping motions were halted by an ethoxy substituent. A hydroxy substituent, however, was ineffective in halting the flipping motions, despite the tight-fitting relationship between the tubular host and the spherical guest. Theoretical calculations of the dynamics revealed that the flipping motions were assisted by OH-π hydrogen bonds between the guest and the carbon-rich wall and that sliding motions of the OH group were also facilitated by deformations of the tube.

Phase Transitions in Finite Random Networks

We analyze ensembles of random networks with fixed numbers of edges, triangles, and nodes. In the limit as the number of nodes goes to infinity, this model is known to exhibit sharp phase transitions as the density of edges and triangles is varied. In this paper we study finite size effects in ensembles where the number of nodes is between 30 and 66. Despite the small number of nodes, the phases and phase transitions are clearly visible. Concentrating on 54 nodes and one particular phase transition, we use spectral data to examine the structure of a typical graph in each phase, and see that is it very similar to the graphon that describes the system as n diverges. We further investigate how graphs change their structure from that of one phase to the other under a natural edge flip dynamics in which the number of triangles is either forced downwards or allowed to drift upwards. In each direction, spectral data shows that the change occurs in three stages: a very fast stage of about 100 edge flips, in which the triangle count reaches the targeted value, a slower second stage of several thousand edge flips in which the graph adopts the qualitative features of the new phase, and a very slow third stage, requiring hundreds of thousands of edge flips, in which the fine details of the structure equilibrate.

Slow ring flips in aromatic cluster of GB1 studied by aromatic 13C relaxation dispersion methods

Ring flips of phenylalanine and tyrosine are a hallmark of protein dynamics. They report on transient breathing motions of proteins. In addition, flip rates also depend on stabilizing interactions in the ground state, like aromatic stacking or cation–π interaction. So far, experimental studies of ring flips have almost exclusively been performed on aromatic rings without stabilizing interactions. Here we investigate ring flip dynamics of Phe and Tyr in the aromatic cluster in GB1. We found that all four residues of the cluster, Y3, F30, Y45 and F52, display slow ring flips. Interestingly, F52, the central residue of the cluster, which makes aromatic contacts with all three others, is flipping significantly faster, while the other rings are flipping with the same rates within margin of error. Determined activation enthalpies and activation volumes of these processes are in the same range of other reported ring flips of single aromatic rings. There is no correlation of the number of aromatic stacking interactions to the activation enthalpy, and no correlation of the ring’s extent of burying to the activation volume. Because of these findings, we speculate that F52 is undergoing concerted ring flips with each of the other rings.

Orthogonally polarized frequency combs in a mode-locked VECSEL

We introduce a spin–flip model for a vertical-external-cavity surface-emitting laser (VECSEL) with a saturable absorber. We demonstrate the possibility, due to the spin–flip dynamics, to generate two orthogonally linearly polarized frequency combs in the mode-locked regime. The two combs are shifted in wavelength due to the birefringence in the VECSEL gain and/or saturable absorption mirror. We show that the polarization degree of freedom may also lead to several pulses being generated per roundtrip in the two orthogonal linear polarizations and to more complicated dynamics with both linear polarizations excited.

Twist-Induced Snapping in a Bent Elastic Rod and Ribbon.

Snapping of a slender structure is utilized in a wide range of natural and manmade systems, mostly to achieve rapid movement without relying on musclelike elements. Although several mechanisms for elastic energy storage and rapid release have been studied in detail, a general understanding of the approach to design such a kinetic system is a key challenge in mechanics. Here we study a twist-driven buckling and fast flip dynamics of a geometrically constrained ribbon by combining experiments, numerical simulations, and an analytical theory. We identify two distinct types of shape transitions: A narrow ribbon snaps, and a wide ribbon forms a pair of localized helices. We construct a phase diagram and explain the origin of the boundary, which is determined largely by the geometry. We quantify the effects of gravity and clarify the timescale dictating the rapid flipping. Our study reveals the unique role of geometric twist-bend coupling in the fast dynamics of a thin constrained structure, which has implications for a wide range of biophysical and applied physical problems.

