Historical reflections on the afterhyperpolarization–firing rate relation of vertebrate spinal neurons

In mammalian spinal motoneurons (MNs), the slow component of the afterhyperpolarization (AHP) that follows the spike of each action potential is a major but not the sole determinant of the cells' firing rate. In this brief historical review, we emphasize four points about the AHP-firing rate relation. (1) There is a relatively sparse literature across vertebrates that directly addresses this topic. (2) After the advent of intracellular recording in the early 1950s, there was evidence from mammals to the contrary of an idea that subsequently became prevalent: that the high-firing rates attainable by spinal interneurons (INs) and low-threshold MNs was attributable to their small AHP at rheobase. (3) Further work is needed to determine whether our present findings on the AHP-firing rate relation of turtle cells generalize to the spinal neurons of other vertebrate species. (4) Relevant to point 3, substantial in vivo and in vitro work is potentially available in raw data used in reports on several mammalian and non-mammalian vertebrates. In summary, the factors in addition to the slow AHP that help determine spinal INs and MN firing rate deserve further evaluation across vertebrates, with relevant data already potentially available in several laboratories.     

Investigation of impact loading rate effects on the ligamentous cervical spinal load-partitioning using finite element model of functional spinal unit C2–C3

The cervical spine functions as a complex mechanism that responds to sudden loading in a unique manner, due to intricate structural features and kinematics. The spinal load-sharing under pure compression and sagittal flexion/extension at two different impact rates were compared using a bio-fidelic finite element (FE) model of the ligamentous cervical functional spinal unit (FSU) C2–C3. This model was developed using a comprehensive and realistic geometry of spinal components and material laws that include strain rate dependency, bone fracture, and ligament failure. The range of motion, contact pressure in facet joints, failure forces in ligaments were compared to experimental findings. The model demonstrated that resistance of spinal components to impact load is dependent on loading rate and direction. For the loads applied, stress increased with loading rate in all spinal components, and was concentrated in the outer intervertebral disc (IVD), regions of ligaments to bone attachment, and in the cancellous bone of the facet joints. The highest stress in ligaments was found in capsular ligament (CL) in all cases. Intradiscal pressure (IDP) in the nucleus was affected by loading rate change. It increased under compression/flexion but decreased under extension. Contact pressure in the facet joints showed less variation under compression, but increased significantly under flexion/extension particularly under extension. Cancellous bone of the facet joints region was the only component fractured and fracture occurred under extension at both rates. The cervical ligaments were the primary load-bearing component followed by the IVD, endplates and cancellous bone; however, the latter was the most vulnerable to extension as it fractured at low energy impact.     

Universality in neural networks: the importance of the ‘mean firing rate’

We present a general analysis of highly connected recurrent neural networks which are able to learn and retrieve a finite number of static patterns. The arguments are based on spike trains and their interval distribution and require no specific model of a neuron. In particular, they apply to formal two-state neurons as well as to more refined models like the integrate-and-fire neuron or the Hodgkin-Huxley equations. We show that the mean firing rate defined as the inverse of the mean interval length is the only relevant parameter (apart from the synaptic weights) that determines the existence of retrieval solutions with a large overlap with one of the learnt patterns. The statistics of the spiking noise (Gaussian, Poisson or other) and hence the shape of the interval distribution does not matter. Thus our unifying approach explains why, and when, all the different associative networks which treat static patterns yield basically the same results, i.e., belong to the same universality class.     

Actions of endomorphins on synaptic transmission of aδ-fibers in spinal cord dorsal horn neurons

The effects of endogenous mu-opioid ligands, endomorphins, on Adelta-afferent-evoked excitatory postsynaptic currents (EPSCs) were studied in substantia gelatinosa neurons in spinal cord slices. Under voltage-clamp conditions, endomorphins blocked the evoked EPSCs in a dose-dependent manner. To determine if the block resulted from changes in transmitter release from glutamatergic synaptic terminals, the opioid actions on miniature excitatory postsynaptic currents (mEPSCs) were examined. Endomorphins (1 microM) reduced the frequency but not the amplitude of mEPSCs, suggesting that endomorphins directly act on presynaptic terminals. The effects of endomorphins on the unitary (quantal) properties of the evoked EPSCs were also studied. Endomorphins reduced unitary content without significantly changing unitary amplitude. These results suggest that in addition to presynaptic actions on interneurons, endomorphins also inhibit evoked EPSCs by reducing transmitter release from Adelta-afferent terminals.     

