Slow Time Scale Research Articles

Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system

Singularly perturbed reaction–diffusion systems such as the Gierer–Meinhardt, Schankenberg, and Gray–Scott models are known to exhibit localized multi-spike solutions in which one of the species concentrates on a discrete collection of well-separated points. A recent focus has been the extension of the analysis, both rigorous and formal, of such localized solutions to the case where classical diffusion is replaced by anomalous diffusion exhibiting Lévy flights. Mathematically, such systems replace the classical Laplacian with the fractional Laplacian (−Δ)s where s is the fractional order. In this paper we consider the formal analysis of multi-spike solutions to the fractional Schnakenberg system with periodic boundary conditions when the fractional order of the activator satisfies 1/4<s1<1 and that of the substrate satisfies 1/2<s2<1. Using the method of matched asymptotic expansions we derive a nonlinear algebraic system that determines the structure of equilibrium solutions, a nonlocal eigenvalue problem that determines its linear stability over a fast, O(1), timescale, as well as a system of ordinary differential equations that determine the dynamics of multi-spike solutions over a slow, O(ɛ−2), timescale. We explicitly construct symmetric multi-spike solutions and derive stability criteria for instabilities arising over both fast and slow timescales. One of the key findings in this paper is that the slow timescale instability thresholds are, barring symmetry considerations, less degenerate than in the classical s2=1 case. In addition we numerically calculate bifurcation diagrams that show how asymmetric multi-spike solutions branch out from symmetric ones at distinct points for solutions with five or more spikes.

Solvation structure and dynamics of a small ion in an organic electrolyte

Organic carbonates are commonly used as electrolytes in commercial lithium-ion batteries. A detailed interpretation of the solvation structure and dynamics of the electrolyte around ions is necessary to understand the charge/discharge process in batteries. This work combines infrared absorption spectroscopy with quantum chemical calculations and molecular dynamics simulations to decipher the solvation structure of propylene carbonate, a cyclic carbonate, around the dissolved thiocyanate ion. Two dimensional infrared spectroscopy and polarization-selective pump probe spectroscopies have been utilized to extract the timescales of solvent fluctuation and the solute reorientational dynamics. The similarity in the slow timescales for the solute and the solvent dynamics signifies that similar processes control both dynamics.

A Dual-Level Model Predictive Control Scheme for Multitimescale Dynamical Systems

So far, many control algorithms have been developed for singularly perturbed systems. However, in many industrial processes, enforcing closed-loop fast-slow dynamics for peculiarly nonseparable ones is a prior request and a crucial issue to be resolved. Aiming at the above problem, this article presents two dual-level model predictive control (MPC) algorithms for multitimescale dynamical systems with unknown bounded disturbances and input constraints. The proposed algorithms, each one composed of two regulators working in slow and fast time scales, are designed to generate closed-loop separable dynamics at high and low levels. As a prominent feature, the proposed algorithms are not only suitable for singularly perturbed systems but also capable of imposing separable closed-loop performance for dynamics that are nonseparable and strongly coupled. The recursive feasibility and convergence properties are proven under suitable assumptions. The simulation results on controlling a boiler turbine (BT) system, including the comparisons with other classic controllers, are demonstrated, which show the effectiveness of the proposed algorithms.

Adaptive Dynamic Programming-Based Cross-Scale Control of a Hydraulic-Driven Flexible Robotic Manipulator

This paper focuses primarily on adaptive dynamic programming (ADP)-based tracking control of the hydraulic-driven flexible robotic manipulator system (HDFRMS) with varying payloads and uncertainties via singular perturbation theory (SPT). Firstly, the dynamics is derived using a driven Jacobin matrix, which represents the coupling between the hydraulic servo-driven system and rigid–flexible manipulator established using the assumed mode method and Lagrange principle. Furthermore, the whole dynamic model of the manipulator system is decoupled into a second slow subsystem (SSS), a second fast subsystem (SFS) and a first fast subsystem (FFS). The three subsystems can describe a large range of movement, flexible vibration and electro-hydraulic servo control, respectively. Hereafter, an adaptive dynamic programming trajectory tracking control law with a critic-only policy iteration algorithm is presented in the second slow timescale, while both robust optimal control (ROC) in the second first timescale and adaptive sliding mode control (ASMC) in the first fast timescale are also designed using the Lyapunov stability theory. Finally, the numerical simulations are carried out to illustrate the rightness and robustness of the singular perturbation decomposition and proposed composite control algorithm.