Gravitational wave beacons

We explore spinning, precessing, unequal mass binary black holes to display the long term orbital angular momentum, $\vec{L}$, flip dynamics. We study two prototypical cases of binaries with mass ratios $q=1/7$ and $q=1/15$ and a misaligned spin of the large black hole (with an intrinsic spin magnitude of $S_2/m_2^2=0.85$). We conduct full numerical simulations, for nearly 14 and 18 orbits respectively, to evolve the binary down to merger and display a full $L$-flip cycle. The pattern of radiation of such systems is particularly interesting, displaying strong polarization-dependent variation of amplitudes at precessional frequencies, leading to distinctive observational consequences for ground, space, and pulsar timing based gravitational wave detectors. These waveform features are strongly directional dependent and measurements of gravitational waves polarizations can be exploited to disentangle the binary's parameters in various astrophysical scenarios.

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature.

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature T_{c}, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼t^{c}, where c is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time-also with exponent c-in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.

Spin crossover dynamics studies on the thermally activated molecular oxygen binding mechanism on a model copper complex.

The theoretical description of the primary dioxygen (O2) binding and activation step in many copper or iron enzymes, suffers from the intrinsically electronic non-adiabaticity of the spin flip events of the triplet dioxygen molecule (3O2), mediated by spin-orbit couplings. In this work, we presented the early-stage ultrafast spin flip dynamics of O2 binding for a simplified monocopper complex, involving the coupled singlet and triplet electronic states. The on-the-fly trajectory surface hopping (TSH) simulations have identified the dynamical effects that may influence the mode of O2 coordination (end-on vs. side-on), and the electronic structures can be viewed as complexes of molecular O2 with Cu(i) or as Cu(ii)-superoxide compounds. In addition, significant spin flip events are obversed within the sub-picosecond regime. We hope this work may provide complimentary insights on the traditional interpretation of O2 binding on copper complexes and subsequent catalytic reaction mechanisms.

Kinetic Ising models with various single-spin-flip dynamics on quenched and annealed random regular graphs.

We investigate a kinetic Ising model with several single-spin-flip dynamics (including Metropolis and heat bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs the situation is far less clear-the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from a continuous to a discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.

Conformal invariance in conditioned stochastic particle systems

We consider space-time correlations in generic one-dimensional stochastic interacting particle systems with short-range interactions that undergo a fluctuation with an atypically activity of particle jumps or reactions or spin flips. We briefly review the approach in the framework of the quantum Hamiltonian formalism and present examples where the dynamics during such large fluctuations is governed not by the typical stationary dynamics, but by ballistic universality classes with dynamical exponent that are described unitary conformally invariant field theories with central charge c. For reaction–diffusion and spin flip dynamics we identify critical points (a) in the Ising universality class with , and (b) in the universality class of the three-states Potts model with . For the Ising universality class we obtain a universal scaling form for the generating function of cumulants of the jump activity. For repulsive driven diffusive systems with one conservation law the regime of an atypically high current or hopping activity is generically conformally invariant with central charge .

Convergence to equilibrium for a directed (1+d)-dimensional polymer

We consider a flip dynamics for directed (1+d)-dimensional lattice paths with length L. The model can be interpreted as a higher dimensional version of the simple exclusion process, the latter corresponding to the case d=1. We prove that the mixing time of the associated Markov chain scales like L^2\log L up to a d-dependent multiplicative constant. The key step in the proof of the upper bound is to show that the system satisfies a logarithmic Sobolev inequality on the diffusive scale L^2 for every fixed d, which we achieve by a suitable induction over the dimension together with an estimate for adjacent transpositions. The lower bound is obtained with a version of Wilson's argument for the one-dimensional case. Keywords: exclusion process, adjacent transpositions, logarithmic Sobolev inequality, mixing time