An overview of a family of cell-surface adhesion and signaling receptors that mediate cell-cell adhesion and cell-extracellular matrix adhesion.

Solving general high-dimensional partial differential equations (PDE) is a long-standing challenge in numerical mathematics. In this paper, we propose a novel approach to solve high-dimensional linear and nonlinear PDEs defined on arbitrary domains by leveraging their weak formulations. We convert the problem of finding the weak solution of PDEs into an operator norm minimization problem induced from the weak formulation. The weak solution and the test function in the weak formulation are then parameterized as the primal and adversarial networks respectively, which are alternately updated to approximate the optimal network parameter setting. Our approach, termed as the weak adversarial network (WAN), is fast, stable, and completely mesh-free, which is particularly suitable for high-dimensional PDEs defined on irregular domains where the classical numerical methods based on finite differences and finite elements suffer the issues of slow computation, instability and the curse of dimensionality. We apply our method to a variety of test problems with high-dimensional PDEs to demonstrate its promising performance.

Although the importance of spaced training trials in the formation of long-term memory (LTM) is widely appreciated, surprisingly little is known about the molecular mechanisms that support interactions between individual trials. The intertrial dynamics of ERK/MAPK activation have recently been correlated with effective training patterns for LTM. However, whether and how MAPK is required to mediate intertrial interactions remains unknown. Using a novel two-trial training pattern which induces LTM inAplysia, we show that the first of two training trials recruits delayed protein synthesis-dependent nuclear MAPK activity that establishes a unique molecular context involving the recruitment of CREB kinase andApC/EBPand is an essential intertrial signaling mechanism for LTM induction. These findings provide the first demonstration of a requirement for MAPK in the intertrial interactions during memory formation and suggest that the kinetics of MAPK activation following individual experiences determines effective training intervals for LTM formation.

Small G-proteins are an extensive family of proteins that bind and hydrolyze GTP. They are ubiquitous inside cells, regulating a wide range of cellular processes. Recently, many studies have examined the role of small G-proteins, particularly the Ras family of G-proteins, in memory formation. Once thought to be primarily involved in the transduction of a variety of extracellular signals during development, it is now clear that Ras family proteins also play critical roles in molecular processing underlying neuronal and behavioral plasticity. We here review a number of recent studies that explore how the signaling of Ras family proteins contributes to memory formation. Understanding these signaling processes is of fundamental importance both from a basic scientific perspective, with the goal of providing mechanistic insights into a critical aspect of cognitive behavior, and from a clinical perspective, with the goal of providing effective therapies for a range of disorders involving cognitive impairments.

The ability to regulate the consolidation and strengthening of memories for threatening experiences is critical for mental health, and its dysregulation may lead to psychopathologies. Re-exposure to the context in which the threat was experienced can either increase or decrease fear response through distinct processes known, respectively, as reconsolidation or extinction. Using a context retrieval-dependent memory enhancement paradigm in rats, we report that memory strengthens through the activation of direct projections from the dorsal hippocampus (dHC) to the prelimbic (PL) cortex and of critical PL molecular mechanisms, which are not required for extinction. Furthermore, while a sustained PL BDNF expression is required for memory consolidation, retrieval engages PL BDNF to regulate the excitatory and inhibitory synaptic proteins neuroligin 1 and neuroligin 2, which promote memory strengthening while inhibiting extinction. Thus, context retrieval-mediated fear memory enhancement results from a concerted action of mechanisms that strengthen memory through reconsolidation while suppressing extinction.