Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Folding properties of cytosine monophosphate kinase from E. coli indicate stabilization through an additional insert in the NMP binding domain

The globular 25 kDa protein cytosine monophosphate kinase (CMPK, EC ID: 2.7.4.14) from E. coli belongs to the family of nucleoside monophosphate (NMP) kinases (NMPK). Many proteins of this family share medium to high sequence and high structure similarity including the frequently found α/β topology. A unique feature of CMPK in the family of NMPKs is the positioning of a single cis-proline residue in the CORE-domain (cis-Pro124) in conjunction with a large insert in the NMP binding domain. This insert is not found in other well studied NMPKs such as AMPK or UMP/CMPK. We have analyzed the folding pathway of CMPK using time resolved tryptophan and FRET fluorescence as well as CD. Our results indicate that unfolding at high urea concentrations is governed by a single process, whereas refolding in low urea concentrations follows at least a three step process which we interpret as follows: Pro124 in the CORE-domain is in cis in the native state (Nc) and equilibrates with its trans-isomer in the unfolded state (Uc - Ut). Under refolding conditions, at least the Ut species and possibly also the Uc species undergo a fast initial collapse to form intermediates with significant amount of secondary structure, from which the trans-Pro124 fraction folds to the native state with a 100-fold lower rate constant than the cis-Pro124 species. CMPK thus differs from homologous NMP kinases like UMP/CMP kinase or AMP kinase, where folding intermediates show much lower content of secondary structure. Importantly also unfolding is up to 100-fold faster compared to CMPK. We therefore propose that the stabilizing effect of the long NMP-domain insert in conjunction with a subtle twist in the positioning of a single cis-Pro residue allows for substantial stabilization compared to other NMP kinases with α/β topology

Cryoradiolytic reduction of crystalline heme proteins: analysis by UV-Vis spectroscopy and X-ray crystallography.

The X-ray crystallographic analysis of redox-active systems may be complicated by photoreduction. Although radiolytic reduction by the probing X-ray beam may be exploited to generate otherwise short-lived reaction intermediates of metalloproteins, it is generally an undesired feature. Here, the X-ray-induced reduction of the three heme proteins myoglobin, cytochrome P450cam and chloroperoxidase has been followed by on-line UV-Vis absorption spectroscopy. All three systems showed a very rapid reduction of the heme iron. In chloroperoxidase the change of the ionization state from ferric to ferrous heme is associated with a movement of the heme-coordinating water molecule. The influence of the energy of the incident X-ray photons and of the presence of scavengers on the apparent reduction rate of ferric myoglobin crystals was analyzed

Cryoradiolytic reduction of crystalline heme proteins: analysis by UV-Vis spectroscopy and X-ray crystallography

The X-ray crystallographic analysis of redox-active systems may be complicated by photoreduction. Although radiolytic reduction by the probing X-ray beam may be exploited to generate otherwise short-lived reaction intermediates of metalloproteins, it is generally an undesired feature. Here, the X-ray-induced reduction of the three heme proteins myoglobin, cytochrome P450cam and chloroperoxidase has been followed by on-line UV-Vis absorption spectroscopy. All three systems showed a very rapid reduction of the heme iron. In chloroperoxidase the change of the ionization state from ferric to ferrous heme is associated with a movement of the heme-coordinating water molecule. The influence of the energy of the incident X-ray photons and of the presence of scavengers on the apparent reduction rate of ferric myoglobin crystals was analyzed

Structure and mechanism of a bacterial light-regulated cyclic nucleotide phosphodiesterase