Rhythmically firing (20–50 Hz) neurons in monkey primary somatosensory cortex: Activity patterns during initiation of vibratory-cued hand movements

The activity patterns of rhythmically firing neurons in monkey primary somatosensory cortex (SI) were studied during trained wrist movements that were performed in response to palmar vibration. Of 1,222 neurons extracellularly recorded in SI, 129 cells (11%) discharged rhythmically (at 30 Hz) during maintained wrist position. During the initiation of vibratory-cued movements, neuronal activity usually decreased at 25 ms after vibration onset followed by an additional decrease in activity at 60 ms prior to movement onset. Rhythmically firing neurons are not likely to be integrate-and-fire neurons because, during activity changes, their rhythmic firing pattern was disrupted rather than modulated. The activity pattern of rhythmically firing neurons was complimentary to that of quickly adapting SI neurons recorded during the performance of this task (Nelson et al., 1991). Moreover, disruptions of rhythmic activity of individual SI neurons were similar to those reported previously for local field potential (LFP) oscillations in sensorimotor cortex during trained movements (Sanes and Donoghue, 1993). However, rhythmic activity of SI neurons did not wax and wane like LFP oscillations (Murthy and Fetz, 1992; Sanes and Donoghue, 1993). It has been suggested that fast (20–50 Hz) cortical oscillations may be initiated by inhibitory interneurons (Cowan and Wilson, 1994; Llinas et al., 1991; Stern and Wilson, 1994). We suggest that rhythmically firing neurons may tonically inhibit quickly adapting neurons and release them from the inhibition at go-cue onsets and prior to voluntary movements. It is possible that rhythmically active neurons may evoke intermittent oscillations in other cortical neurons and thus regulate cortical population oscillations.     

The complete mitochondrial genome of the Keeled box turtle Pyxidea mouhotii and phylogenetic analysis of major turtle groups

The complete mitochondrial genome （16,837 bp） from the Keeled box turtle （Pyxidea mouhotii） was determined. The genome content, gene order, and base composition conformed to the consensus vertebrate type mtDNA. However, a remarkable feature was found in this molecule： a large number of （ATTATATC） n direct tandem repeats followed by （TA） n microsatellite at the 3＇ end of the control region （D-loop）, which might be useful as molecular markers for studying population genetics and helpful for species identification and conservation. Besides, to review phylogenetic relationships among major turtle lineages, maximum-likelihood （ML） and Bayesian （BI） analyses were conducted based on concatenated sequences of 13 protein-coding genes from 16 taxa. The resultant ML and BI analyses showed homological topologies, which only differed on the exact placement of Platysternon. Nevertheless, the results strongly supported that 1） Pyxidea mouhotii and Cuora aurocapitata formed a monophyletic clade, whereas Cyclemys atripons was not closer to the Pyxidea-Cuora than to Chinemys reevesii, suggesting that Cyclemys and the Cuora group （containing Pyxidea） may have originated from two ancestors; 2） the Geoemydidae with Testudinidae was a sister group rather than with the Emydidae.     

