Design research in mathematics education : the case of an ict-rich learning arrangement for the concept of function

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how to design and evaluate a technology-rich learning arrangement that may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a starting point, and the notions of emergent modeling and instrumentation as design heuristics, such a learning arrangement was designed for grade 8 students and field tested. The results suggest that these design heuristics provide fruitful guidelines for the design of both a hypothetical learning trajectory and concrete tasks, and can be generalized to other design processes

Neuromuscular synaptic function in mice lacking major subsets of gangliosides

Gangliosides are a family of sialylated glycosphingolipids enriched in the outer leaflet of neuronal membranes, in particular at synapses. Therefore, they have been hypothesized to play a functional role in synaptic transmission. We have measured in detail the electrophysiological parameters of synaptic transmission at the neuromuscular junction (NMJ) ex vivo of a GD3-synthase knockout mouse, expressing only the O- and a-series gangliosides, as well as of a GM2/GD2-synthase*GD3-synthase double-knockout (dKO) mouse, lacking all gangliosides except GM3. No major synaptic deficits were found in either null-mutant. However, some extra degree of rundown of acetylcholine release at high intensity use was present at the dKO NMJ and a temperature-specific increase in acetylcholine release at 35 °C was observed in GD3-synthase knockout NMJs, compared with wild-type. These results indicate that synaptic transmission at the NMJ is not crucially dependent on the particular presence of most ganglioside family members and remains largely intact in the sole presence of GM3 ganglioside. Rather, presynaptic gangliosides appear to play a modulating role in temperature- and use-dependent fine-tuning of transmitter output

In vitro high-resolution structural dynamics of single germinating bacterial spores

Although significant progress has been achieved in understanding the genetic and biochemical bases of the spore germination process, the structural basis for breaking the dormant spore state remains poorly understood. We have used atomic force microscopy (AFM) to probe the high-resolution structural dynamics of single Bacillus atrophaeus spores germinating under native conditions. Here we show that AFM can reveal previously unrecognized germination-induced alterations in spore coat architecture and topology as well as the disassembly of outer spore coat rodlet structures. These results and previous studies in other microorganisms suggest that the spore coat rodlets are structurally similar to amyloid fibrils. AFM analysis of the nascent surface of the emerging germ cell revealed a porous network of peptidoglycan fibers. The results are consistent with a honeycomb model structure for synthetic peptidoglycan oligomers determined by nuclear magnetic resonance. AFM is a promising experimental tool for investigating the morphogenesis of spore germination and cell wall peptidoglycan structure

Multi-Probe Investigation of Proteomic Structure of Pathogens

Complete genome sequences are available for understanding biotransformation, environmental resistance and pathogenesis of microbial, cellular and pathogen systems. The present technological and scientific challenges are to unravel the relationships between the organization and function of protein complexes at cell, microbial and pathogens surfaces, to understand how these complexes evolve during the bacterial, cellular and pathogen life cycles, and how they respond to environmental changes, chemical stimulants and therapeutics. In particular, elucidating the molecular structure and architecture of human pathogen surfaces is essential to understanding mechanisms of pathogenesis, immune response, physicochemical interactions, environmental resistance and development of countermeasures against bioterrorist agents. The objective of this project was to investigate the architecture, proteomic structure, and function of bacterial spores through a combination of high-resolution in vitro atomic force microscopy (AFM) and AFM-based immunolabeling with threat-specific antibodies. Particular attention in this project was focused on spore forming Bacillus species including the Sterne vaccine strain of Bacillus anthracis and the spore forming near-neighbor of Clostridium botulinum, C. novyi-NT. Bacillus species, including B. anthracis, the causative agent of inhalation anthrax are laboratory models for elucidating spore structure/function. Even though the complete genome sequence is available for B. subtilis, cereus, anthracis and other species, the determination and composition of spore structure/function is not understood. Prof. B. Vogelstein and colleagues at the John Hopkins University have recently developed a breakthrough bacteriolytic therapy for cancer treatment (1). They discovered that intravenously injected Clostridium novyi-NT spores germinate exclusively within the avascular regions of tumors in mice and destroy advanced cancerous lesions. The bacteria were also found to significantly improve the efficacy of chemotherapeutic drugs and radiotherapy (2,3). Currently, there is no understanding of the structure-function relationships of Clostridium novyi-NT spores. As well as their therapeutic interest, studies of Clostridium noyii spores could provide a model for further studies of human pathogenic spore formers including Clostridium botulinum and Clostridium perfringens. This project involved a multi-institutional collaboration of our LLNL group with the groups of Prof. T.J. Leighton (Children's Hospital Oakland Research Institute) and Prof. B. Vogelstein (The Howard Hughes Medical Institute and the Ludwig Center for Cancer Genetics and Therapeutics at The John Hopkins Sidney Kimmel Comprehensive Cancer Center)