The ability to respond to light is crucial for most organisms. BLUF is a recently identified photoreceptor protein domain that senses blue light using a FAD chromophore. BLUF domains are present in various proteins from the Bacteria, Euglenozoa and Fungi. Although structures of single-domain BLUF proteins have been determined, none are available for a BLUF protein containing a functional output domain; the mechanism of light activation in this new class of photoreceptors has thus remained poorly understood. Here we report the biochemical, structural and mechanistic characterization of a full-length, active photoreceptor, BlrP1 (also known as KPN_01598), from Klebsiella pneumoniae. BlrP1 consists of a BLUF sensor domain and a phosphodiesterase EAL output domain which hydrolyses cyclic dimeric GMP (c-di-GMP). This ubiquitous second messenger controls motility, biofilm formation, virulence and antibiotic resistance in the Bacteria. Crystal structures of BlrP1 complexed with its substrate and metal ions involved in catalysis or in enzyme inhibition provide a detailed understanding of the mechanism of the EAL-domain c-di-GMP phosphodiesterases. These structures also sketch out a path of light activation of the phosphodiesterase output activity. Photon absorption by the BLUF domain of one subunit of the antiparallel BlrP1 homodimer activates the EAL domain of the second subunit through allosteric communication transmitted through conserved domain-domain interfaces

Post-COVID-19 syndrome: Retinal microcirculation as a potential marker for chronic fatigue.

Post-COVID-19 syndrome (PCS) is characterized by persisting sequelae after infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). PCS can affect patients with all COVID-19 disease severities. As previous studies have revealed impaired blood flow as a provoking factor triggering PCS, it was the aim of the present study to investigate the potential association between self-reported chronic fatigue and retinal microcirculation in patients with PCS, potentially indicating an objective biomarker. A prospective study was performed, including 201 subjects: 173 patients with PCS and 28 controls. Retinal microcirculation was visualized by OCT angiography (OCT-A) and quantified using the Erlangen-Angio-Tool as macula and peripapillary vessel density (VD). Chronic fatigue (CF) was assessed according to the variables of Bell’s score, age and gender. VDs in the superficial vascular plexus (SVP), intermediate capillary plexus (ICP) and deep capillary plexus (DCP) were analyzed, considering the repetitions (12 times). Seropositivity for autoantibodies targeting G protein-coupled receptors (GPCR-AAbs) was determined by an established cardiomyocyte bioassay. Taking account of the repetitions, a mixed model was performed to detect possible differences in the least square means between the different groups included in the analysis. An age effect in relation to VD was observed between patients and controls (p < 0.0001). Gender analysis showed that women with PCS showed lower VD levels in the SVP compared to male patients (p = 0.0015). The PCS patients showed significantly lower VDs in the ICP as compared to the controls (p = 0.0001 (CI: 0.32; 1)). Moreover, considering PCS patients, the mixed model revealed a significant difference between those with chronic fatigue (CF) and those without CF with respect to VDs in the SVP (p = 0.0033 (CI: −4.5; −0.92)). The model included variables of age, gender and Bell’s score, representing a subjective marker for CF. Consequently, retinal microcirculation might serve as an objective biomarker in subjectively reported chronic fatigue in patients with PCS

Long COVID: Association of functional autoantibodies against G-protein-coupled receptors with an impaired retinal microcirculation.

Long COVID (LC) describes the clinical phenotype of symptoms after infection with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Diagnostic and therapeutic options are limited, as the pathomechanism of LC is elusive. As the number of acute SARS-CoV-2 infections was and is large, LC will be a challenge for the healthcare system. Previous studies revealed an impaired blood flow, the formation of microclots, and autoimmune mechanisms as potential factors in this complex interplay. Since functionally active autoantibodies against G-protein-coupled receptors (GPCR-AAbs) were observed in patients after SARS-CoV-2 infection, this study aimed to correlate the appearance of GPCR-AAbs with capillary microcirculation. The seropositivity of GPCR-AAbs was measured by an established cardiomyocyte bioassay in 42 patients with LC and 6 controls. Retinal microcirculation was measured by OCT–angiography and quantified as macula and peripapillary vessel density (VD) by the Erlangen-Angio Tool. A statistical analysis yielded impaired VD in patients with LC compared to the controls, which was accentuated in female persons. A significant decrease in macula and peripapillary VD for AAbs targeting adrenergic β2-receptor, MAS-receptor angiotensin-II-type-1 receptor, and adrenergic α1-receptor were observed. The present study might suggest that a seropositivity of GPCR-AAbs can be linked to an impaired retinal capillary microcirculation, potentially mirroring the systemic microcirculation with consecutive clinical symptoms