Cooperative dynamics across distinct structural elements regulate PTP1B activity

Protein-tyrosine phosphatase 1B (PTP1B) is the canonical enzyme for investigating how distinct structural elements influence enzyme catalytic activity. Although it is recognized that dynamics are essential for PTP1B function, the data collected thus far have not resolved whether distinct elements are dynamically coordinated or, alternatively, whether they fulfill their respective functions independently. To answer this question, we performed a comprehensive 13C-methyl relaxation study of Ile, Leu, and Val (ILV) residues of PTP1B, which, because of its substantially increased sensitivity, provides a comprehensive understanding of the influence of protein motions on different time scales for enzyme function. We discovered that PTP1B exhibits dynamics at three distinct time scales. First, it undergoes a distinctive slow motion that allows for the dynamic binding and release of its two most N-terminal helices from the catalytic core. Second, we showed that PTP1B 13C-methyl group side chain fast time-scale dynamics and 15N backbone fast time-scale dynamics are fully consistent, demonstrating that fast fluctuations are essential for the allosteric control of PTP1B activity. Third, and most importantly, using 13C ILV constant-time Carr–Purcell–Meiboom–Gill relaxation measurements experiments, we demonstrated that all four catalytically important loops—the WPD, Q, E, and substrate-binding loops—work in dynamic unity throughout the catalytic cycle of PTP1B. Thus, these data show that PTP1B activity is not controlled by a single functional element, but instead all key elements are dynamically coordinated. Together, these data provide the first fully comprehensive picture on how the validated drug target PTP1B functions.

Non-linear population discrete models with two time scales: re-scaling of part of the slow process

In this work we present a reduction result for discrete-time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly speaking, the iterates of a map as well as their differentials must converge uniformly on compact sets. Here, we eliminate the hypothesis of uniform convergence of the differentials at no significant cost in the conclusions of the result. This new result is then used to extend to non-linear cases the reduction of some population discrete models involving processes acting at different time scales. In practical cases, some processes that occur at a fast time scale are often only measured at slow time intervals, notably mortality. For a general class of linear models that include such a kind of processes, it has been shown that a more realistic approach requires the re-scaling of those processes to be considered at the fast time scale. We develop the same type of re-scaling in some non-linear models and prove the corresponding reduction results. We also provide an application to a particular model of a structured population in a two-patch environment.

The Dance of the Interneurons: How Inhibition Facilitates Fast Compressible and Reversible Learning in Hippocampus

The hippocampus is capable of rapidly learning incoming information, even if that information is only observed once. Further, this information can be replayed in a compressed format in either forward or reversed modes during Sharp Wave Ripples (SPW-R). We leveraged state-of-the-art techniques in training recurrent spiking networks to demonstrate how primarily inhibitory networks of neurons in CA3 and CA1 can: 1) generate internal theta sequences or “time-cells” to bind externally elicited spikes in the presence of septal inhibition, 2) reversibly compress the learned representation in the form of a SPW-R when septal inhibition is removed, 3) generate and refine gamma-assemblies during SPW-R mediated compression, and 4) regulate the inter-ripple-interval timing between SPW-R’s in ripple clusters. From the fast time scale of neurons to the slow time scale of behaviors, inhibitory networks serve as the scaffolding for one-shot learning by replaying, reversing, refining, and regulating spike sequences.

A very fast time scale of human motor adaptation: within movement adjustments of internal representations during reaching

Humans and other animals adapt motor commands to predictable disturbances within tens of trials in laboratory conditions. A central question is how does the nervous system adapt to disturbances in natural conditions when exactly the same movements cannot be practiced several times. Because motor commands and sensory feedback together carry continuous information about limb dynamics, we hypothesized that the nervous system could adapt to unexpected disturbances online. We tested this hypothesis in two reaching experiments during which velocity-dependent force fields were randomly applied. We found that within-movement feedback corrections gradually improved, despite the fact that the perturbations were unexpected. Moreover, when participants were instructed to stop at a via-point, the application of a force field prior to the via-point induced mirror-image after-effects after the via-point, consistent with within-trial adaptation to the unexpected dynamics. These findings suggest a fast time-scale of motor learning, which complements feedback control and supports adaptation of an ongoing movement.Significance StatementAn important function of the nervous system is to adapt motor commands in anticipation of predictable disturbances, which supports motor learning when we move in novel environments such as force fields. Here we show that movement control when exposed to unpredictable disturbances exhibit similar traits: motor corrections become tuned to the force field, and they evoke after effects within an ongoing sequence of movements. We propose and discuss the framework of adaptive control to explain these results: a real-time learning algorithm, which complements feedback control in the presence of model errors. This candidate model potentially links movement control and trial-by-trial adaptation of motor commands.

On Boussinesq Dynamics near the Tropopause

The near-tropopause energy spectrum closely follows a −5/3 power law at mesoscales. Most theories addressing the mesoscale spectrum assume unbalanced dynamics but ignore the tropopause (near which the bulk of the data were collected). Conversely, it has also been proposed that the mesoscale spectrum results from tropopause-induced alterations of geostrophic turbulence. This paper seeks to reconcile these a priori mutually exclusive theories by presenting simulations that permit both unbalanced motion and tropopause-induced effects. The model integrates the nonhydrostatic Boussinesq equations in the presence of a rapidly varying background stratification profile (an idealized tropopause). Decaying turbulence simulations were performed over a wide range of Rossby numbers. In the limit of weak flow (U ≲ 1 m s−1), the essential features of the Boussinesq simulations are well captured by a quasigeostrophic version of the model: secondary roll-ups of filaments and shallow spectral slopes are observed near the tropopause but not elsewhere. However, these tropopause-induced effects rapidly disappear with increasing flow strength. For flow strengths more typical of the tropopause (U ~ 10 m s−1), the spectrum develops a shallow, near −5/3 tail associated with fast-time-scale, unbalanced motion. In contrast to weak flows, this spectral shallowing is evident at any altitude and regardless of the presence of a tropopause. Diagnostics of the fast component of motion reveal significant inertia–gravity wave activity at large horizontal scales (where the balanced flow dominates). However, no evidence points to such activity in the shallow range. That is, the mesoscale of the model is dominated by unbalanced turbulence, not waves. Implications and limitations of these findings are discussed.

Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

Based on singularly perturbed bilinear quadratic problems, this paper proposes to decompose the full-order system into two subsystems of a slow-time and fast-time scale. Utilizing the fixed point iterative algorithm to solve cross-coupled algebraic Riccati equations, equilibrium strategies of the two subsystems can be obtained, and further the composite strategy of the original full-order system. It was proved that such a composite strategy formed ano(ε) (near) Stackelberg equilibrium, and a numerical result of the algorithm was presented in the end.