Ildikó Papp

Expression of hyperpolarization-activated and cyclic nucleotide-gated cation channel subunit 2 in axon terminals of peptidergic nociceptive primary sensory neurons in the superficial spinal dorsal horn of rats

Hyperpolarization‐activated cyclic nucleotide‐gated cation channel proteins (HCN1–4), which are potentially able to modulate membrane excitability, are abundantly expressed by neurons in spinal dorsal root ganglia (DRG). In the present experiment, we investigated whether HCN2 protein is confined exclusively to the perikarya of DRG neurons or is transported from the somata to the central axons of DRG neurons that terminate in the spinal dorsal horn. Using immunohistochemical methods, we have demonstrated that laminae I‐IIo of the superficial spinal dorsal horn of the adult rat spinal cord show a strong punctate immunoreactivity for HCN2. Dorsal rhizotomy resulted in a complete loss of immunostaining in the dorsal horn, suggesting that HCN2 is confined to axon terminals of primary afferents. In double labelling immunohistochemical studies, we have also shown that HCN2 widely co‐localizes with calcitonin gene‐related peptide, but is almost completely segregated from isolectin‐B4 binding, indicating that HCN2 is primarily expressed in peptidergic nociceptive primary afferents. The expression of HCN2 in central terminals of peptidergic primary afferents was also verified with electron microscopy. Utilizing the pre‐embedding nanogold method, we found that HCN2 is largely confined to axon terminals with dense‐core vesicles. Within these terminals, some of the silver grains marking the accurate location of HCN2 molecules were associated with the cell membrane, and others were scattered in the axoplasm. Within the cell membrane, HCN2 was found almost exclusively in extrasynaptic locations. The results suggest that HCN2 may contribute to the modulation of membrane excitability of nociceptive primary afferent terminals in the spinal dorsal horn.

Hyperpolarization-activated and cyclic nucleotide-gated cation channel subunit 2 ion channels modulate synaptic transmission from nociceptive primary afferents containing substance P to secondary sensory neurons in laminae I-IIo of the rodent spinal dorsal horn.

We have previously demonstrated that hyperpolarization‐activated and cyclic nucleotide‐gated cation channel subunit 2 (HCN2) is expressed by terminals of peptidergic nociceptive primary afferents in laminae I–IIo of the rat spinal dorsal horn. In this study, we investigated the possible neurotransmitters and postsynaptic targets of these HCN2‐expressing primary afferent terminals in the superficial spinal dorsal horn by using immunocytochemical methods. We demonstrated that HCN2 widely colocalizes with substance P (SP), and that HCN2‐positive terminals that are also immunoreactive for SP form serial close appositions with dendrites and perikarya of neurokinin 1 receptor‐immunoreactive neurons. It was also found that HCN2‐immunoreactive terminals are frequently apposed to neurons that are immunoreactive for calbindin, µ‐opioid receptor and the α‐amino‐3‐hydroxy‐5‐methylisoxazole‐4‐propionate receptor subunit GluR2, markers for excitatory interneurons. Investigating HCN2 immunoreactivity in glutamic acid decarboxylase 65‐green fluorescent protein transgenic mice, we found that HCN2‐positive terminals occasionally also contact cells that contain an isoform of glutamic acid decarboxylase (glutamic acid decarboxylase 65), a marker for GABAergic inhibitory neurons. Application of ZD7288, an antagonist of HCN channels, onto neurons that were recorded in spinal cord slices with whole‐cell patch‐clamp electrodes reduced the number of monosynaptic excitatory postsynaptic potentials evoked by electrical stimulation of primary afferents at nociceptive intensities. The results suggest that HCN2 may contribute to the modulation of membrane excitability of SP‐containing nociceptive primary afferent terminals, may increase the reliability of synaptic transmission from primary afferents to secondary sensory neurons and thus may play a role in the fine‐tuning of pain transmission from nociceptive primary afferents to neurons in the spinal dorsal horn.

