Intermediate Time Scales Research Articles

Memory in repetitive protein–protein interaction series

Interactions between proteins coordinate biological processes in an organism and may impact its responses to changing environments and diseases through feedback systems. Feedback systems function by using changes in the past to influence behaviors in the future, which we refer to here as memory. Here, we summarized several observations made, ideas conceptualized, and mathematical models developed for quantitatively analyzing memory effects in repetitive protein–protein interactions (PPIs). Specifically, we consider how proteins on the cell or in isolation retain information about prior interactions to impact current interactions. The micropipette, biomembrane force probe, and atomic force microscopic techniques were used to repeatedly assay PPIs. The resulting time series were analyzed by a previous and two new models to extract three memory indices of short (seconds), intermediate (minutes), and long (hours) timescales. We found that interactions of cell membrane, but not soluble, T cell receptor (TCR) with peptide-major histocompatibility complex (pMHC) exhibits short-term memory that impacts on-rate, but not off-rate of the binding kinetics. Peptide dissociation from MHC resulted in intermediate- and long-term memories in TCR–pMHC interactions. However, we observed no changes in kinetic parameters by repetitive measurements on living cells over intermediate timescales using stable pMHCs. Parameters quantifying memory effects in PPIs could provide additional information regarding biological mechanisms. The methods developed herein also provide tools for future research.

Human–coastal coupled systems: Ten questions

Abstract Given the inevitability of sea-level rise, investigating processes of human-altered coastlines at the intermediate timescales of years to decades can sometimes feel like an exercise in futility. Returning to the big picture and long view of feedbacks, emergent dynamics, and wider context, here we offer 10 existential questions for research into human–coastal coupled systems.

Antiphase response of the Indonesian–Australian monsoon to millennial-scale events of the last glacial period

Antiphase behaviour of monsoon systems in alternate hemispheres is well established at yearly and orbital scales in response to alternating sensible heating of continental landmasses. At intermediate timescales without a sensible heating mechanism both in-phase and antiphase behaviours of northern and southern hemisphere monsoon systems are recorded at different places and timescales. At present, there is no continuous, high resolution, precisely dated record of millennial-scale variability of the Indonesian–Australian monsoon during the last glacial period with which to test theories of paleomonsoon behaviour. Here, we present an extension of the Liang Luar, Flores, speleothem δ18O record of past changes in southern hemisphere summer monsoon intensity back to 55.7 kyr BP. Negative δ18O excursions (stronger monsoon) occur during Heinrich events whereas positive excursions (weaker monsoon) occur during Dansgaard-Oeschger interstadials—a first order antiphase relationship with northern hemisphere summer monsoon records. An association of negative δ18O excursions with speleothem growth phases in Liang Luar suggests that these stronger monsoons are related to higher rainfall amounts. However, the response to millennial-scale variability is inconsistent, including a particularly weak response to Heinrich event 3. We suggest that additional drivers such as underlying orbital-scale variability and drip hydrology influence the δ18O response.

A tractable mathematical model for rectified diffusion

A core unresolved challenge in rectified diffusion is the lack of predictive models, which allow accurate modelling of the growth of bubbles over millions of cycles of oscillation. The spherically symmetric problem involves two asymptotic regions in space for the convection and diffusion of the dissolved gas in the liquid, an inner region adjacent to the bubble and an outer region. It also involves three time scales: the shortest time scale associated with the bubble oscillation, the intermediate and the longest time scales for the mass transport across the bubble interface and the outer region, respectively. The problem is analysed systematically using matched asymptotic expansions in space and multi-scales in time, the large parameter being the Péclet number for mass transfer. A tractable mathematical model is formulated for rectified diffusion. It comprises the Rayleigh–Plesset equation for the spherical oscillations of the bubble on the shortest time scale, an ordinary differential equation for the mass of gas in the bubble on the intermediate time scale and a diffusion equation on the longest time scale and the long length scale. Predictions of this simplified model have excellent agreement with experimental results for a single spherical bubble in the bulk over millions of cycles of oscillation. A parametric study is undertaken with several new phenomena/features observed for acoustic frequencies in the range 12 to 62 kHz, acoustic field $0.12$ to $0.22$ bar and the initial gas concentration in the liquid being $0.95$ to $1.0$ of the saturation concentration.