Rapid Robust Control of a Marine-Vehicle Manipulator with Series Elastic Actuators Based on Variable Power Log Reaching Law

Marine-vehicle manipulators, which represent a kind of mechanical systems installed on marine surface or underwater vehicles, are mostly suffering from the problem of waves (or ocean currents)-caused base oscillations. The oscillations have a significant impact on system stability. Numerous control strategies have been investigated, but the majority of them are concentrated on the control’s robust performance. This study focuses on an innovative marine-vehicle manipulator (ammunition transfer manipulator on warships) with novel compliant actuators (series elastic actuators), for which the control performance of convergence speed and flexible-vibration suppression should also be considered. To address these issues, this paper proposes a unique hybrid control based on the singular perturbation method, by which the control problem is decomposed into two time scales. In the slow time-scale, it is given a rapid trajectory tracking controller that integrates the computed torque method and the terminal sliding mode control law with a novel reaching law (variable power log reaching law). For the fast time-scale control, a derivative-type controller is used to achieve the suppression of the flexible vibrations. To demonstrate the effectiveness of the proposed control method, theoretical proofs and numerical simulations are both presented. According to our knowledge, this study presents the first control strategy for rapid robust control of marine-vehicle manipulators that are subject to base-oscillation-caused disturbance and compliant-actuator-induced flexible vibrations.

Integrating comparative modeling and accelerated simulations reveals conformational and energetic basis of actomyosin force generation

Muscle contraction is performed by arrays of contractile proteins in the sarcomere. Serious heart diseases, such as cardiomyopathy, can often be results of mutations in myosin and actin. Direct characterization of how small changes in the myosin-actin complex impact its force production remains challenging. Molecular dynamics (MD) simulations, although capable of studying protein structure-function relationships, are limited owing to the slow timescale of the myosin cycle as well as a lack of various intermediate structures for the actomyosin complex. Here, employing comparative modeling and enhanced sampling MD simulations, we show how the human cardiac myosin generates force during the mechanochemical cycle. Initial conformational ensembles for different myosin-actin states are learned from multiple structural templates with Rosetta. This enables us to efficiently sample the energy landscape of the system using Gaussian accelerated MD. Key myosin loop residues, whose substitutions are related to cardiomyopathy, are identified to form stable or metastable interactions with the actin surface. We find that the actin-binding cleft closure is allosterically coupled to the myosin motor core transitions and ATP-hydrolysis product release from the active site. Furthermore, a gate between switch I and switch II is suggested to control phosphate release at the prepowerstroke state. Our approach demonstrates the ability to link sequence and structural information to motor functions.

Dynamics of Photoinduced Intramolecular and Intermolecular Electron Transfers in Ligand-Conjugated Ir(III)–Re(I) Photocatalysts

We report the electron transfer (ET) dynamics in a series of Ir(III)-Re(I) photocatalysts where two bipyridyl ligands of Ir and Re moieties are conjugated at the meta (m)- or para (p)-position of each side. Femtosecond transient absorption (TA) measurements identify the intramolecular ET (IET) dynamics from the Ir to Re moiety, followed by the formation of one-electron-reduced species (OERS) via the intermolecular ET with a sacrificial electron donor (SED). The IET rate depends on the bridging ligand (BL) structures (∼25 ps for BLmm/mp vs ∼68 ps for BLpm/pp), while the OERS formation happens on an even slower time scale (∼1.4 ns). Connecting the Re moiety at the meta-position of the bipyridyl of the Ir moiety can restrict the rotation around a covalent bond between two bipyridyl ligands by steric hindrances and facilitate the IET process. This highlights the importance of BL structures on the ET dynamics in photocatalysts.

