Slow Time Scale Research Articles

Known Evolutionary Paths Are Accessible to Engineered ß-Lactamases Having Altered Protein Motions at the Timescale of Catalytic Turnover.

The evolution of new protein functions is dependent upon inherent biophysical features of proteins. Whereas, it has been shown that changes in protein dynamics can occur in the course of directed molecular evolution trajectories and contribute to new function, it is not known whether varying protein dynamics modify the course of evolution. We investigate this question using three related ß-lactamases displaying dynamics that differ broadly at the slow timescale that corresponds to catalytic turnover yet have similar fast dynamics, thermal stability, catalytic, and substrate recognition profiles. Introduction of substitutions E104K and G238S, that are known to have a synergistic effect on function in the parent ß-lactamase, showed similar increases in catalytic efficiency toward cefotaxime in the related ß-lactamases. Molecular simulations using Protein Energy Landscape Exploration reveal that this results from stabilizing the catalytically-productive conformations, demonstrating the dominance of the synergistic effect of the E014K and G238S substitutions in vitro in contexts that vary in terms of sequence and dynamics. Furthermore, three rounds of directed molecular evolution demonstrated that known cefotaximase-enhancing mutations were accessible regardless of the differences in dynamics. Interestingly, specific sequence differences between the related ß-lactamases were shown to have a higher effect in evolutionary outcomes than did differences in dynamics. Overall, these ß-lactamase models show tolerance to protein dynamics at the timescale of catalytic turnover in the evolution of a new function.

Local Postsynaptic Signaling on Slow Time Scales in Reciprocal Olfactory Bulb Granule Cell Spines Matches Asynchronous Release.

In the vertebrate olfactory bulb (OB), axonless granule cells (GC) mediate self- and lateral inhibitory interactions between mitral/tufted cells via reciprocal dendrodendritic synapses. Locally triggered release of GABA from the large reciprocal GC spines occurs on both fast and slow time scales, possibly enabling parallel processing during olfactory perception. Here we investigate local mechanisms for asynchronous spine output. To reveal the temporal and spatial characteristics of postsynaptic ion transients, we imaged spine and adjacent dendrite Ca2 +- and Na+-signals with minimal exogenous buffering by the respective fluorescent indicator dyes upon two-photon uncaging of DNI-glutamate in OB slices from juvenile rats. Both postsynaptic fluorescence signals decayed slowly, with average half durations in the spine head of t1/2_Δ[Ca2 +]i ∼500 ms and t1/2_Δ[Na+]i ∼1,000 ms. We also analyzed the kinetics of already existing data of postsynaptic spine Ca2 +-signals in response to glomerular stimulation in OB slices from adult mice, either WT or animals with partial GC glutamate receptor deletions (NMDAR: GluN1 subunit; AMPAR: GluA2 subunit). In a large subset of spines the fluorescence signal had a protracted rise time (average time to peak ∼400 ms, range 20 to >1,000 ms). This slow rise was independent of Ca2 + entry via NMDARs, since similarly slow signals occurred in ΔGluN1 GCs. Additional Ca2 + entry in ΔGluA2 GCs (with AMPARs rendered Ca2 +-permeable), however, resulted in larger ΔF/Fs that rose yet more slowly. Thus GC spines appear to dispose of several local mechanisms to promote asynchronous GABA release, which are reflected in the time course of mitral/tufted cell recurrent inhibition.

Optimizing energetic cost of uncertainty in a driven system with and without feedback.

Many biological functions require dynamics to be necessarily driven out of equilibrium. In contrast, in various contexts, a nonequilibrium dynamics at fast timescales can be described by an effective equilibrium dynamics at a slower timescale. In this work, we study two different aspects: (i) the energy-efficiency tradeoff for a specific nonequilibrium linear dynamics of two variables with feedback and (ii) the cost of effective parameters in a coarse-grained theory as given by the "hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics. To meaningfully discuss the tradeoff between energy consumption and the efficiency of the desired function, a one-to-one mapping between function(s) and energy input is required. The function considered in this work is the variance of one of the variables. We get a one-to-one mapping by considering the minimum variance obtained for a fixed entropy production rate and vice versa. We find that this minimum achievable variance is a monotonically decreasing function of the given entropy production rate. When there is a timescale separation, in the effective equilibrium limit, the cost of the effective potential and temperature is the associated "hidden" entropy production rate.