Bacillus atrophaeus Outer Spore Coat Assembly and Ultrastructure

Our previous atomic force microscopy (AFM) studies successfully visualized native Bacillus atrophaeus spore coat ultrastructure and surface morphology. We have shown that the outer spore coat surface is formed by a crystalline array of {approx}11 nm thick rodlets, having a periodicity of {approx}8 nm. We present here further AFM ultrastructural investigations of air-dried and fully hydrated spore surface architecture. In the rodlet layer, planar and point defects, as well as domain boundaries, similar to those described for inorganic and macromolecular crystals, were identified. For several Bacillus species, rodlet structure assembly and architectural variation appear to be a consequence of species-specific nucleation and crystallization mechanisms that regulate the formation of the outer spore coat. We propose a unifying mechanism for nucleation and self-assembly of this crystalline layer on the outer spore coat surface

Recovery of mouse neuromuscular junctions from single and repeated injections of botulinum neurotoxin A

Botulinum neurotoxin type A (BoNT/A) paralyses muscles by blocking acetylcholine (ACh) release from motor nerve terminals. Although highly toxic, it is used clinically to weaken muscles whose contraction is undesirable, as in dystonias. The effects of an injection of BoNT/A wear off after 3–4 months so repeated injections are often used. Recovery of neuromuscular transmission is accompanied by the formation of motor axon sprouts, some of which form new synaptic contacts. However, the functional importance of these new contacts is unknown. Using intracellular and focal extracellular recording we show that in the mouse epitrochleoanconeus (ETA), quantal release from the region of the original neuromuscular junction (NMJ) can be detected as soon as from new synaptic contacts, and generally accounts for > 80% of total release. During recovery the synaptic delay and the rise and decay times of endplate potentials (EPPs) become prolonged approximately 3-fold, but return to normal after 2–3 months. When studied after 3–4 months, the response to repetitive stimulation at frequencies up to 100 Hz is normal. When two or three injections of BoNT/A are given at intervals of 3–4 months, quantal release returns to normal values more slowly than after a single injection (11 and 15 weeks to reach 50% of control values versus 6 weeks after a single injection). In addition, branching of the intramuscular muscular motor axons, the distribution of the NMJs and the structure of many individual NMJs remain abnormal. These findings highlight the plasticity of the mammalian NMJ but also suggest important limits to it

Distortions of Subjective Time Perception Within and Across Senses

Background: The ability to estimate the passage of time is of fundamental importance for perceptual and cognitive processes. One experience of time is the perception of duration, which is not isomorphic to physical duration and can be distorted by a number of factors. Yet, the critical features generating these perceptual shifts in subjective duration are not understood. Methodology/Findings: We used prospective duration judgments within and across sensory modalities to examine the effect of stimulus predictability and feature change on the perception of duration. First, we found robust distortions of perceived duration in auditory, visual and auditory-visual presentations despite the predictability of the feature changes in the stimuli. For example, a looming disc embedded in a series of steady discs led to time dilation, whereas a steady disc embedded in a series of looming discs led to time compression. Second, we addressed whether visual (auditory) inputs could alter the perception of duration of auditory (visual) inputs. When participants were presented with incongruent audio-visual stimuli, the perceived duration of auditory events could be shortened or lengthened by the presence of conflicting visual information; however, the perceived duration of visual events was seldom distorted by the presence of auditory information and was never perceived shorter than their actual durations. Conclusions/Significance: These results support the existence of multisensory interactions in the perception of duration and, importantly, suggest that vision can modify auditory temporal perception in a pure timing task. Insofar as distortions in subjective duration can neither be accounted for by the unpredictability of an auditory, visual or auditory-visual event, we propose that it is the intrinsic features of the stimulus that critically affect subjective time distortions