Head tilt–translation combinations distinguished at the level of neurons

Angular and linear accelerations of the head occur throughout everyday life, whether from external forces such as in a vehicle or from volitional head movements. The relative timing of the angular and linear components of motion differs depending on the movement. The inner ear detects the angular and linear components with its semicircular canals and otolith organs, respectively, and secondary neurons in the vestibular nuclei receive input from these vestibular organs. Many secondary neurons receive both angular and linear input. Linear information alone does not distinguish between translational linear acceleration and angular tilt, with its gravity-induced change in the linear acceleration vector. Instead, motions are thought to be distinguished by use of both angular and linear information. However, for combined motions, composed of angular tilt and linear translation, the infinite range of possible relative timing of the angular and linear components gives an infinite set of motions among which to distinguish the various types of movement. The present research focuses on motions consisting of angular tilt and horizontal translation, both sinusoidal, where the relative timing, i.e. phase, of the tilt and translation can take any value in the range −180° to 180°. The results show how hypothetical neurons receiving convergent input can distinguish tilt from translation, and that each of these neurons has a preferred combined motion, to which the neuron responds maximally. Also shown are the values of angular and linear response amplitudes and phases that can cause a neuron to be tilt-only or translation-only. Such neurons turn out to be sufficient for distinguishing between combined motions, with all of the possible relative angular–linear phases. Combinations of other neurons, as well, are shown to distinguish motions. Relative response phases and in-phase firing-rate modulation are the key to identifying specific motions from within this infinite set of combined motions.     

The turnover rate of rabbit urinary Tamm–Horsfall glycoprotein

1. The turnover rate of urinary Tamm-Horsfall glycoprotein in rabbits was determined by two different methods. The first involved measurement of the pool size of the glycoprotein in rabbit kidney and the daily urinary excretion rate by a radioimmunoassay from which the turnover rate was calculated. 2. The second method made use of the incorporation in vivo of Na(2) (14)CO(3) and sodium [(14)C]acetate. After a single intramuscular injection of one of these compounds, urine collections were made every 24h and the glycoprotein was isolated and its specific radioactivity was determined. 3. Incorporation of the label into urinary HCO(3) (-), urea and plasma fibrinogen was also examined. The specific radio-activities of the O-acetyl, sialic acid, aspartic acid and glutamic acid residues isolated from the Tamm-Horsfall glycoprotein were compared and their half-lives were compared with that of the intact glycoprotein. The two methods gave results in quite close agreement and indicated a half-life for the glycoprotein of approx. 9h. 4. An attempt was made to localize the glycoprotein within the kidney and within the cell. It is present throughout the kidney, but was not detected in the brush-border fraction isolated from the proximal tubules. From differential cell-centrifugation studies, the glycoprotein seemed to be predominantly present in the soluble fraction (100000g supernatant). This suggests that it is either largely a soluble cytoplasmic component or is very loosely bound to a membrane, being readily released under the gentlest homogenization procedure. 5. The half-life of Tamm-Horsfall glycoprotein in human kidney was found by the radioimmunoassay method to be approx. 16h. The similarity between the composition of Tamm-Horsfall glycoprotein and human erythropoietin is discussed.     

Heterozygous carrier rate for type I–IV proximal spinal muscular atrophy in Chuvashes, Udmurts, and residents of the Moscow region

The first estimation of the heterozygous carrier rates for the SMN1 gene deletions and SMN2 gene duplications in populations of Russia has been performed. The numbers of SMN gene copies have been deter-mined in samples from Chuvash and Udmurt populations, as well the population of the Moscow region, by means of multiplex ligation-dependent probe amplification. The heterozygous carrier rates for the CMA gene were 2.7% (1: 37 people), 2.8% (1: 36 people), and 2.8% (1: 36 people) in Chuvashes, Udmurts, and residents of the Moscow region, respectively. The SMN2 duplication frequencies have been determined in the studied groups. It is 1.5, 4, and 2.5% in Chuvashes, Udmurts, and residents of the Moscow region, respectively. The high SMN2 duplication frequency in Udmurts may explain why the SMN1 heterozygous carriage frequency in this population was overestimated in earlier PCR-RFLP analyses.     