Analysis of runaway electron discharge formation during Joint European Torus plasma start-up

Joint European Torus (JET) plasma initiations that form a significant quantity of runaway electrons have been studied. It is shown that there is no direct relationship between the prefill pressure and breakdown electric field and signs of runaway electrons during the plasma initiation. Runaway electron generation is determined by the electric field and density development at and after burn-through. A clear criterion of density and electric field at one given point in time, which would ensure the avoidance of runaway electron generation, cannot be determined, because the timescales for the formation of runaway electrons and for the dynamics of the density differ significantly. Moreover, the formation process can be reversed, reducing the influence of runaway electrons on the discharge. Ensuring a high enough density will reduce the likelihood that runaway electron discharges are formed. It is also found that at JET the electric field often exceeds the critical electric field during the early stages of the current ramp-up phase, even when no signs of runaway electrons are present. Expected runaway current dynamics have been analysed using the discharge circuit equation. The comparison of the expected runaway electron current dynamics shows it to be significantly slower compared to theoretical expectations in the presence of a hot and dense thermal background plasma. This could be explained by an enhanced critical electric field and/or a reduced confinement of runaway electrons. The latter is shown to be affected by bursts of magnetohydrodynamic activity that are characteristic during the current ramp-up. The development of discharges in which the current is fully carried by runaway electrons happens on a slow timescale of several seconds, limited by the available flux. Such timescales are sufficient for improved active control of these events, avoiding runaway currents at plasma initiation exceeding values at which they could damage in-vessel components. The results provide insight into the improvement and interpretation of self-consistent modelling of runaway electron generation during the start-up of International Thermonuclear Experimental Reactor discharges.

Predicting N-Strain Coexistence from Co-colonization Interactions: Epidemiology Meets Ecology and the Replicator Equation

Multi-type infection processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to analyze and to understand on a fundamental level. Here, we study a multi-strain susceptible-infected-susceptible model with coinfection. A host already colonized by one strain can become more or less vulnerable to co-colonization by a second strain, as a result of facilitating or competitive interactions between the two. Fitness differences between N strains are mediated through N^2 altered susceptibilities to secondary infection that depend on colonizer-cocolonizer identities (K_{ij}). By assuming strain similarity in such pairwise traits, we derive a model reduction for the endemic system using separation of timescales. This ‘quasi-neutrality’ in trait space sets a fast timescale where all strains interact neutrally, and a slow timescale where selective dynamics unfold. We find that these slow dynamics are governed by the replicator equation for N strains. Our framework allows to build the community dynamics bottom-up from only pairwise invasion fitnesses between members. We highlight that mean fitness of the multi-strain network, changes with their individual dynamics, acts equally upon each type, and is a key indicator of system resistance to invasion. By uncovering the link between N-strain epidemiological coexistence and the replicator equation, we show that the ecology of co-colonization relates to Fisher’s fundamental theorem and to Lotka-Volterra systems. Besides efficient computation and complexity reduction for any system size, these results open new perspectives into high-dimensional community ecology, detection of species interactions, and evolution of biodiversity.

Guaranteed Cost for an Event-Triggered Consensus Strategy for Interconnected Two Time-Scales Systems With Structured Uncertainty.

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

An Adaptive Distributionally Robust Model for Three-Phase Distribution Network Reconfiguration

Distributed generator (DG) volatility has a great impact on system operation, which should be considered beforehand due to the slow time scale of distribution network reconfiguration (DNR). However, it is difficult to derive accurate probability distributions (PDs) for DG outputs and loads analytically. To remove the assumptions on accurate PD knowledge, a deep neural network is first devised to learn the reference joint PD from historical data in an adaptive way. The reference PD along with the forecast errors are enveloped by a distributional ambiguity set using Kullback-Leibler divergence. Then a distributionally robust model for three-phase unbalanced DNR is proposed to obtain the optimal configuration under the worst-case PD of DG outputs and loads within the ambiguity set. The result inherits the advantages of stochastic optimization and robust optimization. Finally, a modified column-and-constraint generation method with efficient scenario decomposition is investigated to solve this model. Numerical tests are carried out using an IEEE unbalanced benchmark and a practical-scale system in Shandong, China. Comparison with the deterministic, stochastic and robust DNR methods validates the effectiveness of the proposed method.

Timescales of motor memory formation in dual-adaptation.

