A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Integrin-mediated Signaling Events in Human Endothelial Cells

Vascular endothelial cells are important in a variety of physiological and pathophysiological processes. The growth and functions of vascular endothelial cells are regulated both by soluble mitogenic and differentiation factors and by interactions with the extracellular matrix; however, relatively little is known about the role of the matrix. In the present study, we investigate whether integrin-mediated anchorage to a substratum coated with the extracellular matrix protein fibronectin regulates growth factor signaling events in human endothelial cells. We show that cell adhesion to fibronectin and growth factor stimulation trigger distinct initial tyrosine phosphorylation events in endothelial cells. Thus, integrin-dependent adhesion of endothelial cells leads to tyrosine phosphorylation of both focal adhesion kinase and paxillin, but not of several growth factor receptors. Conversely, EGF stimulation causes receptor autophosphorylation, with no effect on focal adhesion kinase or paxillin tyrosine phosphorylation. Adhesion to fibronectin, in the absence of growth factors, leads to activation of MAPK. In addition, adhesion to fibronectin also potentiates growth factor signaling to MAPK. Thus, polypeptide growth factor activation of MAPK in anchored cells is far more effective than in cells maintained in suspension. Other agonists known to activate MAPK were also examined for their ability to activate MAPK in an anchorage-dependent manner. The neuropeptide bombesin, the bioactive lipid lysophosphatidic acid (LPA), and the cytokine tumor necrosis factor α, which signal through diverse mechanisms, were all able to activate MAPK to a much greater degree in fibronectin-adherent cells than in suspended cells. In addition, tumor necrosis factor α activation of c-Jun kinase (JNK) was also much more robust in anchored cells. Together, these data suggest a cooperation between integrins and soluble mitogens in efficient propagation of signals to downstream kinases. This cooperation may contribute to anchorage dependence of mitogenic cell cycle progression.

Synaptic Vesicles Form by Budding from Tubular Extensions of Sorting Endosomes in PC12 Cells

The putative role of sorting early endosomes (EEs) in synaptic-like microvesicle (SLMV) formation in the neuroendocrine PC12 cell line was investigated by quantitative immunoelectron microscopy. By BSA-gold internalization kinetics, four distinct endosomal subcompartments were distinguished: primary endocytic vesicles, EEs, late endosomes, and lysosomes. As in other cells, EEs consisted of vacuolar and tubulovesicular subdomains. The SLMV marker proteins synaptophysin and vesicle-associated membrane protein 2 (VAMP-2) localized to both the EE vacuoles and associated tubulovesicles. Quantitative analysis showed that the transferrin receptor and SLMV proteins colocalized to a significantly higher degree in primary endocytic vesicles then in EE-associated tubulovesicles. By incubating PC12 cells expressing T antigen-tagged VAMP (VAMP-TAg) with antibodies against the luminal TAg, the recycling pathway of SLMV proteins was directly visualized. At 15°C, internalized VAMP-TAg accumulated in the vacuolar domain of EEs. Upon rewarming to 37°C, the labeling shifted to the tubular part of EEs and to newly formed SLMVs. Our data delineate a pathway in which SLMV proteins together with transferrin receptor are delivered to EEs, where they are sorted into SLMVs and recycling vesicles, respectively.

Memory systems in the brain and localization of a memory

It is now clear that there are a number of different forms or aspects of learning and memory that involve different brain systems. Broadly, memory phenomena have been categorized as explicit or implicit. Thus, explicit memories for experience involve the hippocampus–medial temporal lobe system and implicit basic associative learning and memory involves the cerebellum, amygdala, and other systems. Under normal conditions, however, many of these brain–memory systems are engaged to some degree in learning situations. But each of these brain systems is learning something different about the situation. The cerebellum is necessary for classical conditioning of discrete behavioral responses (eyeblink, limb flexion) under all conditions; however, in the “trace” procedure where a period of no stimuli intervenes between the conditioned stimulus and the unconditioned stimulus the hippocampus plays a critical role. Trace conditioning appears to provide a simple model of explicit memory where analysis of brain substrates is feasible. Analysis of the role of the cerebellum in basic delay conditioning (stimuli overlap) indicates that the memories are formed and stored in the cerebellum. The phenomenon of cerebellar long-term depression is considered as a putative mechanism of memory storage.

Simple neural networks for the amplification and utilization of small changes in neuron firing rates

I describe physiologically plausible “voter-coincidence” neural networks such that secondary “coincidence” neurons fire on the simultaneous receipt of sufficiently large sets of input pulses from primary sets of neurons. The networks operate such that the firing rate of the secondary, output neurons increases (or decreases) sharply when the mean firing rate of primary neurons increases (or decreases) to a much smaller degree. In certain sensory systems, signals that are generally smaller than the noise levels of individual primary detectors, are manifest in very small increases in the firing rates of sets of afferent neurons. For such systems, this kind of network can act to generate relatively large changes in the firing rate of secondary “coincidence” neurons. These differential amplification systems can be cascaded to generate sharp, “yes–no” spike signals that can direct behavioral responses.