Non-monotonic radial structures of fluctuating temperatures and densities associated with fishbone activities in KSTAR

General characteristics of a fishbone mode in KSTAR are investigated. Fishbone activities are observed with a Mirnov coil, an electron cyclotron emission radiometer (from the core to the edge of plasmas) and an beam emission spectroscopy system (core or edge plasmas) which are measuring fluctuations of poloidal magnetic fields, electron temperatures, and densities, respectively. Temporal evolutions of these fluctuations are similar to the observations from other tokamaks. An interesting and notable feature found in KSTAR fishbone modes is that radial coherence structures of electron temperature and density with respect to magnetic fluctuations are non-monotonic that they have a local minimum at r/a∼0.7 and a maximum at r/a∼0.9 in addition to the usual global peak near the q = 1 surface, where r/a is the normalized minor radius and q is the safety factor. Furthermore, the associated temporal evolution of the electron temperatures in slow-time scale, i.e., less than 1 kHz, with the fishbone activities show that there exist a drop in temperature or increase in temperature depending on inside or outside the q = 1 surface, respectively, from the core to the edge plasmas except that there are almost no temperature changes in the intermediate region which seems to be correlated with the non-monotonic coherence profile. Such a non-monotonic structure and the slow temporal evolution of temperatures are explained with barely trapped resonating fast ions with the banana orbit widths of the order of the minor radius, so that they transit the core and the edge regions simultaneously without trespassing the mid-plane intermediate region.

Unraveling coupled folding and binding dynamics of ribonuclease S with transient infrared spectroscopy

Molecular interactions of proteins consisting of coupled disorder-to-order transitions and spontaneous binding have a crucial role in understanding their biological function and working mechanism. Here we investigate a well-known globular binding system, ribonuclease S (RNase S), to study the dynamics of protein-peptide interaction. Various biophysical approaches have investigated the binding mechanism of two proteolytic fragments, S-peptide and S-protein, which non-covalently bind to form an active enzyme RNase S. Due to challenges in dissecting the coupled nature of protein binding and folding, molecular level details remain elusive. Here, we use amide-I vibrations as a label-free probe of protein secondary structure and temperature as a control variable. By temperature-jump two-dimensional infrared spectroscopy (t-2DIR), we track the thermally-induced conformational changes associated with relaxation time that span from nanoseconds to many minute timescales. Additionally, we compare the results of an unlabeled complex with one containing a 13C=18O isotope-label of a residue buried within the helical segment of S-peptide. t‑2DIR measurements of labeled- and unlabeled- RNase S and isolated S-protein reveal two kinetic components on millisecond (fast) and second (slow) time scales. Both slow and fast phases are dominated by β-sheet disordering signatures that indicate S-protein unfolding. The isotope-label exhibits significant amplitude in the slow phase, suggesting this time window corresponds to both unbinding and unfolding of the S-peptide. Together, these results indicate that thermally-induced partial unfolding of the S-protein destabilizes the hydrophobic binding pocket containing S-peptide that, in turn, promotes unbinding and unfolding of the S-peptide. Our direct observations from transient spectroscopic data demonstrate the role of a conformational transition state during assembly of the RNase S complex.

Time evolution of the substrate-induced millisecond allosteric activation of imidazole glycerol phosphate synthase.