The timescales of adaptation to novel dynamics are well explained by a dual-rate model with slow and fast states. This model can predict interference, savings and spontaneous recovery, but cannot account for adaptation to multiple tasks, as each new task drives unlearning of the previously learned task. Nevertheless, in the presence of appropriate contextual cues, humans are able to adapt simultaneously to opposing dynamics. Consequently this model was expanded, suggesting that dual-adaptation occurs through a single fast process and multiple slow processes. However, such a model does not predict spontaneous recovery within dual-adaptation. Here we assess the existence of multiple fast processes by examining the presence of spontaneous recovery in two experimental variations of an adaptation-de-adaptation-error-clamp paradigm within dual-task adaptation in humans. In both experiments, evidence for spontaneous recovery towards the initially learned dynamics (A) was found in the error-clamp phase, invalidating the one-fast-two-slow dual-rate model. However, as adaptation is not only constrained to two timescales, we fit twelve multi-rate models to the experimental data. BIC model comparison again supported the existence of two fast processes, but extended the timescales to include a third rate: the ultraslow process. Even within our single day experiment, we found little evidence for decay of the learned memory over several hundred error-clamp trials. Overall, we show that dual-adaptation can be best explained by a two-fast-triple-rate model over the timescales of adaptation studied here. Longer term learning may require even slower timescales, explaining why we never forget how to ride a bicycle.

Liquid‐to‐solid transitions in nanoparticle‐filled brush block copolymer composites

AbstractThe natural self‐assembly of densely grafted brush block copolymers (BBCP) is used to direct functional nanoparticles (NP) into well‐ordered structures with large lattice spacings and high NP content. Understanding the NP's impact on the phase behavior and viscoelastic properties is necessary for optimizing the processing windows for such materials. Thermo‐structural and thermo‐rheological properties are investigated in a model nanocomposite system composed of a di‐block bottlebrush (dbBB) poly(tert‐butyl acrylate)‐block‐poly(ethylene oxide) (PtBA‐b‐PEO), complexed with surface functionalized zirconium oxide (ZrO2) NPs. The NPs selectively sequester into the microphase separated PEO domains through coordinated hydrogen bonding. Loading up to φ = 30 wt% NP is achieved, and the lamellar morphologies are stable in the melt state according to temperature controlled small angle X‐ray scattering (SAXS). Systematic transitions in the linear viscoelasticity, determined by small amplitude oscillatory shear (SAOS) suggest that at slow timescales, the NP superstructure inhibits the highly mobile relaxation processes inherent to the dbBB architecture. Further analysis of the relaxation time spectrum H(τ) is used to describe the constraint of such relaxation mechanisms. The structure–property relationships realized by SAOS and SAXS enable future manipulation of mechanical properties and processing of BBCP/NP composites for both established and emergent applications.

Bifurcation Patterns of Bursting within pre-Bötzinger Complex and Their Control

A variety of firing rhythms can be generated spontaneously in the pre-Bötzinger complex. External stimuli can cause changes in the pattern of the firing rhythm, which may cause different physiological effects in the body. In this study, by the fast and slow time scale dynamics, with one- and two-parameter bifurcation analysis, we study the bursting patterns and their transition mechanisms of the pre-Bötzinger complex under washout filter controller. The results may help us understand the relationship between different firing patterns of neurons and external stimuli, and further reveal the mechanisms of disease due to external stimuli.

The amyloid cascade hypothesis and Alzheimer’s disease: A mathematical model

The paper presents a conceptual mathematical model for Alzheimer’s disease (AD). According to the so-called amyloid cascade hypothesis, we assume that the progression of AD is associated with the presence of soluble toxic oligomers of beta-amyloid. Monomers of this protein are produced normally throughout life, but a change in the metabolism may increase their total production and, through aggregation, ultimately results in a large quantity of highly toxic polymers. The evolution from monomeric amyloid produced by the neurons to senile plaques (long and insoluble polymeric amyloid chains) is modelled by a system of ordinary differential equations (ODEs), in the spirit of the Smoluchowski equation. The basic assumptions of the model are that, at the scale of suitably small representative elementary volumes (REVs) of the brain, the production of monomers depends on the average degradation of the neurons and in turn, at a much slower timescale, the degradation is caused by the number of toxic oligomers. To mimic prion-like diffusion of the disease in the brain, we introduce an interaction among adjacent REVs that can be assumed to be isotropic or to follow given preferential patterns. We display the results of numerical simulations which are obtained under some simplifying assumptions. For instance, the amyloid cascade is modelled by just three ordinary differential equations (ODEs), and the simulations refer to abstract 2D domains, simplifications which can be easily avoided at the price of some additional computational costs. Since the model is suitably flexible to incorporate other mechanisms and geometries, we believe that it can be generalised to describe more realistic situations.