Temporal heterogeneity in photosystem II photochemistry in Artemisia ordosica under a fluctuating desert environment.

Acclimation strategies in xerophytic plants to stressed environmental conditions vary with temporal scales. Our understanding of environmentally-induced variation in photosystem II (PSII) processes as a function of temporal scales is limited, as most studies have thus far been based on short-term, laboratory-controlled experiments. In a study of PSII processes, we acquired near-continuous, field-based measurements of PSII-energy partitioning in a dominant desert-shrub species, namely Artemisia ordosica, over a six-year period from 2012-2017. Continuous-wavelet transformation (CWT) and wavelet coherence analyses (WTC) were employed to examine the role of environmental variables in controlling the variation in the three main PSII-energy allocation pathways, i.e., photochemical efficiency and regulated and non-regulated thermal dissipation, i.e., Φ PSII, Φ NPQ, and Φ NO, respectively, across a time-frequency domain from hours to years. Convergent cross mapping (CCM) was subsequently used to isolate cause-and-effect interactions in PSII-energy partitioning response. The CWT method revealed that the three PSII-energy allocation pathways all had distinct daily periodicities, oscillating abruptly at intermediate timescales from days to weeks. On a diurnal scale, WTC revealed that all three pathways were influenced by photosynthetically active radiation (PAR), air temperature (T a), and vapor pressure deficit (VPD). By comparing associated time lags for the three forms of energy partitioning at diurnal scales, revealed that the sensitivity of response was more acutely influenced by PAR, declining thereafter with the other environmental variables, such that the order of influence was greatest for T a, followed by VPD, and then soil water content (SWC). PSII-energy partitioning on a seasonal scale, in contrast, displayed greater variability among the different environmental variables, e.g., Φ PSII and Φ NO being more predisposed to changes in T a, and Φ NPQ to changes in VPD. CCM confirmed the causal relationship between pairings of PSII-energy allocation pathways, according to shrub phenology. A. ordosica is shown to have an innate ability to (i) repair damaged PSII-photochemical apparatus (maximum quantum yield of PSII photochemistry, with F v/F m > 0.78), and (ii) acclimatize to excessive PAR, dry-air conditions, and prolonged drought. A. ordosica is relatively sensitive to extreme temperature and exhibits photoinhibition.

Extension and dynamical phases in random walkers depositing and following chemical trails

Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its local environment that in turn influences the motion of the walker at a later time. We perform direct numerical simulations of the walker in a discrete lattice with the walker actively depositing a chemical which attracts the walker trajectory and also evaporates in time. We propose a method to look at the structural transitions of the trajectory using radius of gyration for finite time walks. The extension over a definite time window shows a non-monotonic change with the deposition rate characteristic of a coil-globule transition. At certain regions of the parameter space of the chemical deposition and evaporation rates, the extensions of the walker shows a re-entrant behavior. The dynamics, characterised by the mean-squared displacement, shows deviation from diffusive scaling at intermediate time scales, returning to diffusive behavior asymptotically. A mean-field theory captures the variation of the asymptotic diffusivity.

Establishment and inheritance of epigenetic transcriptional memory.

For certain inducible genes, the rate and molecular mechanism of transcriptional activation depends on the prior experiences of the cell. This phenomenon, called epigenetic transcriptional memory, accelerates reactivation and requires both changes in chromatin structure and recruitment of poised RNA Polymerase II (RNAPII) to the promoter. Forms of epigenetic transcriptional memory have been identified in S. cerevisiae, D. melanogaster, C. elegans, and mammals. A well-characterized model of memory is found in budding yeast where memory of inositol starvation involves a positive feedback loop between gene-and condition-specific transcription factors, which mediate an interaction with the nuclear pore complex and a characteristic histone modification: histone H3 lysine 4 dimethylation (H3K4me2). This histone modification permits recruitment of a memory-specific pre-initiation complex, poising RNAPII at the promoter. During memory, H3K4me2 is essential for recruitment of RNAPII and faster reactivation, but RNAPII is not required for H3K4me2. Unlike the RNAPII-dependent H3K4me2 associated with active transcription, RNAPII-independent H3K4me2 requires Nup100, SET3C, the Leo1 subunit of the Paf1 complex and can be inherited through multiple cell cycles upon disrupting the interaction with the Nuclear Pore Complex. The H3K4 methyltransferase (COMPASS) physically interacts with the potential reader (SET3C), suggesting a molecular mechanism for the spreading and re-incorporation of H3K4me2 following DNA replication. Thus, epigenetic transcriptional memory is a conserved adaptation that utilizes a heritable chromatin state, allowing cells and organisms to alter their gene expression programs in response to recent experiences over intermediate time scales.