Deciphering the molecular mechanisms of enzymatic allosteric regulation requires the structural characterization of functional states and also their time evolution toward the formation of the allosterically activated ternary complex. The transient nature and usually slow millisecond time scale interconversion between these functional states hamper their experimental and computational characterization. Here, we design a computational strategy that combines molecular dynamics simulations, enhanced sampling techniques, and dynamical networks to describe the millisecond allosteric activation of imidazole glycerol phosphate synthase (IGPS) from the inactive substrate-free form to the formation of the enzyme active complex. IGPS is a heterodimeric enzyme complex whose HisH subunit is responsible for hydrolysing glutamine and delivering ammonia for the cyclase activity in HisF. Essential molecular details of the long-range millisecond allosteric activation of IGPS remain hidden. Without using a priori information of the active state, our simulations uncover how IGPS, with the allosteric effector bound, spontaneously captures glutamine in a catalytically inactive HisH conformation, subsequently attains a closed HisF:HisH interface, and finally forms the oxyanion hole in HisH for efficient glutamine hydrolysis. We show that the combined effector and substrate binding dramatically decreases the conformational barrier associated with the oxyanion hole formation, in line with experimentally observed 4500-fold activity increase in glutamine hydrolysis. This computational strategy tailored to describe millisecond timescale events can be generalized to study other allosterically regulated enzymes.

Nonlinear characterization of azimuthal combustion instability exhibiting flame transient phenomena

This article characterizes the nonlinear features observed in an annular combustor exhibiting self-excited azimuthal thermoacoustic instability. The annular combustor consists of 12 burners with flames stabilized by bluff bodies protruding into the combustion chamber. This burner configuration closely resembles the flame stabilization geometry and flame shape in ramjet and afterburners configurations. As a first step, two different bluff bodies stabilize the flame: 1) circular and 2) conical and associated instability dynamics are characterized. The combustor exhibits intermittent oscillation in pressure with dominant 1A-1L (first azimuthal - first longitudinal) acoustic mode at about 630 Hz. The duration of periodic oscillation in the intermittent pressure fluctuation varies non-monotonically with the airflow rate. Further, relatively large amplitude pressure fluctuations are observed for intermediate values of airflow rate in both flame stabilization. During these large-amplitude pressure fluctuations, localized flame extinction in certain burners is observed, leading to partial blow-off operation of the combustor. This localized flame extinction is subsequently followed by either successful or unsuccessful re-ignition, leading to introduction of slow time scale heat release rate modulation in the problem. Further, this slow time scale heat release rate modulation is stochastic, contributing to the appearance of intermittent oscillation in pressure.

Quasi Markov state models elucidates the role of bacterial RNA polymerase loading gate and trigger loop dynamics in antibiotics inhibition.

The rise of antibiotic resistance urges the development of new antibiotics. Bacterial RNA Polymerase (RNAP) transcribes DNA to RNA and is an effective target for antibiotics. RNAP has a crab-claw-like shape with two pincers, clamp and β-lobe domains, forming a loading gate. During the initiation of transcription,the opening of the loading gate is necessary to load the template DNA. Myx is an antibiotic that binds to the switch 2 region, under the clamp, to prevent clamp closing/opening and inhibit transcription initiation. To study the inhibition mechanism of Myx in atomic resolution, we built quasi-Markov State Models (qMSM) based on extensive molecular dynamics (MD) simulations. qMSM can obtain the slow timescale dynamics of complex conformational change using shorter MD simulations compared to traditional MSM. qMSM identifies four states of clamp opening: closed, two partially closed, and open states. We have shown that the opening of the Myx binding site only occurs in a partially closed state, which allows binding of Myx. This suggests that Myx selectively binds to a partially closed state and follows the conformational selection mechanism. Notably, we find that β-lobe opening is sufficient for loading of DNA during transcription initiation. This highlights the critical role of β-lobe to initiate transcription and β-lobe's potential as a target for future antibiotics development. We also utilize qMSMto study the folding of the trigger loop (TL) of RNAP. During RNA elongation, TL closes/folds to stabilize the NTP substrate in the active site for catalysis. CBR is antibiotics that inhibit the folding of TL. Studying the molecular mechanism of TL folding will be useful to understand the inhibition mechanism of antibiotics, CBR, and future drug design targeting TL.

Loop dynamics and evolvability in the TIM-barrel proteins of histidine and tryptophan biosynthesis.