Parareal computation of stochastic differential equations with time-scale separation: a numerical convergence study

The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine propagator is based on a (high-dimensional, slow-fast) stochastic microscopic model, and the coarse propagator is based on a low-dimensional approximate effective dynamics at slow time scales. At the microscopic level, we use an ensemble of Monte Carlo particles, whereas the approximate coarse propagator uses the (deterministic) Fokker-Planck equation for the slow degrees of freedom. The required coupling between microscopic and macroscopic representations of the system introduces several design options, specifically on how to generate a microscopic probability distribution consistent with a required macroscopic probability distribution and how to perform the coarse-level updating of the macroscopic probability distribution in a meaningful manner. We numerically study how these design options affect the efficiency of the algorithm in a number of situations. The choice of the coarse-level updating operator strongly impacts the result, with a superior performance if addition and subtraction of the quantile function (inverse cumulative distribution) is used. How microscopic states are generated has a less pronounced impact, provided a suitable prior microscopic state is used.

Derivation of a slow phase model of vortex-induced vibrations for smooth and turbulent oncoming flows

This paper analyzes the influence of turbulence on a wake-oscillator model. Turbulence is introduced by randomizing the model proposed by Facchinetti et al. under the quasi-steady assumption. A multiple scale analysis of the deterministic model shows that the response is governed by a dimensionless group D, expressed as a function of the amplitudes of the forcing terms in the two governing equations, the total (aerodynamic plus structural) damping and the parameter ε of the fluid Van der Pol oscillator. The influence of turbulence is interpreted as a stochastic noise of small intensity and with a slower timescale than the (fast) oscillations, which is typical of wind engineering applications. A slow phase model of the problem is then derived by assuming that the small turbulence drives the system only slightly away from its limit cycle in smooth flow conditions. Standard modeling techniques borrowed from other fields of physics, in particular the observation of phase shifts and their accumulation, are used to highlight conditions under which the turbulence of the oncoming flow might reduce the amplitudes of vibrations of the body. The slow phase model is derived in smooth flow conditions, then extended to turbulent flow. It recalls that the phase plays a central role in synchronization problems, and that the response amplitude should only be considered as a sub-product of the slow phase. The slow phase model is expressed by means of a first order nonlinear differential equation for the phase and a memoryless transformation for the response amplitudes. Its solution is explicit and simple in some limiting cases. In particular, for small turbulence intensity, the response is shown to be insensitive to turbulence when its frequency content is not low enough. This major dependence upon the frequency content of the turbulence explains that the reduction of VIV due to turbulence cannot be explained by the turbulence intensity only, as usually considered today. The required relative smallnesses of the turbulence and its frequency content naturally appear in the derivation, which is led in a dimensionless manner. Finally, the present study constitutes an analysis of a phenomenological model which could be used in a much wider concept than of the elastically-mounted circular cylinder.

The dominant role of memory-based capacitive hysteretic currents in operation of photovoltaic perovskites

The potential opportunities of perovskite-based technology to further advance in the photovoltaic field and implement an extensive industrial application, will mainly depend on whether some of its weaknesses, such as current density-voltage ( J − V ) hysteresis, can be overcome. In this sense, a critical aspect is the understanding and the subsequent accurate description of hysteresis in perovskite cells. Here, we present the theoretical underpinnings to interpret non-ideal transient dynamics in stepwise- JV measurements, using electrical analysis strategies and fractional calculus tools. Our model was validated with experimental measurements of CsFAPbIBr-based photovoltaic perovskites of different active layer thicknesses with persistent long-range time photocurrents. It is reported that hysteresis phenomena increase with more pronounced non-ideal capacitive effects suggesting that more trapping events limit ion motion and carrier transport. Our main interest is to provide valuable information about the memory-based slow timescale dynamics, which exhibits a significant impact on the appearance of hysteresis and, to a large extent, on the operation of the solar cell. • Analysis and interpretation of the non-ideal capacitive behavior in J - V curves. • Fractional calculus was used for the first time to gain further insight regarding hysteresis. • Relation between impedance response and anomalous transient dynamics. • Hysteresis depends on the fractional-order pattern and the underlying memory effects. • High-efficient perovskites were studied by using the proposed method.

Virtual Service Placement for Edge Computing Under Finite Memory and Bandwidth

Edge computing allows an edge server to adaptively place virtual instances to serve different types of data. This article presents a new algorithm which jointly optimizes virtual service placement farsightedly and service data admission instantly to maximize the time-average service throughput of edge computing. The data admission is optimized, adapting to fast-changing data arrivals and wireless channels. The service placement is transformed into a two-dimensional knapsack problem by approximating future arrivals and channels with past observations, and solved over a slow timescale to allow services to be properly installed. Different from existing studies, our algorithm considers practical aspects of edge servers, such as finite memory size and bandwidth. We prove that the algorithm is asymptotically optimal and the optimality loss resulting from the approximation diminishes. Simulations show that our approach can improve the time-average throughput of existing alternatives by 16% for our considered simulation setup. The improvement becomes higher, as the memory size becomes increasingly tight. The number of services to be replaced is reduced without loss of throughput, after being placed farsightedly.