Conserved conformational dynamics determine enzyme activity.

Homologous enzymes often exhibit different catalytic rates despite a fully conserved active site. The canonical view is that an enzyme sequence defines its structure and function and, more recently, that intrinsic protein dynamics at different time scales enable and/or promote catalytic activity. Here, we show that, using the protein tyrosine phosphatase PTP1B, residues surrounding the PTP1B active site promote dynamically coordinated chemistry necessary for PTP1B function. However, residues distant to the active site also undergo distinct intermediate time scale dynamics and these dynamics are correlated with its catalytic activity and thus allow for different catalytic rates in this enzyme family. We identify these previously undetected motions using coevolutionary coupling analysis and nuclear magnetic resonance spectroscopy. Our findings strongly indicate that conserved dynamics drives the enzymatic activity of the PTP family. Characterization of these conserved dynamics allows for the identification of novel regulatory elements (therapeutic binding pockets) that can be leveraged for the control of enzymes.

Structural relaxation dynamics of colloidal nanotrimers.

By Molecular Dynamics simulation, we investigate the dynamics of isotropic fluids of colloidal nanotrimers whose interactions are described by varying the strength of attractive and repulsive terms of the Mie potential. To provide a consistent comparison between the systems described by different force fields, we determine the phase diagram and critical points of each system, characterize the morphology of high-density liquid phases at the same reduced temperature and density, and finally investigate their long-time relaxation dynamics. In particular, we detect an especially complex dynamics that reveals the existence of slow and fast nanotrimers and the resulting occurrence of non-Gaussianity, which develops at intermediate timescales. Deviations from Gaussianity are temporary and vanish within the timescales of the system's density fluctuations decay, when a Fickian-like diffusion regime is eventually observed.

Human and Bacterial Toll-Interleukin Receptor Domains Exhibit Distinct Dynamic Features and Functions.

Toll-interleukin receptor (TIR) domains have emerged as critical players involved in innate immune signaling in humans but are also expressed as potential virulence factors within multiple pathogenic bacteria. However, there has been a shortage of structural studies aimed at elucidating atomic resolution details with respect to their interactions, potentially owing to their dynamic nature. Here, we used a combination of biophysical and biochemical studies to reveal the dynamic behavior and functional interactions of a panel of both bacterial TIR-containing proteins and mammalian receptor TIR domains. Regarding dynamics, all three bacterial TIR domains studied here exhibited an inherent exchange that led to severe resonance line-broadening, revealing their intrinsic dynamic nature on the intermediate NMR timescale. In contrast, the three mammalian TIR domains studied here exhibited a range in terms of their dynamic exchange that spans multiple timescales. Functionally, only the bacterial TIR domains were catalytic towards the cleavage of NAD+, despite the conservation of the catalytic nucleophile on human TIR domains. Our development of NMR-based catalytic assays allowed us to further identify differences in product formation for gram-positive versus gram-negative bacterial TIR domains. Differences in oligomeric interactions were also revealed, whereby bacterial TIR domains self-associated solely through their attached coil-coil domains, in contrast to the mammalian TIR domains that formed homodimers and heterodimers through reactive cysteines. Finally, we provide the first atomic-resolution studies of a bacterial coil-coil domain and provide the first atomic model of the TIR domain from a human anti-inflammatory IL-1R8 protein that undergoes a slow inherent exchange.

Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching.

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.

Large deviations for Hamiltonian systems on intermediate time scales

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and nondegenerate. As a result, the process consists of the fast motion along the level curves and slow motion across them. On finite time intervals, the large deviation principle applies, while on time scales that are inversely proportional to the size of the perturbation, the averaging principle holds, i.e. the projection of the process onto the Reeb graph converges to a Markov process. In our paper, we consider the intermediate time scales and prove the large deviation principle, with the action functional determined in terms of the averaged process on the graph.