Plasticity of hyperpolarization-activated and cyclic nucleotid-gated cation channel subunit 2 expression in the spinal dorsal horn in inflammatory pain

A great deal of experimental evidence has already been accumulated that hyperpolarization‐activated and cyclic nucleotide‐gated cation channels (HCN) expressed by peripheral nerve fibers contribute to the initiation of nerve activities leading to pain. Complementing these findings, we have recently demonstrated that HCN subunit 2 (HCN2) channel protein is also widely expressed by axon terminals of substance P (SP)‐containing peptidergic nociceptive primary afferents in laminae I‐IIo of the spinal dorsal horn, and postulated that they may play a role in spinal pain processing. In the present study, we investigated how the expression of HCN2 ion channels in the spinal dorsal horn may change in inflammatory pain evoked by unilateral injection of complete Freund’s adjuvant (CFA) into the hind paw of rats. We found that 3 days after CFA injection, when the nociceptive responsiveness of the inflamed hind paw had substantially increased, the numbers of HCN2‐immunolabeled axon terminals were also significantly augmented in laminae I‐IIo of the spinal dorsal horn ipsilateral to the site of CFA injection. The elevation of HCN2 immunoreactivity was paralleled by an increase in SP immunoreactivity. In addition, similarly to control animals, the co‐localization between HCN2 and SP immunoreactivity was remarkably high, suggesting that central axon terminals of nociceptive primary afferents that increased their SP expression in response to CFA injection into the hind paw also increased their HCN2 expression. The results indicate that HCN2 ion channel mechanisms may play a role in SP‐mediated spinal pain processing not only in naive animals but also in chronic inflammatory pain.

Isoptics of Bézier curves

Given a planar curve s(t), the locus of those points from which the curve can be seen under a fixed angle is called isoptic curve of s(t). Isoptics are well-known and widely studied, especially for some classical curves such as e.g. conics (Loria, 1911). They can theoretically be computed for a large class of parametric curves by the help of their support functions or by direct computation based on the definition, but unfortunately these computations are extremely complicated even for simple curves. Our purpose is to describe the isoptics of those curves which are still frequently used in geometric modeling - the Bezier curves. It turns out that for low degree Bezier curves the direct computation is possible, but already for degree 4 or 5 the formulas are getting too complicated even for computer algebra systems. Thus we provide a new way to solve the problem, proving some geometric relations of the curve and their isoptics, and computing the isoptics as the envelope of envelopes of families of isoptic circles over the chords of the curve.

3D Modeling and Printing Interpreted in Terms of Cognitive Infocommunication

Digital technologies tend to appear in more and more fields in our life. But what is obvious in the real life, may be rather complicated to represent and reproduce in a digital environment. Nowadays, a growing number of technologies and devices have an associated property called 3D, referring to their ability of approximating reality. This study aims to investigate rather popular 3D-related technologies (3D modeling and printing) in connection of the importance to bring them into the education. Term of cognitive infocommunication is also introduced providing the opportunity to comment the sections in point of its view. Overviewing the main functionalities and properties of four 3D modeling software products gives the reader guidance in this special world, while the case study highlights the additional benefits of acquiring a 3D printer by an institution.

Interaction Between 3D Printing and Geometry Studies

Recently, intensive emergence and spreading of 3D printing can be observed. Educational institutions become owners of desktop 3D printers implying the need of rethinking what to teach at schools at different levels. Since 3D printing needs a 3D model too, users have to refresh or acquire some mathematical knowledge to become successful modelers. Especially geometric and spatial skills are of high importance when designing a new model, while it provides also a brilliant motivation why to study theory and concepts, and why to understand more precisely the different elements of geometry. Nevertheless, users have to get to know new concepts (such as rafts, supports) and properties (such as watertight) as well, which appropriate usage is essential to be able to print the model correctly. Parallely, they will experience, that some traditional geometric concepts, terms may be interpreted in a more flexible way in the context of the currently used 3D modeling software. The objective of the paper is to investigate how the terms mentioned in the title interact with each other and to demonstrate it by examples. Paying attention to these altered, reinterpreted concepts is crucial in order that we could avoid misunderstandings in math class.