Recent years have witnessed increasing interest in the role of conformational dynamics in enzyme evolution and engineering. In this context, TIM-barrel proteins are important model systems, as the TIM-barrel is ubiquitous, highly evolvable, supports a diverse range of chemistry, and the active site is typically decorated by one or more mobile loops that play an important role in catalysis and/or regulation of these enzymes. Here, the TIM-barrel proteins of histidine and tryptophan biosynthesis (HisA, TrpF and PriA) stand out, as their active sites are decorated by up to three long mobile loops, that move independently of each other, and the conformations of which are critically important for catalysis. These motions appear to be ligand-gated and occur on sufficiently slow timescales (ms or slower) to be at least partially rate-limiting. In recent work, we combined conventional and enhanced molecular dynamics simulations with empirical valence bond simulations to investigate the conformational behavior of the catalytic loops in these enzymes, and the link between their dynamical behavior and substrate selectivity and catalysis. We have explored the role of loop dynamics in facilitating the bifunctionality of PriA towards substrates ProFAR and PRA (precursors for histidine and tryptophan biosynthesis, respectively), as well as during the real-time evolution of HisA to yield HisA-specific, TrpF-specific and bifunctional variants. Finally, the insights this provides emphasizes the potential of loop engineering as a powerful tool to manipulate the selectivity and substrate scope of the TIM-barrel scaffold, which has historically been one of the most important scaffolds for de novo enzyme design.

Conformational and energetic basis of actomyosin force generation.

Interactions between myosin and actin are essential in producing different types of cellular forces. Two key players in muscle contraction, myosin and actin, slide along each other to produce force using the energy from ATP hydrolysis. Targeting the motor domain of cardiac myosin, several small molecules have been proposed to treat cardiomyopathy. A clear mechanistic picture for the allosteric control in the actomyosin complex can facilitate computer-aided drug discovery. Atomistic simulation approaches such as molecular dynamics (MD) are limited for studying the motor functional cycle owing to the slow timescale as well as a lack of various intermediate structures. Here, integrating comparative modeling and enhanced sampling simulations, we reveal how the human cardiac myosin generates force in the cross-bridge cycle at atomic resolution. Initial conformational ensembles for different actomyosin states are learned from multiple structural templates with Rosetta. This enables us to efficiently sample the energy landscape of the system using Gaussian accelerated MD. Key myosin loop residues, whose substitutions are related to cardiomyopathy, are identified to form stable or transient interactions with actin. We find that the actin-binding cleft closure is allosterically coupled to the myosin core transitions and products release from the active site. Furthermore, a gate between switch I and II is suggested to control phosphate release at the pre-powerstroke state. The predicted metastable states and corresponding energetics are consistent with available experimental data and provide insights into the timing of elementary mechanochemical events.

Autoencoding slow representations for semi-supervised data-efficient regression

The slowness principle is a concept inspired by the visual cortex of the brain. It postulates that the underlying generative factors of a quickly varying sensory signal change on a different, slower time scale. By applying this principle to state-of-the-art unsupervised representation learning methods one can learn a latent embedding to perform supervised downstream regression tasks more data efficient. In this paper, we compare different approaches to unsupervised slow representation learning such as L_p norm based slowness regularization and the SlowVAE, and propose a new term based on Brownian motion used in our method, the S-VAE. We empirically evaluate these slowness regularization terms with respect to their downstream task performance and data efficiency in state estimation and behavioral cloning tasks. We find that slow representations show great performance improvements in settings where only sparse labeled training data is available. Furthermore, we present a theoretical and empirical comparison of the discussed slowness regularization terms. Finally, we discuss how the Fréchet Inception Distance (FID), commonly used to determine the generative capabilities of GANs, can predict the performance of trained models in supervised downstream tasks.

Dynamic Image Representation in a Spiking Neural Network Supplied by Astrocytes

The mathematical model of the spiking neural network (SNN) supplied by astrocytes is investigated. The astrocytes are a specific type of brain cells which are not electrically excitable but induce chemical modulations of neuronal firing. We analyze how the astrocytes influence images encoded in the form of the dynamic spiking pattern of the SNN. Serving at a much slower time scale, the astrocytic network interacting with the spiking neurons can remarkably enhance the image representation quality. The spiking dynamics are affected by noise distorting the information image. We demonstrate that the activation of astrocytes can significantly suppress noise influence, improving the dynamic image representation by the SNN.