Dynamics of active polar ring polymers.

The conformational and dynamical properties of isolated semiflexible active polar ring polymers are investigated analytically. A ring is modeled as a continuous Gaussian polymer exposed to tangential active forces. The analytical solution of the linear non-Hermitian equationof motion in terms of an eigenfunction expansion shows that ring conformations are independent of activity. In contrast, activity strongly affects the internal ring dynamics and yields characteristic time regimes, which are absent in passive rings. On intermediate timescales, flexible rings show an activity-enhanced diffusive regime, while semiflexible rings exhibit ballistic motion. Moreover, a second active time regime emerges on longer timescales, where rings display a snake-like motion, which is reminiscent to a tank-treading rotational dynamics in shear flow, dominated by the mode with the longest relaxation time.

Microscopic mechanisms of frictional aging

Frictional aging is observed at a wide range of length- and time-scales, and plays a crucial role in functioning of micro- and nanomachines, as well as in the nucleation and recurrence of earthquakes. Here, we developed an analytical model for description of frictional aging mediated by dynamical formation and rupture of microscopic interfacial contacts. The model accounts for the presence of various types of contacts at the frictional interface and exhibits three different aging regimes: (i) linear aging at short hold times, (ii) logarithmic (or logarithmic-like) aging for intermediate time scales and (iii) levelling off in the static friction for long hold times. It is demonstrated that the linear aging regime is a universal feature of frictional aging for the interfaces including various types of contacts, and the slope of variation of the static friction with the hold time depends on a distribution of energy barriers for contact formation. The conditions for the existence of a pronounced logarithmic aging regime, covering a long-time interval, have been established. Frictional aging has been found to manifest itself not only in slide-hold-slide measurements, but also in sliding experiments exhibiting stick-slip mode of motion, and a relationship has been established between these two regimes of aging. The predicted dependencies of frictional aging on the normal load and temperature are in good agreement with the experimental observations. Our work shows that experimental studies of load and temperature dependencies of aging, carried out over a wide range of time scales, offer promising opportunities for understanding the microscopic mechanisms of frictional aging and revealing the physical meaning of state variables that determine temporal evolution of friction described by phenomenological rate and state laws.

Approximation of the Filter Equation for Multiple Timescale, Correlated, Nonlinear Systems

This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation process. The signal process is considered fully coupled, taking values in $\mathbb{R^{m}} \times \mathbb{R^{n}}$ and without periodicity assumptions on coefficients. It is proved that in the weak topology, the solution of the filtering equation converges in probability to a solution of a lower dimensional averaged filtering equation in the limit of large timescale separation. The method of proof uses the perturbed test function approach (method of corrector) to handle the intermediate timescale in showing tightness and characterization of limits. The correctors are solutions of Poisson equations.

Investigating the response of leaf area index to droughts in southern African vegetation using observations and model simulations

Abstract. In many regions of the world, frequent and continual dry spells are exacerbating drought conditions, which have severe impacts on vegetation biomes. Vegetation in southern Africa is among the most affected by drought. Here, we assessed the spatiotemporal characteristics of meteorological drought in southern Africa using the standardized precipitation evapotranspiration index (SPEI) over a 30-year period (1982–2011). The severity and the effects of droughts on vegetation productiveness were examined at different drought timescales (1- to 24-month timescales). In this study, we characterized vegetation using the leaf area index (LAI) after evaluating its relationship with the normalized difference vegetation index (NDVI). Correlating the LAI with the SPEI, we found that the LAI responds strongly (r=0.6) to drought over the central and southeastern parts of the region, with weaker impacts (r<0.4) over parts of Madagascar, Angola, and the western parts of South Africa. Furthermore, the latitudinal distribution of LAI responses to drought indicates a similar temporal pattern but different magnitudes across timescales. The results of the study also showed that the seasonal response across different southern African biomes varies in magnitude and occurs mostly at shorter to intermediate timescales. The semi-desert biome strongly correlates (r=0.95) to drought as characterized by the SPEI at a 6-month timescale in the MAM (March–May; summer) season, while the tropical forest biome shows the weakest response (r=0.35) at a 6-month timescale in the DJF (December–February; hot and rainy) season. In addition, we found that the spatial pattern of change of LAI and SPEI are mostly similar during extremely dry and wet years, with the highest anomaly observed in the dry year of 1991, and we found different temporal variability in global and regional responses across different biomes. We also examined how well an ensemble of state-of-the-art dynamic global vegetation models (DGVMs) simulate the LAI and its response to drought. The spatial and seasonal response of the LAI to drought is mostly overestimated in the DGVM multimodel ensemble compared to the response calculated for the observation-based data. The correlation coefficient values for the multimodel ensemble are as high as 0.76 (annual) over South Africa and 0.98 in the MAM season over the temperate grassland biome. Furthermore, the DGVM model ensemble shows positive biases (3 months or longer) in the simulation of spatial distribution of drought timescales and overestimates the seasonal distribution timescales. The results of this study highlight the areas to target for further development of DGVMs and can be used to improve the models' capability in simulating the drought–vegetation relationship.