Large deviation for two-time-scale stochastic burgers equation

A Freidlin–Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast component is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [A. Budhiraja and P. Dupuis, A variational representation for positive functionals of infinite dimensional Brownian motion, Probab. Math. Statist. 20 (2000) 39–61].

Dual-Rate Adaptive Optimal Tracking Control for Dense Medium Separation Process Using Neural Networks

Dense medium separation (DMS) is of great significance for coal cleaning. The DMS control system always involves dense medium density adjustment and ash content control that are operating on fast and slow time scales, respectively. The inherent time-varying and strongly nonlinear characteristics of the DMS process give rise to challenges for the design of this multitime scale control system. To address this issue, this article proposes a dual-rate adaptive optimal tracking control approach for the DMS system. For the basic loop process, a nonlinear adaptive PI controller containing a neural network (NN)-based unmodeled dynamics compensator is proposed. Then, a lifting technique is used to unify the time scales of the two loops accompanied by formulating a generalized controlled object, whose dynamics is completely unknown. On this basis, a data-driven operation optimization control method that combines adaptive dynamic programming algorithm and reference control is developed, which is implemented using NNs. Finally, the stability of the proposed method is analyzed. The simulation results indicate its effectiveness.

The influence of proline isomerization on potency and stability of anti-HIV antibody 10E8

Monoclonal antibody (mAb) 10E8 recognizes a highly conserved epitope on HIV and is capable of neutralizing > 95% of circulating viral isolates making it one of the most promising Abs against HIV. Solution instability and biochemical heterogeneity of 10E8 has hampered its development for clinical use. We identify the source of 10E8 heterogeneity being linked to cis/trans isomerization at two prolines within the YPP motif in the CRD3 loop that exists as two predominant conformers that interconvert on a slow timescale. The YtransP conformation conformer can bind the HIV gp41 epitope, while the YcisP is not binding competent and shows a higher aggregation propensity. The high barrier of isomerization and propensity to adopt non-binding competent proline conformers provides novel insight into the slow binding kinetics, low potency, and poor solubility of 10E8. This study highlights how proline isomerization should be considered a critical quality attribute for biotherapeutics with paratopes containing potential cis proline amide bonds.

Low-dimensional dynamics for working memory and time encoding.

Our decisions often depend on multiple sensory experiences separated by time delays. The brain can remember these experiences and, simultaneously, estimate the timing between events. To understand the mechanisms underlying working memory and time encoding, we analyze neural activity recorded during delays in four experiments on nonhuman primates. To disambiguate potential mechanisms, we propose two analyses, namely, decoding the passage of time from neural data and computing the cumulative dimensionality of the neural trajectory over time. Time can be decoded with high precision in tasks where timing information is relevant and with lower precision when irrelevant for performing the task. Neural trajectories are always observed to be low-dimensional. In addition, our results further constrain the mechanisms underlying time encoding as we find that the linear "ramping" component of each neuron's firing rate strongly contributes to the slow timescale variations that make decoding time possible. These constraints rule out working memory models that rely on constant, sustained activity and neural networks with high-dimensional trajectories, like reservoir networks. Instead, recurrent networks trained with backpropagation capture the time-encoding properties and the dimensionality observed in the data.

Timescales of Human Hair Cortisol Dynamics.

SummaryCortisol is a major human stress hormone, secreted within minutes of acute stress. Cortisol also has slower patterns of variation: a strong circadian rhythm and a seasonal rhythm. However, longitudinal cortisol dynamics in healthy individuals over timescales of months has rarely been studied. Here, we measured longitudinal cortisol in 55 healthy participants using 12 cm of hair, which provides a retrospective measurement over one year. Individuals showed (non-seasonal) fluctuations averaging about 22% around their baseline. Fourier analysis reveals dominant slow frequencies with periods of months to a year. These frequencies can be explained by a mathematical model of the hormonal cascade that controls cortisol, the HPA axis, when including the slow timescales of tissue turnover of the glands. Measuring these dynamics is important for understanding disorders in which cortisol secretion is impaired over months, such as mood disorders, and to test models of cortisol feedback control.