Development of an integrated CAD–FEA system for patient-specific design of spinal cages

Spinal cages are used to create a suitable mechanical environment for interbody fusion in cases of degenerative spinal instability. Due to individual variations in bone structures and pathological conditions, patient-specific cages can provide optimal biomechanical conditions for fusion, strengthening patient recovery. Finite element analysis (FEA) is a valuable tool in the biomechanical evaluation of patient-specific cage designs, but the time- and labor-intensive process of modeling limits its clinical application. In an effort to facilitate the design and analysis of patient-specific spinal cages, an integrated CAD–FEA system (CASCaDeS, comprehensive analytical spinal cage design system) was developed. This system produces a biomechanical-based patient-specific design of spinal cages and is capable of rapid implementation of finite element modeling. By comparison with commercial software, this system was validated and proven to be both accurate and efficient. CASCaDeS can be used to design patient-specific cages with a superior biomechanical performance to commercial spinal cages.     

Regulation of ClC-1 and KATP channels in action potential–firing fast-twitch muscle fibers

Action potential (AP) excitation requires a transient dominance of depolarizing membrane currents over the repolarizing membrane currents that stabilize the resting membrane potential. Such stabilizing currents, in turn, depend on passive membrane conductance (G_m), which in skeletal muscle fibers covers membrane conductances for K⁺ (G_K) and Cl⁻ (G_Cl). Myotonic disorders and studies with metabolically poisoned muscle have revealed capacities of G_K and G_Cl to inversely interfere with muscle excitability. However, whether regulation of G_K and G_Cl occur in AP-firing muscle under normal physiological conditions is unknown. This study establishes a technique that allows the determination of G_Cl and G_K with a temporal resolution of seconds in AP-firing muscle fibers. With this approach, we have identified and quantified a biphasic regulation of G_m in active fast-twitch extensor digitorum longus fibers of the rat. Thus, at the onset of AP firing, a reduction in G_Cl of ∼70% caused G_m to decline by ∼55% in a manner that is well described by a single exponential function characterized by a time constant of ∼200 APs (phase 1). When stimulation was continued beyond ∼1,800 APs, synchronized elevations in G_K (∼14-fold) and G_Cl (∼3-fold) caused G_m to rise sigmoidally to ∼400% of its level before AP firing (phase 2). Phase 2 was often associated with a failure to excite APs. When AP firing was ceased during phase 2, G_m recovered to its level before AP firing in ∼1 min. Experiments with glibenclamide (K_ATP channel inhibitor) and 9-anthracene carboxylic acid (ClC-1 Cl⁻ channel inhibitor) revealed that the decreased G_m during phase 1 reflected ClC-1 channel inhibition, whereas the massively elevated G_m during phase 2 reflected synchronized openings of ClC-1 and K_ATP channels. In conclusion, G_Cl and G_K are acutely regulated in AP-firing fast-twitch muscle fibers. Such regulation may contribute to the physiological control of excitability in active muscle.     

Material basis for inhibition of Dragon’s Blood on evoked discharges of wide dynamic range neurons in spinal dorsal horn of rats

In vivo experiments were designed to verify the analgesic effect of Dragon’s Blood and the material basis for this effect. Extracellular microelectrode recordings were used to observe the effects of Dragon’s Blood and various combinations of the three components (cochinchinenin A, cochinchinenin B, and loureirin B) extracted from Dragon’s Blood on the discharge activities of wide dynamic range (WDR) neurons in spinal dorsal horn (SDH) of intact male Wistar rats evoked by electric stimulation at sciatic nerve. When the Hill's coefficients describing the dose-response relations of drugs were dif-ferent, based on the concept of dose equivalence, the equations of additivity surfaces which can be applied to assess the interaction between three drugs were derived. Adopting the equations and Tal-larida's isobole equations used to assess the interaction between two drugs with dissimilar dose-response relations, the effects produced by various combinations of the three components in modulating the evoked discharge activities of WDR neurons were evaluated. Results showed that Dragon’s Blood and its three components could inhibit the evoked discharge frequencies of WDR neurons in a concentration-dependent way. The Hill's coefficients describing dose-response relations of three components were different. Only the combined effect of cochinchinenin A, cochinchinenin B and loureirin B was similar to that of Dragons Blood. Furthermore, the combined effect was synergistic. This investigation demonstrated that through the synergistic interaction of the three components Dragon’s Blood could interfere with the transmission and processing of pain signals in spinal dorsal horn. All these further proved that the combination of cochinchinenin A, cochinchinenin B, and loureirin B was the material basis for the analgesic effect of Dragon’s Blood.     