The cavity method for minority games between arbitrageurs on financial markets

We use the cavity method from statistical physics for analyzing the transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On the level of linear response the method allows to include the reaction of the market to individual actions of the agents as well as the reaction of the agents to individual information items of the market. This way we derive a self-consistent solution to the minority game. In particular we analyze the impact of general nonlinear price functions on the amount of arbitrage if noise from external fluctuations is present. We identify the conditions under which arbitrage gets reduced due to the presence of noise. When the cavity method is extended to time dependent response of the market price to previous actions of the agents, the individual contributions of noise can be pursued over different time scales in the transient dynamics until a stationary state is reached and when the stationary state is reached. The contributions are from external fluctuations in price and information and from noise due to the choice of strategies. The dynamics explains the time evolution of scores of the agents’ strategies: it changes from initially a random walk to non-Markovian dynamics and bounded excursions on an intermediate time scale to effectively random switching in the choice between strategies on long time scales. In contrast to the Curie–Weiss level of a mean-field approach, the market response included by the cavity method captures the realistic feature that the agents can have a preference for a certain choice of strategies without getting stuck to a single choice. The breakdown of the method in the phase transition region indicates possible market mechanisms leading to critical volatility and a possible regime shift.

Finite-time Response of Dynamo Mean-field Effects in Magnetorotational Turbulence

Abstract Accretion disk turbulence along with its effect on large-scale magnetic fields plays an important role in understanding disk evolution in general, and the launching of astrophysical jets in particular. Motivated by enabling a comprehensive subgrid description for global long-term simulations of accretions disks, we aim to further characterize the transport coefficients emerging in local simulations of magnetorotational disk turbulence. For the current investigation, we leverage a time-dependent version of the test-field method, which is sensitive to the turbulent electromotive force (EMF) generated as a response to a set of pulsating background fields. We obtain Fourier spectra of the transport coefficients as a function of oscillation frequency. These are well approximated by a simple response function, describing a finite-time buildup of the EMF as a result of a time-variable mean magnetic field. For intermediate timescales (i.e., slightly above the orbital frequency), we observe a significant phase lag of the EMF compared to the causing field. Augmented with our previous result on a nonlocal closure relation in space, and incorporated into a suitable mean-field description that we briefly sketch out here, the new framework will allow us to drop the restrictive assumption of scale separation.

Caging dynamics in bacterial colonies

In colonies, bacteria are often densely packed due to strong attractive forces between neighboring cells. For organisms where aggregation is mediated by type 4 pili interactions, the pilus-mediated motor activity fluidizes these colonies, but it is unclear how close packaging affects bacterial motility. Here, we characterize the dynamics of single cells over five orders of magnitude in time. At short timescales, we find pilus-driven ballistic dynamics, which depending on the volume fraction of cells, transitions to caged or diffusive dynamics at intermediate timescales. Long-term dynamics are dominated by growth-induced radial motion overcoming caging at high packings. Reducing attractive interactions by antibiotic treatment delays caging and introduces long-ranged collective motion.

Quasiconserved quantities in the perturbed spin- 12 XXX model

We consider the isotropic spin-$1/2$ Heisenberg spin chain weakly perturbed by a local translationally- and $SU(2)$-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation the quasi-conserved quantities indeed exist, and we construct an explicit form for the first few of them.