Disentangling the Effect of Pressure and Mixing on a Mechanochemical Bromination Reaction by Solid-State NMR Spectroscopy.

Mechanical forces, including compressive stresses, have a significant impact on chemical reactions. Besides the preparative opportunities, mechanochemical conditions benefit from the absence of any organic solvent, the possibility of a significant synthetic acceleration and unique reaction pathways. Together with an accurate characterization of ball-milling products, the development of a deeper mechanistic understanding of the occurring transformations at a molecular level is critical for fully grasping the potential of organic mechanosynthesis. We herein studied a bromination of a cyclic sulfoximine in a mixer mill and used solid-state nuclear magnetic resonance (NMR) spectroscopy for structural characterization of the reaction products. Magic-angle spinning (MAS) was applied for elucidating the product mixtures taken from the milling jar without introducing any further post-processing on the sample. Ex situ 13 C-detected NMR spectra of ball-milling products showed the formation of a crystalline solid phase with the regioselective bromination of the S-aryl group of the heterocycle in position 4. Completion is reached in less than 30 minutes as deduced from the NMR spectra. The bromination can also be achieved by magnetic stirring, but then, a longer reaction time is required. Mixing the solid educts in the NMR rotor allows to get in situ insights into the reaction and enables the detection of a reaction intermediate. The pressure alone induced in the rotor by MAS is not sufficient to lead to full conversion and the reaction occurs on slower time scales than in the ball mill, which is crucial for analysing mixtures taken from the milling jar by solid-state NMR. Our data suggest that on top of centrifugal forces, an efficient mixing of the starting materials is required for reaching a complete reaction.

Slicing and Dicing: Optimal Coarse-Grained Representation to Preserve Molecular Kinetics.

The aim of molecular coarse-graining approaches is to recover relevant physical properties of the molecular system via a lower-resolution model that can be more efficiently simulated. Ideally, the lower resolution still accounts for the degrees of freedom necessary to recover the correct physical behavior. The selection of these degrees of freedom has often relied on the scientist's chemical and physical intuition. In this article, we make the argument that in soft matter contexts desirable coarse-grained models accurately reproduce the long-time dynamics of a system by correctly capturing the rare-event transitions. We propose a bottom-up coarse-graining scheme that correctly preserves the relevant slow degrees of freedom, and we test this idea for three systems of increasing complexity. We show that in contrast to this method existing coarse-graining schemes such as those from information theory or structure-based approaches are not able to recapitulate the slow time scales of the system.

Nonlinear mechanisms for opposite responses of bursting activities induced by inhibitory autapse with fast and slow time scale

Nonlinear mechanisms for opposite responses of bursting activities induced by inhibitory autapse with fast and slow time scale

White-matter degradation and dynamical compensation support age-related functional alterations in human brain.

Structural connectivity of the brain at different ages is analyzed using diffusion-weighted magnetic resonance imaging (MRI) data. The largest decrease of streamlines is found in frontal regions and for long inter-hemispheric links. The average length of the tracts also decreases, but the clustering is unaffected. From functional MRI we identify age-related changes of dynamic functional connectivity (dFC) and spatial covariation features of functional connectivity (FC) links captured by metaconnectivity. They indicate more stable dFC, but wider range and variance of MC, whereas static features of FC did not show any significant differences with age. We implement individual connectivity in whole-brain models and test several hypotheses for the mechanisms of operation among underlying neural system. We demonstrate that age-related functional fingerprints are only supported if the model accounts for: (i) compensation of the individual brains for the overall loss of structural connectivity and (ii) decrease of propagation velocity due to the loss of myelination. We also show that with these 2 conditions, it is sufficient to decompose the time-delays as bimodal distribution that only distinguishes between intra- and inter-hemispheric delays, and that the same working point also captures the static FC the best, and produces the largest variability at slow time-scales.