Comparison of regulated passive membrane conductance in action potential–firing fast- and slow-twitch muscle

In several pathological and experimental conditions, the passive membrane conductance of muscle fibers (G_m) and their excitability are inversely related. Despite this capacity of G_m to determine muscle excitability, its regulation in active muscle fibers is largely unexplored. In this issue, our previous study (Pedersen et al. 2009. J. Gen. Physiol. doi:10.1085/jgp.200910291) established a technique with which biphasic regulation of G_m in action potential (AP)-firing fast-twitch fibers of rat extensor digitorum longus muscles was identified and characterized with temporal resolution of seconds. This showed that AP firing initially reduced G_m via ClC-1 channel inhibition but after ∼1,800 APs, G_m rose substantially, causing AP excitation failure. This late increase of G_m reflected activation of ClC-1 and K_ATP channels. The present study has explored regulation of G_m in AP-firing slow-twitch fibers of soleus muscle and compared it to G_m dynamics in fast-twitch fibers. It further explored aspects of the cellular signaling that conveyed regulation of G_m in AP-firing fibers. Thus, in both fiber types, AP firing first triggered protein kinase C (PKC)-dependent ClC-1 channel inhibition that reduced G_m by ∼50%. Experiments with dantrolene showed that AP-triggered SR Ca²⁺ release activated this PKC-mediated ClC-1 channel inhibition that was associated with reduced rheobase current and improved function of depolarized muscles, indicating that the reduced G_m enhanced muscle fiber excitability. In fast-twitch fibers, the late rise in G_m was accelerated by glucose-free conditions, whereas it was postponed when intermittent resting periods were introduced during AP firing. Remarkably, elevation of G_m was never encountered in AP-firing slow-twitch fibers, even after 15,000 APs. These observations implicate metabolic depression in the elevation of G_m in AP-firing fast-twitch fibers. It is concluded that regulation of G_m is a general phenomenon in AP-firing muscle, and that differences in G_m regulation may contribute to the different phenotypes of fast- and slow-twitch muscle.     

Force–length relation of skeletal muscles: from sarcomeres to myofibril

Sarcomeres are building blocks of skeletal muscles. Given force–length relations of sarcomeres serially connected in a myofibril, the myofibril force–length relation can be uniquely determined. Necessary and sufficient conditions are derived for capability of fully lengthening or completely shortening a myofibril under isometric, eccentric or concentric contraction, and for the myofibril force–length relation to be a continuous single-valued function. Intriguing phenomena such as sarcomere force–length hysteresis and myofibril regularity are investigated and their important roles in determining myofibril force–length relations are explored. The theoretical analysis leads to experimentally verifiable predictions on myofibril force–length relations. For illustration, simulated force–length relations of a myofibril portion consisting of a sarcomere pair are presented.     

How do hatcheries influence embryonic development of sea turtle eggs? Experimental analysis and isolation of microorganisms in leatherback turtle eggs

Many conservation programs consider translocation of turtle nests to hatcheries as a useful technique. The repeated use of the same incubation substrate over several seasons in these hatcheries could, however, be harmful to embryos if pathogens were able to accumulate or if the physical and chemical characteristics of the incubation environment were altered. However, this hypothesis has yet to be tested. We conducted two field experiments to evaluate the effects of hatchery sand and eggshell decay on the embryonic development of leatherback sea turtle eggs in Colombia. We identified the presence of both fungi and bacteria species on leatherback turtle eggs. Sea turtle eggs exposed to previously used hatchery substrates or to decaying eggshells during the first and middle third of the embryonic development produced hatchlings that were smaller and/or weighed less than control eggs. However, this did not negatively influence hatching success. The final third of embryonic development seems to be less susceptible to infection by microorganisms associated with decaying shells. We discuss the mechanisms that could be affecting sea turtle egg development when in contact with fungi. Further studies should seek to understand the infection process and the stages of development in which the fungi are more virulent to the eggs of this critically endangered species.